jntuk r13 physics lab manual.pdf

ENGINEERING PHYSICS LABORATORY MANUAL I - B. Tech, I – SEMESTER, ECE AND EEE BRANCHES (R13)

NAME:

REGD. NO: BRANCH:

GAYTRI VIDYA PARISHAD COLLEGE OF ENGINEERING FOR WOMEN MADHURAWADA, VISAKHAPATNAM.

Certificate

Certified record of practical work done by Ms………………………………………………........ of first B.Tech, …………….. Semester, ……………………… Branch bearing registered number…………………… in the Engineering Physics laboratories of Gayatri Vidya Parishad College of Engineering for Women, Madhurawada, Visakhapatnam during the academic year 2013-14. No. of experiments done and certified:

Lecturer in charge

Date

Examiners:

1.

2.

INDEX

S.NO. DATE NAME OF THE EXPERIMENT MARKS SIGNATURE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

ENGINEERING PHYSICS LABORATORY

TH 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

T

THERMISTOR THEORY:

The name thermistor comes from thermally

sensitive resistor. They are basically

semiconducting materials and are of two distinct

classes:

1. METAL OXIDES: They are made from fine

powders that are compressed and sintered at high

temperature. Mn2O3 (manganese oxide), Ni O

(nickel oxide), Co O3 (cobalt oxide), Cu2O3

(copper oxide), Fe2O3 (iron oxide), TiO3

(titanium oxide) U2O3 (uranium oxide) etc, are

the few examples. They are suitable for

temperatures 200-700 K. If the temperature is

higher than this range then Al2O3, Be O, Mg O,

ZrO2 Y2O3 and Dy2O3 (Dy :dysprosium) are

used.

2. SINGLE CRYSTAL SEMICONDUCTORS:

They are usually Germanium and Silicon doped

with 1016

to 1017

dopant atoms/cm3. Ge

thermistors are suitable for cryogenic range 1-

100 K. Si thermistors are suitable for 100-250 K.

After 250 K the Silicon thermistors will become

PTC (positive temperature coefficient) from

NTC.

The resistivity and the conductivity of the

thermistor are related to the concentration of

electrons and holes n and p of the semiconductor

though the relation,

( ) ………………... (1)

The concentrations n and p are strongly

dependent on temperature T in Kelvin.

Where Ea is called activation energy which is

related to the energy band gap of that

semiconductor. Hence, As temperature

increases, the resistance R(T) changes according

to the relation,

( [

]) ……………. (2)

Where RO is the resistance of the thermistor at

absolute temperature To. Here To is usually the

reference room temperature. B is a characteristic

temperature that lies between 2000K to 5000K.

The temperature coefficient of resistance is

defined as the ratio of fractional change in

resistance (

) to the infinitesimal change in

temperature .

……….. (3)

The typical value of is about 0.05/K. It is

almost 10 times more sensitive compared with

ordinary metals. Thermistors are available from

1KΩ to 1MΩ.

Advantages:

They are low cost, compact and highly

temperature sensitive devices. Hence are more

useful than conventional thermometric devices.

Using eq. (2) at some constant reference

temperature, say TO= 300K, the resistance will

be

(

)

Where, (

)

To make the expression to look like a linear

relation to determine the values of A and B

constants, take natural logarithm on both sides of

the above expression,

…………………….. (4)

The exponential curve now became linear. If we

plot the variable

, we will get A and

B constants from the intercept and slope of the

straight line.

DESIGN OF EXPERIMENT:

PRINCIPLE: If we measure the resistance R of

thermistor at various temperatures (T), we can

plot the

graph and obtain the

values of A and B.

How to vary the temperature T?

Using an electric heater we can change the

temperature roughly from 30 to 60 .

How to measure the resistance R?

Using Wheatstone’s bridge.

Wheatstone’s bridge principle:

The circuit shown here is a Wheatstone’s bridge

and it consists of four resistors R1, R2, R3 and R4,

a galvanometer

(G) and a Battery

(V). Suppose the

resistance R4 be

unknown. The

voltage applied

to this circuit by

the battery is

only to set up

some current and

its magnitude has

no importance, i.e. whether or 2V or 5V it does

not matter at all. Wheatstone bridge gets

balanced, i.e. the Galvanometer shows a zero

deflection when,

G

R3 R4

V

R1 R2



T

Or

If the resistances R1 and R2 are equal, then the

bridge will be balanced, i.e. the null deflection in

Galvanometer, when R4 = R3. If we choose R3 as

a variable resistor, like a decade resistance box,

the unknown resistance R4 will be equal to the

resistance maintained in the box.

Measurement of resistance of thermistor:

Here in this experiment we employ a

1KΩ (at room temperature) thermistor. We form

a wheatstone’s bridge with two fixed value

resistors each of 1KΩ resistance along with a

variable decade resistance box. Two arms of the

bridge are formed by 1KΩ resistors and the other

two arms, one with thermistor and the other with

decade resistance box. The reason for choosing a

1KΩ fixed resistor. The sensitivity of

measurement of resistance will be better when

all the four resistors here are of same

(comparable) magnitude hence the remaining

R’s are 1KΩ each.

Applications of thermistors:

1. They are used as temperature sensing

elements in microwave ovens, heaters

and also in some electronic

thermometers.

2. Used as sensor in cryogenic liquid

storage flasks.

3. Used as compensator for providing

thermal stability to transistor based

circuits.

4. Used in fire alarms, Infrared detectors as

sensor.

THERMISTOR EXPERIMENT Aim:

1. To study the variation of resistance of a thermistor with temperature.

2. To find the temperature (thermoelectric) coefficient of resistance (α) of the thermistor.

3. To determine I and B coefficients.

Apparatus: Thermistor (1 KΩ), electric heater (max 70°C), 1.5 volt battery or a D.C. power supply, mercury

or benzene thermometer (0 – 110 ), test tube containing insulating oil (edible oil / castor oil),

resistors (1kΩ - 2 No.s), Galvanometer (30 – 0 – 30), resistance box (1 to 1000Ω range),

connecting wires.

Formulae:

(

)

Procedure:

1. Construct the bridge according to the

circuit diagram (Maintain at least 1000 Ω

resistance in the Resistance box before

connecting the circuit, i.e. remove the 1000Ω

plug key).

2. The 1 KΩ resistors are already connected at the bottom panel of the board. Hence no

need to connect them again.

3. If a variable D.C. source is given instead

of a battery, set the voltage to 1.5 or 2 Volt

with the help of a multimeter.

4. The bridge gets balanced (Galvanometer

shows “0” deflection) when the resistance of

thermistor gets equal to that of the resistance

box. Remove the plug keys of resistance box

and find out the null point resistance.

T

G

RB RT

1.5 V

R1=1KΩ R2=1KΩ

Electric heater

Test tube with Coconut oil

Ther

mo

met

er

T

G

1.5 V

R2=1KΩ R1=1KΩ

RB



T

5. Start heating the thermistor by turning on the heater switch on the board.

6. Measure the resistance of thermistor for every two degrees centigrade rise in temperature. Note

the readings up to 60°C in steps of 2°C.

7. At each temperature bridge is not balanced initially and it shows some deflection. It can be made

zero by adjusting the resistances in the variable resistance box. Tabulate the readings.

8. Remove the power supply or battery, soon after you complete the experiment. If you forget

doing this, it will cause the galvanometer to deflect more causing damage to its restore spring.

Graph:

A graph is plotted by taking R versus T (K). This graph gives the value of α.

Another graph is plotted between ln R and (1/T(K)). The slope of this graph gives B and its

intercept on y (ln R) axis gives ln A from which A can be calculated. But it is not possible to find

out the intercept from the graph. It can be done with the help of least square fit method as

described in the Appendix.

Use this method to compute both slope (B) and intercept (ln A) of the straight line. Here assume X as

(1/T) and Y as lnR. The intercept C gives the value of ln A and the slope will give B (in K). From the

intercept find out the value of A (in Ω).

Precautions:

1. Temperature of the thermistor should be

less than 70°C.

2. Thermistor must be immersed completely

inside the hot oil bath.

3. Readings of thermometer must be noted

without parallax.

4. Connections should be made properly

without any loose contact.

5. Resistance must be varied quickly in the

resistance box to get the null point within

the 2°C intervals.

6. Battery must be disconnected immediately

after completion of the experiment.

Viva-Voce Questions:

1. Where do you find applications of

thermistor? Name a few of them. They are useful in temperature sensing and

controlling equipments. Ex. Microwave

ovens, Infrared heat sensors, Liquefied gas

temperature sensors in cryogenics.

2. Explain the principle of Wheatstone’s

bridge.

In the bridge circuit, the potential at the two

nodes across which the galvanometer is

connected will be same when the four

resistors R1 to R4 satisfy the relation

3. After obtaining the data from this

experiment, you will have the values of A

and B coefficients. Can you determine

the temperature of your body? I will

provide you only a thermistor and a

multimeter. If yes, describe the method.

If No, justify your answer. Yes, it is possible. Suppose that you want

to measure your body temperature. Just

keep it in tight contact with your body

(cover it tightly with skin). Use the

multimeter to measure the resistance of this

thermistor. After few seconds of contact

with body, thermistor attains constant

resistance. With the known A and B

coefficients, we can measure the body

temperature by substituting in

(

)

(

)

T1 T2

T in K

R1

R2

in K-1

Slope = B

ln R


BG 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

REFERENCES:

1. Physics of semiconductor devices, S. M. Sze, 3rd

ed, John Wiley publications, chapter 14, sensors,

Thermal sensors, p.744-746.

2. The art of Electronics, Paul Horowitz, 2nd

ed, Cambridge university press, chapter 15,

Measurement transducers, Thermistors, p.992-993

3. Electronic devices and circuit theory, R. Boylestad, 7th

ed, Prentice hall publications, Art. 20.11

Thermistors, p.837-838

4. Electronic sensor circuits and projects, Forrest Mims – III, Master publishing, p.13, 46-47.

5. Advanced level physics, Nelkon and Parker, 3rd

Ed, Wheatstone’s bridge, p.829-834

BAND GAP OF SEMICONDUCTOR USING PN JUNCTION DIODE

THEORY: PN junction diode is an example for extrinsic

semiconductor. It can be biased in both

forward and reverse directions. The current

that flow through the diode when its junction

is biased with a voltage V will be

(

)

With

.

Where,

V = applied voltage across junction

Is = Reverse saturation current, a constant

dependent on temperature of junction

η = a constant equal to 1 for Ge (high

rated currents) and 2 for Si (low rated

currents)

VT = Volt equivalent of temperature

=

, T = Temperature of junction in

Kelvin

A = area of cross – section of junction

e = elementary charge = C

Dp(n)= Diffusion constant for holes

(electrons)

for holes and

for electrons

= mobility of holes

Lp(n) = Diffusion length for holes (electrons)

pno = equilibrium concentration of holes (p)

in the n – type material

=

npo = equilibrium concentration of

electrons (n) in p – type material

=

ni = intrinsic carrier concentration (/cm3)

ni2 =

B = a constant independent of T

EG = Energy band gap of semiconductor

(in Joule)

NA = Acceptor ion concentration (/m3)

ND = Donor ion concentration (/m3)

The term Is is highly temperature dependent.

The expression for it can be written as

(

)

(

)

(

)

(

)

(

)

(

)(

)

(

)(

)(

)

(

)

Experimentally it was observed that the

mobility term in the bracket varies as .

Hence,

………………………… (1)

is a constant whose magnitude is in nano or

pico ampere.

Under reverse biased condition applied

voltage V will be negative and hence the

expression for current through diode will be,

(

)



Diode will have only the reverse saturation

current flowing through it. The negative sign

indicates that the current is flowing in opposite

direction to that of forward bias. Hence the

current ID through diode in reverse bias will be

(

)…………. (2)

Applying natural logarithms on both sides

implies,

[ (

)]

(

) ……………. (3)

This is the equation of the straight line with

ln(ID) as ordinate(y – axis) and 1/T as abscissa

(x – axis). ln(I0) is the y intercept of the graph.

If we plot 1/T versus ln(ID) graph, its slope

with x – axis gives the value of (–

). By

knowing the Boltzmann constant kB we can

evaluate the energy band gap of the

semiconductor, similarly we can estimate the

value of Boltzmann constant if we know the

energy band gap of the given semiconductor.

Applications:

1. We can use this to make a diode

thermometer.


PRINCIPLE: If we measure the reverse

saturation current through the diode by

varying its temperature, we can plot the

graph and obtain slope (–

).

Which diode is suitable for this?

OA79, Germanium diode, used as envelope

detector in amplitude demodulation circuits.

Why this OA 79? Why not any other?

Because reverse current variation is more in

the case of Germanium than with silicon.

Hence for a small temperature range of

variation (30°C to 60°C), it is better to choose

Ge diode than any other silicon diodes. If we

want to do this experiment with silicon diodes,

we must have an electric heater capable of

giving temperatures up to 150°C.

How to vary the temperature T?

Using an electric heater we can change the

temperature roughly from 30°C to 60°C.

How to measure the reverse current?

Using a moving coil micro ammeter.

Biasing the diode:

Use a constant voltage D.C. power supply or a

battery to bias it in reverse direction. The

voltage applied must be very low, 2 Volt. In

case of an ideal diode the reverse current does

not vary with applied reverse voltage. But in

practical diode case, it increases with increase

in reverse voltage. This is due to the increase

of leakage currents across the junction with

applied voltage. At room temperature, the

reverse current may be small and different for

same type of diodes, but it follows the

equation (2). The values of Io may vary from

diode to diode.

Description of heater:

The heater contains an electric heating

element attached to a stainless steel container

holding some cold water. A test tube

containing oil is immersed in the water bath.

Oil is an insulator of electricity and hence it

is used for heating the diode. This also

provides uniform heating of diode. The diode

with properly insulated connecting wires is

immersed in the oil bath. Thermometer is also

kept inside the oil bath to measure its

temperature. We cannot directly insert the

diode inside the water bath as tap water

contains lots of minerals dissolved in it and

acts like conductor. This will short circuit the

diode.

Useful data:

From the data sheet of the OA 79 diode:

Material of the diode is Germanium.

Maximum surrounding temperature is

60°C.

Maximum allowed reverse current

through the diode is 60µA.



VD

ID

T

Stainless steel container water bath

Test tube containing oil

A

2 V

+ +

_ _

+

Electric Heater

BAND GAP OF SEMICONDUCTOR EXPERIMENT

Aim: To determine the energy band gap of the

material of the semiconductor by studying the

variation of reverse saturation current through

given PN junction diode with temperature.

Apparatus: OA 79 Ge diode, heater (max 60°C),

thermometer, test tube containing insulating

oil (edible oil or castor oil), power supply (2V

D.C.), connecting wires, micro ammeter (0 -

50 µA) and a voltmeter or multimeter.

Formula:

Reverse current through diode is given by

(

)

Where, EG is the energy band gap of the

material of the semi conductor diode, T is the

absolute temperature of the diode junction and

kB = 1.38 x 10-23

J/K is Boltzmann constant.

Circuit diagram:

Caution: Set the applied reverse bias voltage

at 2 Volt. Do not increase this value more. Do

not heat the diode beyond 60°C.

Procedure:

1. Build the circuit as shown in the circuit

diagram.

2. Observe the initial temperature of the

thermometer. If it is high (>30°C) then

replace the water in the heater jar with

some cold water and try to reduce the

temperature below 30°C.

3. Apply the reverse voltage (2 Volt) by

adjusting the potentiometer (if a battery is

given, then there is no need of doing this

adjustment).

4. Switch on the heater. Note down the

reverse current in the micro ammeter for

say, every 2°C rise, in temperature of the

diode (if micro ammeter is not available,

you can use a multimeter in D.C. current

mode under 200 µA ranges).

5. Tabulate the readings.

6. Complete the calculations relevant to the

tabular form and get the answer for slope.

7. Plot a graph between lnI and 1/T to obtain

its slope.

8. Calculate the EG from both slopes obtained

from graph and table.

Precautions:

1. Readings of thermometer must be noted

without any parallax error.

2. Reverse bias voltage must be regulated at 2

Volt throughout the experiment.

3. Diode should be completely immersed

inside the oil bath.

GRAPH:

Plot a graph by taking the values of ln I vs

1/T. Find out the slope of the curve. Do not

consider the origin of this graph.

Usually we start at 300K and go up to 333K,

hence 1/T varies roughly from to . So start at

2.98 and go up to 3.34 by choosing the scale

On 1/T axis as

Usually ID varies from 2 µA to 60 µA. So ln

ID varies roughly from to – 13.2. So start

at – 9.7 and go up to – 13.2 by choosing the

scale



On ln I axis as

Slope (EG/kB) can be calculated from both

straight line data fit as well as from the

graph.

Viva-Voce questions:

1. Distinguish intrinsic and extrinsic

semiconductor.

If the semiconductor material consists of no

impurities (dopants), then it will be intrinsic

(pure) semiconductor. If it contains dopants

acceptor type [p-type] – III group elements

or Donor type [n-type] – IV group elements

then it will be an extrinsic semiconductor.

2. What are the band gaps of Silicon and

Germanium?

For silicon; (eV = electron volt)

For Germanium,

T is the temperature of the sample in Kelvin.

At 300K, EG = 0.72 eV for Ge; EG= 1.1 eV

for Si.

3. How do you test the diode for its polarity

using a multimeter?

There will be a symbol of diode on the

multimeter’s mode changing dial. Turn the

dial to diode testing mode. Connect the two

leads of the multimeter to the two leads of

the diode. If the multimeter shows infinite

resistance (it shows a “1 ” Or “OL” means

out of range, very large), then it is reverse

biased and the terminal of diode that is

connected to positive (red probe) of

multimeter will be the cathode of the diode

and the other one will obviously be the

anode. Similarly, if the meter shows some

finite resistance like few hundred (150, 540

etc), then it is forward biased, i.e. the

terminal of diode that is connected to positive

(red probe) of multimeter will be the Anode

of the diode and the other one will be the

Cathode. During this process, multimeter

applies some known voltage across its leads

and measures its resistance.

4. If I reveal the material of the diode used,

can you estimate the Boltzmann constant

from this experiment? If yes, describe how

do you do it, if no, say why?

(Think and answer)

5. Why do we observe small current (of the

order of Micro amp) in this experiment?

What are responsible for this small

current?

Because reverse current is due to the

minority carries only. As their number is

very small the current is also small.

6. In which biasing of diode are you doing

this experiment?

Reverse bias.

7. Can you determine the band gap by

changing the bias of the diode? If yes,

describe how you do it. If no, explain

why? (think and answer)

8. If I give you a silicon diode and the same

experimental set up (micro ammeter 0-

50range), can you find out its band gap?

Justify your answer.

No, the reverse current variation is very

small of the order of few nano amperes per

degree centigrade and hence it not possible

to observe the variation in reverse current

with the micro ammeter for a temperature

range of 30-60°C

9. What is the magnitude of reverse current

in silicon at moderate temperatures?

Few tens of nano amperes.

10. Can you make a diode thermometer

using this setup? If yes, say how? If no,

say why?

Yes, once if we know the value of I0

(antilog of intercept of lnI vs 1/T graph)

from the experiment, we can measure the

T. Just bring the diode in contact with the

body whose temperature is to be measured

and measure the reverse current (ID)

accurately. As we know the I0 and ID we

can determine the T in Kelvin for that body

using the relation (

).

References:

1. Electronic devices and circuits, Millman and Halkias, McGraw hill student edition

p.126-132.

2. Semiconductor device physics and technology, SM Sze, M K Lee, 3rd

Ed, John wiley,

P.107


ZD 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

JUNCTION DIODE AND ZENER DIODE VOLT – AMPERE CHARACTERISTICS

THEORY:

Semiconductors are basically of two types.

Intrinsic semiconductors: These are in their

purest form, without any impurities (Dopants).

Extrinsic semiconductors: These are

impurity added (Doped) intrinsic

semiconductors. Doping is a process of adding

impurity atoms to the pure semiconductors.

The reason for this doping is only to increase

the conductivity of the semiconductors. By

adding Group III elements Boron, Aluminum,

Gallium, Indium (Trivalent impurity) to the

pure semiconductors, it becomes P – type. By

adding Group V elements Nitrogen,

phosphorus, Arsenic, Antimony, Bismuth

(pentavalent impurity) it becomes N – type. P

– type has excess of holes as majority carriers

and N – type has excess of electrons as

majority carriers.

Diode is a semiconductor based electronic

component. It is formed by joining a p – type

section of semiconductor with n – type

section. It has anode (p – type) and cathode (n

– type). It is a polar device, i.e. its operation

will depend on the direction of connection

(biasing).

The above symbol represents an ordinary

P – N junction diode. A denotes the positive

(high potential end) Anode and K denotes the

negative (low potential end) of the diode.

Diode acts like a mechanical check valve,

that conducts (allows flow of liquid) only

when the Anode is at relatively high potential

with respect to the cathode. Suppose that A is

at 10 Volt potential and K is at 9.3 Volt

potential. Then the diode will conduct (closed

switch or Forward Bias) a current from anode

to cathode in the direction of arrow shown in

diode symbol. If the potentials are reversed,

i.e. A at 9.3V and K at 10V, it does not

conduct, acts like infinite resistance (open

switch or Reverse bias).

Forward Bias: Anode of the diode will be at a

relatively high potential that that of cathode.

In this bias the diode conducts and acts like a

closed switch.

Reverse bias: Cathode of the diode will be at

a relatively high potential than that of Anode.

In this bias the diode acts like open switch and

offer infinite resistance, i.e. do not conduct.

FOR DETAILS ABOUT THE

CONDUCTION IN DIODES REFER TO

THE THEORY PART OF BAND GAP OF

SEMICONDUCTOR EXPERIMENT.

MECHANISM OF CONDUCTION IN

JUNCTION DIODE:

When a PN junction is forward biased as

shown in the figure, there will be an electric

force on the carries of the diode due to the

potential difference applied by the battery.

This field on holes of P – region will be

towards the depletion region (junction) and

hence the holes of P – region will try to move

away from the + ve plate. Similarly in the N –

region the electrons are repelled by the

negative potential of the battery and hence

they too try to move towards the depletion

region from the N – region. Initially the

neutral barrier at the junction (depletion

region) prevents the flow of carriers through

it. To overcome this, carriers need some

potential energy that is just equal to the barrier

potential of the junction. In case of silicon

diodes it will be 0.7 volt for

Germanium it will be 0.3 volt

(approximately). After applying this much

voltage across junction conduction starts. The

minimum voltage at which the diode starts

conducting is called its cut – in voltage.



During reverse bias the Holes of P – region are

attracted towards the negative plate and

electrons of N – region are attracted towards

the positive plate of the battery. This makes

the depletion region to expand in size and it

becomes thicker. Due this the conduction in

diode due to majority carriers ceases. Still

there are minority carriers which enjoy

forward bias, to contribute some weak current

across the junction known as Reverse

saturation current. The value of this in most of

the commercial Junction diodes is in nano

ampere range.

V – I CHARACTERISTICS OF

JUNCTION DIODE:

During forward bias of the diode, initially

we would not observe any current up to say

0.5 to 0.6 V across the diode. Later the current

through diode increases exponentially as

shown in the figure. Even at higher forward

voltages across the diode the voltage does not

increase much. But it raises slightly in a

practical diode due to the Ohmic resistance of

the semiconductor as well the metal contacts

of the diode.

During reverse bias, the current through

diode is very small of the order of few micro

amperes. To observe this we must use a micro

ammeter in place of milli ammeter that was

used during forward bias. To reach the break

down region a PN diode needs a relatively

high voltage. In case of rectifier type diodes it

will be as high as 1000 Volt. Hence it is not

possible in our lab to break down this PN

junction diode as we do not have such a high

voltage source.

Zener and Avalanche diodes are heavily

doped p-n junction diodes. Their circuit

symbol is

The doping levels (amounts of added

impurities) are considerably different from

those normally found in a rectifier (PN) diode.

This diode preferably used in REVERSE

BIAS.

A rectifier diode cannot be used in the

breakdown region as it makes permanent

damage to the junction. However, zener and

avalanche diodes are designed to use in the

breakdown region. These diodes are used for

voltage reference and voltage regulator

circuits. There are two mechanisms that cause

a reverse-biased p-n junction to break down:

the Zener effect and avalanche breakdown.

Either of the two may occur independently, or

they may both occur simultaneously. Diode

junctions that break down below 5 V are

caused by the Zener effect.

Junctions that experience break down above

Depletion region

Heavily doped

N – Side

Moderately doped P – Side

Denotes atoms/ions

A REVERSE BIASED ZENER DIODE

Bubbles ( ) denote holes and black dots ( ) denote electrons



5 V are caused by avalanche breakdown.

Junctions that break down around 5 V are

usually caused by a combination of the two

effects.

A zener diode is produced by moderately

doping the p-type semiconductor and heavily

doping the n-type material (see Fig below).

Observe that the depletion region extends

more deeply into the p-type region.

Under the influence of a high-intensity electric

field, large numbers of bound electrons within

the depletion region will break their covalent

bonds to become free. This is ionization by an

electric field. When ionization occurs, the

increase in the number of free electrons in the

depletion region converts it from being

practically an insulator, to being a conductor.

As a result, a large reverse current may flow

through the junction. The actual electric field

intensity required for the Zener effect to occur

is approximately 3 X 107 Volt/meter. From

basic circuit theory we recall that the electric

field intensity E is given by

V = E d

where

E = electric field intensity (volts per meter)

V = potential difference (volts)

d = distance (meters)

In terms of the p-n junction depicted in above

Fig. we note that the applied reverse voltage is

V and the depletion region width is the

distance d. The narrower the depletion region,

the smaller the required reverse bias to cause

Zener breakdown. A small reverse bias can

produce a sufficiently strong electric field in a

narrow depletion region. By controlling the

doping levels, manufacturers can control the

magnitudes of the reverse biases required for

Zener breakdown to occur. Only certain

standard zener diode voltages are available.

These range from 2.4 to 5.1 V. With lightly

doped p-type material, the depletion region

may be too wide for the electric field intensity

to become sufficient for Zener breakdown to

occur. In these cases, the breakdown of the

reverse-biased junction is caused by avalanche

breakdown (see Fig below). The depletion

region is wider because it extends more deeply

into the p region. Reverse saturation current is

a current flow across a reverse-biased p-n

junction due to minority carriers. Even though

the electric field strength is not large enough

to ionize the atoms in the depletion region, it

may accelerate the minority carriers

sufficiently to allow them to cause ionization

by collision. The specifics may be outlined as

follows:

1. The depletion region is too wide to allow

an electric field intensity of at least 3 X107

V/m.

2. The minority carriers are accelerated by the

applied electric field.

3. The minority carriers gain kinetic energy.

4. The minority carriers collide with atoms in

the depletion region.

5. The valence electrons of the atoms receive

enough energy from the collisions to

become free (conduction band) electrons.

6. As a result, the number of free electrons in

the depletion region increases to support a

large reverse current. This avalanche of

carriers is also termed as “carrier

multiplication" since one minority carrier

may ultimately cause many free electrons.

The V- I characteristic curve for a zener diode

will be similar to rectifier diode in forward

bias condition. Its behavior in reverse bias is

different from rectifier diode.

Depletion region

Heavily doped

N – Side

Moderately doped P – Side

The black dotted electrons on the P-side are minority carriers that are “Feeling” forward bias and travelling with high speed, colliding with ions of depletion region causing them to release electrons. Their number increases drastically and an avalanche (flood) of electrons are released (Avalanche breakdown)

MECHANISM OF AVALANCHE BREAKDOWN



IMPORTANT POINTS FROM V – I

CHARACTERISTICS:

1. Cut – in Voltage (Vγ): During forward bias

of the diode, if we slowly vary the voltage

across the diode, there will be no

observable current up to a characteristic

voltage known as Cut – In or Break – in

voltage or Knee voltage. The minimum

forward voltage to be applied to the diode

to make it just conducting is called its Cut –

in voltage. For Silicon diodes, this cut – in

voltage will be approximately 0.6 to 0.7

Volt. For Germanium diodes it will be

approximately 0.2 to 0.3 Volt.

2. Break – down voltage (VZ): During

reverse biasing of diode, initially there will

be no current through the diode.

(Exception: if we use a micro ammeter, we

can observe some small current, a milli –

ammeter does not show any current ) As we

increase the magnitude of reverse voltage,

there will be a characteristic voltage for the

diode at which it starts conducting

infinitely. Sudden raise of current will be

observed at this point leaving the voltage

across diode almost constant. This voltage

is called the Break – down voltage. For

voltages less than 5V zener break down is

dominant and for voltages greater than 5V,

Avalanche breakdown is dominant.

3. Dynamic Resistance (RF and RZ): During

forward or reverse biasing of diode there

are points at which the current through

diode increase rapidly. At these points the

variation of current with voltage is non –

linear, reflecting that these devices are non

– Ohmic. For Ohmic devices, that obey

Ohm’s law, the resistance does not change

with applied voltage and hence they have

some fixed value of resistance. But here in

the case of diode, the resistance changes

with applied voltage. So we define the ratio

of differential change in Voltage across the

diode with the corresponding differential

change in current through it as the Dynamic

Resistance.

4. Material of the diode: Depending the cut

– in and break – down voltages as

described above, we can decide the make of

the diode.

APPLICATIONS:

1. As voltage regulators for both line

regulation and load regulation in D.C.

power supplies.

2. Used in generating reference voltages

for transistor based and integrated

circuits.


PRINCIPLE: To study the V – I

characteristics of the Junction diode / zener

diode, we must measure the current through

the diode by applying various voltages to the

diode in both forward and reverse biases. This

can be done with a variable voltage D.C.

source and a milli – ammeter.

What is the D.C. source?

A variable D.C. power supply with zero

minimum voltage to at least 15 to 20 V

maximum voltage. Its power rating must be

sufficient to draw at least 100 mA current at

these voltages. In our lab we are going to use a

0 – 20 V variable D.C. source with 1 Ampere

maximum current.

mA

RS

FORWARD BIAS V VD

VR



How to choose the diode?

The zener break – down voltage should not

exceed the maximum voltage supplied by the

D.C. source. As a rule of thumb, the difference

between maximum voltage of the source and

the break – down voltage of the diode must be

greater than at least 5V. If the D.C. source has

maximum voltage of 15 Volt, we can use

zener diodes of break – down voltages up to

10V. The power rating of the diode is

specified by the manufacturer. If we want

more current through the diode, we must use

high power rated diodes. In our lab we use

either half watt or one watt rated zener

diodes. Their voltage ratings usually vary from

5V to 13V.

For PN junction diode we use 1N 4001 – 4007

family of rectifier diodes. In our lab we use

1N 4007 diode made of silicon that has a PIV

rating of 1000V (PIV – peak inverse voltage,

the maximum reverse voltage a diode can

withstand; break down voltage)

How to recognize its polarity?

There will a ring (band) on the cathode side it

will be the negative of diode and obviously the

other one will be positive of diode. If the band

is not visible, you can test it with a muti-

meter.

How to test a diode with a multi-meter?

There will be a diode symbol on the multi-

meter dial knob. Turn it to the diode testing

mode. Join the positive (red probe) of multi-

meter to one end of the diode and the negative

(black probe) to the other end of diode. If the

meter shows a low resistance of say few

hundred, it means that the diode is forward

biased, i.e. the leg of diode connected to

positive (red probe) is it’s positive and vice –

versa. If the multi-meter shows an infinite

resistance, it means that it is in reverse bias,

i.e. the leg of diode connected to the positive

(red probe) of multimeter is its cathode

(negative) and vice – versa.

How to check whether a diode is working or

spoiled?

To check whether the diode is working or

spoiled use the multimeter test as described

above. If the diode shows very low resistance

in both directions, it is spoiled. If it shows

high resistance only in one direction, it is in

good condition.

What is the function of series resistance RS?

RS is used for limiting (controlling) the current

through diode. The value of this resistor can

be decided by the power rating of the diode.

How to measure the current?

In our lab we have milli – ammeters of 0 – 50

and 0-100 range. We can also use the digital

multimeter (DMM) in current measuring

mode.

Fixing the values of components:

Apply KVL to the forward bias circuit.

During forward bias VD =0.7 V approximately

for silicon diode. If the power rating of Zener

is P, maximum current it can hold without

being destroyed is imax, then,

Or

This will tell us the maximum current the

diode can withstand when a voltage of VD is

applied to it. The resistor must be capable of

controlling the current to this threshold value.

As a rule of thumb, we restrict our self

to a threshold current value which is much

lower than the value predicted by the above

expression for imax. If the predicted value is

say 90 mA, then we restrict to ¼ of this value,

say 20 to 25 mA. Take this value as imax. This

is to ensure the durability of the diode. If the

applied maximum voltage by the D.C. source

is say 20 V, then

(In forward bias)

Suppose that the zener is a half watt rated.

Then,

. Hence it

can withstand 700 mA. But our milli –

ammeter has only 50 or 100 mA range, it is

better to restrict up to 30 mA in forward bias.

So, Imax is 0.03Amp. Hence,

or

.

mA

RS

REVERSE BIAS V VD

VR



The nearest standard resistance value is 680Ω.

The power rating of the resistor can be

calculated using .

Suppose that the maximum current goes up to

30 mA in the resistor, then,

Nearest standard wattage is 1 Watt. If we use a

1KΩ resistor in place of 680Ω, the current

drops and even a 1KΩ half watt resistor can

withstand the maximum current. So, when we

wish to reduce the resistance we must increase

its power rating and vice versa.

For reverse bias replace VD with the break

down voltage of the zener diode, say 5.6V, ½

watt rating, then,

.

So, restrict only to 25 mA.

or

, nearest standard value

is 680Ω. So it is better to use 680Ω or more in

both forward and reverse biasing of the circuit.

ZENER DIODE V – I CHARACTERISTICS EXPERIMENT

Aim: 1. To study the volt – ampere

characteristics of the given zener

diode.

2. To determine the Cut – in, Break –

down and dynamic resistances of the

diode from the characteristic curves.

Apparatus: Zener diode (½W), Resistors (1 KΩ, ½W),

Variable voltage D.C. power supply, milli –

ammeter (0 – 50 or 100), Multimeter, bread

board, connecting wires.

Procedure:

FORWARD BIAS:

Circuit:

1. Construct the circuit on bread board

according to the circuit diagram for

forward bias. Zener diode has a black

band on it. It shows the cathode of diode.

2. Vary the potentiometer (knob on the

power supply) and apply various voltages

to the diode in steps of 0.1 Volt. Note the

current in milli ampere as shown by the

ammeter.

3. Initially, there will be no current through

the diode up to a characteristic voltage,

known as Cut-In voltage. Note values of

current until this characteristic voltage as

zero. Observe carefully for this voltage

and note it down.

4. From here onwards note down the

voltage that you observe across the

diode as function of current through

diode in steps of 2 mA by varying the

potentiometer.

REVERSE BIAS:

Circuit:

1. Connect the circuit in reverse bias as

shown in the circuit diagram, i.e. just

reverse the ends of the diode in the

forward bias circuit.



to the diode in steps of 1 volt starting from

zero.

3. Note the value of current in milli ampere

as shown by the ammeter (initially you

wouldn’t get any current, note them as

zero).

mA

RS

REVERSE BIAS V VD mA

RS

FORWARD BIAS V VD



4. At a characteristic voltage known as

Break down voltage, you will get a

sudden raise in the current through the

diode. Observe this carefully and note

down the value.





potentiometer.

Graph: Plot a graph by taking the current through diode versus voltage across diode both for

forward and reverse biases. Split the graph into four quadrants.

Choose the scale on voltage axis (horizontal) as 1 division = 0.1Volt on the positive side and 1

division = 1 volt on the negative side.

Choose the scale on current axis (vertical) as 1division = 1 mA on both positive and negative sides.

From each curve on first and third quadrants, calculate the slope of the graph near cut – in and

break – down points. These slopes will give the dynamic conductances of diode. Inverse of

conductance gives the dynamic resistance of the diode.

Precautions:

1. Do not short the ends of the power supply. This will damage your power supply.

2. Connections on the breadboard must be tight. Avoid loose contacts.

3. Check the polarity of diode carefully.

4. Do not connect the diode without current limiting resistor. This will burn out the diode in any

bias.

Viva – voce questions:

1. What is the basic application of a zener

diode?

It is used as a voltage regulator.

2. I have a silicon made zener diode with

VZ=5.2V connected in reverse bias with

a series resistor of 100Ω and a variable

D.C. source of 0-20V. Estimate the

maximum current flowing in the circuit.

Determine the current in the circuit if

the diode direction is reversed. Suggest

the minimum power ratings for both

zener diode and resistor in both

connections.

In reverse bias,

For diode,

For resistor,

.

In forward bias, for Silicon VZ = 0.7 V

For diode,

For resistor,

.

3. Design a voltage regulating circuit

which drives a cell phone charging unit

with required output at 5.6 Volt, 300mA

with input voltage of 10 Volt D.C.

Imax for the zener is 300mA, i.e. 0.3A.

Zener voltage rating is 5.6V, for diode,

For resistor,

Voltage drop across it will be 10–5.6= 4.4V

; This circuit will

work will a load (cell phone) of resistance

greater than 18.66 Ω. If the load resistance is

further reduced, the circuit will not work.

4. What do you mean by dynamic

resistance?

It is the resistance offered by the diode due

to the changes occurred in input voltage.

Static resistance of a diode refers to a fixed

resistance at a fixed voltage. But dynamic

resistance is some kind of average

RS

10V 5.6



resistance offered by the diode when the

input voltage changes between two closely

separated voltage levels.

5. Which bias would you suggest for

operating the zener diode to exploit to

maximum extent?

Reverse bias only.

6. Can we use an ordinary PN junction

diode to regulate the voltage instead of a

Zener diode? Justify your answer.

Yes, Junction diode offers a forward drop

of about 0.7 Volt (for silicon). Hence by

using a combination of forward biased

diodes we can achieve voltage regulation

even in forward bias. A serial combination

of two forward biased silicon diodes will

provide a forward drop of 1.4V.

7. What is the basic difference between

Zener break down and avalanche

breakdown?

Zener break down is due to the breaking of

bonds in the depletion region because of

applied external reverse voltage.

Avalanche breakdown is due to the rupture

of bonds in depletion region by the

collisions of minority carriers that are

accelerated by the applied reverse voltage.

As the temperature increases, the minority

carrier concentration also increases, giving

more chance for avalanche breakdown.

REFERENCES:

1. Electronic devices and circuits – Discrete and integrated, Stephen Fleeman, Prentice hall, Art.

2-8, zener and avalanche diodes, p.32-36 (taken verbatim).

2. Electronic devices, 9th

Ed, Thomas L Floyd, Prentice hall, unit-3, special purpose diodes,

p.113-126.

3. Electronic devices and circuit theory, R. Boylestad, 7th

ed, Prentice hall publications, Art,

semiconductor diode p.10.


PN VI.1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

PN JUNCTION DIODE V – I CHARACTERISTICS EXPERIMENT

Aim: To study the volt – ampere characteristics of

the given PN junction diode.

Apparatus: 1N 4007 rectifier diode / 1n 4148 signal diode,

Resistors (470 Ω or 1 KΩ, ½W), Variable

voltage D.C. power supply, milli – ammeter

(0 – 50 or 100), micro ammeter (0 – 50) range,

Multimeter, bread board, connecting wires.

PROCEDURE:

FORWARD BIAS:

Circuit:

1. Construct the circuit on bread board

according to the circuit diagram for

forward bias. Junction diode has a band

on it. It shows the cathode of diode.



to the diode in steps of 0.1 Volt. Note the

current in milli ampere as shown by the

ammeter.

3. Initially, there will be no current through

the diode up to a characteristic voltage,

known as Cut-In voltage. Note values of

current until this characteristic voltage as

zero. Observe carefully for this voltage

and note it down.





potentiometer.

REVERSE BIAS:

Circuit:

1. Connect the circuit in reverse bias as

shown in the circuit diagram, i.e. just

reverse the ends of the diode in the

forward bias circuit.



to the diode in steps of 1 volt starting from

zero.

3. Note the value of current in micro ampere

as shown by the ammeter. (If you connect

a milli – ammeter in place of this you will

not observe any current)

4. Just continue doing this until you reach the

maximum D.C. source voltage.

5. Use these values to estimate the reverse

resistance of the diode. Usually it will be

in mega Ohms.

Graph: Plot a graph by taking the current through diode versus voltage across diode both for

forward and reverse biases. Split the graph into four quadrants.

Choose the scale on voltage axis (horizontal) as 1 division = 0.1Volt on the positive side and 1

division = 1 volt on the negative side.

Choose the scale on current axis (vertical) as 1division = 1 mA on both positive and negative sides.

From each curve on first and third quadrants, calculate the slope of the graph near cut – in in

forward bias and anywhere in the reverse bias. These slopes will give the dynamic conductances of

diode. Inverse of conductance gives the dynamic resistance of the diode.

Precautions:

1. Do not short the ends of the power supply. This will damage your power supply.

2. Connections on the breadboard must be tight. Avoid loose contacts.

3. Check the polarity of diode carefully.

4. Do not connect the diode without current limiting resistor. This will burn out the diode in

forward bias.

µA

RS

REVERSE BIAS V VD

mA

RS

FORWARD BIAS V VD


S.G.1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

STEWART AND GEE APPARATUS

MAGNETIC FIELD ALONG THE AXIS OF CIRCULAR CURRENT CONDUCTOR

THEORY:

Biot – Savart’s Law:

Consider a current carrying conductor (of

arbitrary orientation) as shown in figure. It

carries a current of I. The magnetic field at

a point P at distance from an element of

the conductor will be given by

| |

|

|

| |

Here θ is the angle between the radius vector r

and the length element ds.

, is the free

space permeability constant.

Direction of magnetic field is in the direction

of the cross product of ds and r, given by right

hand screw rule.

Magnetic Field on the Axis of a Circular

Current Loop:

Consider a circular wire loop of radius R

located in the yz plane and carrying a steady

current I, as shown in Figure. We are going to

calculate the magnetic field at an axial point P

at a distance x from the center of the loop.

Consider element of the wire. Using Biot

savart’s law, the field at P due to this will

be

The angle between the ds and r is 900. So,

And its direction is indicated in the figure.

Also from the figure the angle between vector

r and the y – axis (smaller angle side) is . So,

makes an angle with the x – direction.

Its components along X and Y – directions are

and respectively. When we consider

the entire elements of the loop, their y –

components will cancel with each other

due to the circular symmetry of the coil and

only the x – components survive. So, the total

field at P due to all elements will be,

∮ ∮

Throughout the loop the values of θ and r

remains unchanged and hence can be taken

outside the integral.

∮

∮ is the circumference of the coil.

From the figure,

√

Therefore,

(√ )

√

If the coil contains n number of turns, then the

field gets multiplied by that factor.

The direction of this b is always either parallel

or anti – parallel to the axis of the coil.

The field B at the centre of the coil can be

obtained by putting x = 0,



At ,

( )

√

Hence, the field B falls to

√ times of its

maximum value Bo at the center. We can

use this point to calculate the radius of the

coil, without measuring it physically with a

scale, from the experiment.


PRINCIPLE:

The variation in B along the axis of the

circular coil can be studied experimentally

with the help of a Tangent Galvanometer.

How to measure B?

The coil will produce a magnetic field . There is a huge EARTH magnet that will

produce another field , known as the

horizontal component of Earth’s magnetic

field. The plane containing the axis of the

hypothetical Earth bar magnet is called the

MAGNETIC MERIDIAN.

If we place the plane of the coil in the

magnetic meridian, then there will be two

mutually perpendicular magnetic fields, one in

the North – South direction (Earth) and the

other in the East – West direction (coil). If we

use a magnetic compass near the coil (which is

already set in magnetic meridian), it will

experience a toque due to the action of the two

magnetic fields and will settle ultimately in the

resultant direction of the two fields.

H = 0.38 Oersted or 0.38 X 10 - 4

Tesla

By measuring θ we can estimate the

experimental value of using the above

relation.

What is the coil?

A circular frame holding the coil of variable

number of turns is mounted vertically on a

platform. The platform can be adjusted to

make it horizontal with the help of two

leveling screws. The set up has 2 turns, 50

turns and 500 turns of coil for experimenting.

We use only the 50 turn coil.

How to set up the current in the coil?

Using a fixed voltage D.C. source.

How to measure the current?

Using an ammeter of 0 – 3 Amp range.

How to vary the current the circuit?

By using a 20 Ω Rheostat.

Why to adjust the current?

As we measure the magnetic field as a

function of angle, it is necessary to restrict our

self to some fixed range (30°-60°). Hence it is

required to adjust the current to get the desired

value of deflection θ.

Why to restrict only to 300-60

0 range?

When using the instrument it is important to

adjust matters so that the deflection is never

outside the range 25° to 65° and preferably it

should be between 30° and 60°. This is

because the value of θ is to be used in the form

tan θ and an effect which can be called 'error

magnification' arises. The matter will be made

clear by considering the following examples:

Suppose the deflection can only be

observed with an accuracy of half a degree.

Let us consider how this possible error will

affect the values of the tangents of deflections

10°. tan 10° 30' = 0.1853 and tan 9° 30' =

0.1673 thus tan 10° 30' - tan 9° 30' = 0.0180.

Now tan 10° 00' = 0.1763.Thus an observation

of θ = 10° ± 0.5° leads to a statement that tan θ

= 0.1763 ± 0.0090. This represents a possible

error of over 5% in tan θ.

N



STEWART AND GEE APPARATUS EXPERIMENT

AIM:

To study the variation in magnetic field with

distance along the axis of circular current

carrying conductor.

APPARATUS:

Stewart and Gee type galvanometer, battery

(D.C. Source 2 Volt - 1Amp), commutator,

rheostat, Ammeter and connecting wires.

CIRCUIT DIAGRAM:

FORMULA:

Where

0 = 4 X 10-7

Henry/meter

n = No. of turn in the coil

i = Current flowing through the circuit

x = Distance of the magnetic compass

from the center of the coil

a = Radius of the coil.

If x and a are expressed in centimeter, then the

resultant expression will be

In gauss, the same formula will be,

DESCRIPTION OF EQUIPMENT:

It consists of a circular coil in a vertical plane

fixed to a horizontal frame at its middle point.

The ends of the coil are connected to binding

screws. A magnetic compass is arranged such

that it can slide along the horizontal scale

passing through the center of the coil and is

perpendicular to the plane of the coil. The

magnetic compass consists of a small magnet

and an aluminum pointer is fixed

perpendicular to the small magnet situated at

the center of the compass. The circular scale in

the magnetic compass is divided into four

quadrants to read the angles from 0 to 90

and 900 to 0

0. A plane mirror is fixed below

the pointer such that the deflections can be

observed without parallax.

PROCEDURE:

1. The circuit should be connected as shown

in the diagram.

2. Remove the power connection applied to

the circuit.

3. Place the compass exactly at the centre of

the coil.

4. Adjust the arms of the magnetometer until

the pointer of compass becomes parallel to

it. Rotate the compass until the pointer

reads 0°- 0°.

5. Suppose that the coil is placed in magnetic

meridian and switch on the power to

circuit. It will show some deflection.

Carefully adjust the rheostat and bring the

deflection to 60° - 60°.

6. Interchange the plug keys of the

commutator and reverse the current

direction in the coil. Note down the

deflections of compass.

7. If your coil is exactly in magnetic meridian,

then the readings of compass should not

differ by more than 5° from their previous

values, before interchanging the

commutator. If this is not satisfied, once

again turn off the power and make the

pointer parallel to the magnetometer and

repeat this until you get all four deflections

within 5° variations.

8. Move the compass to 10 cm distance on

both east and west directions on the

magnetometer and obtain the deflections

with both directions of current.

9. If all the eight deflections that you have

obtained in above case lie within 5°, you

can start taking deflections at various

positions. Now the instrument should not

be disturbed while moving the compass.

Otherwise repeat the adjustment by

disconnecting the power.

A

C

S.G. coil

Rh (20Ω) 2 VOLT D.C.

0 to 3 Amp



Tanθ

Position of compass

East 0 West

Tanθ

East 2R West

√

10. Start at 0 cm position and obtain four

deflections. Vary the position to 2 cm either

East or West and obtain four more

readings. Tabulate them.

11. Proceed in the same way at 2, 4, 6…. cm

on both East and West until the deflection

falls less than 20°. Tabulate the readings.

PRECAUTIONS:

1. The Stewart and Gee apparatus should

not be disturbed after the adjustments.

2. Observations are noted down without

parallax.

3. The ammeter and rheostat should be

kept far away from the deflection

magnetometer

Graph:

A graph is plotted taking distance of the compass from the

center of the coil along X-axis and tan along Y-axis. The

shape of the curve is as shown in the figure and is symmetric

about Y-axis. The magnetic field is found to be maximum at

the center of the coil. The radius of the coil ‘a’ is determined by

measuring its circumference. The current flowing through the

circuit ‘i’ and the number of turns in the coil ‘n’ are noted. The

value of magnetic induction is calculated from the above

formula and is compared with the experimental formula B = H

tan θ.

Viva-Voce questions:

1. What are the magnetic forces acting on

the compass when it is mounted on the

axis of the coil? Mention their directions.

The forces are, due to Earth’s magnetic

field along the geographic north direction

and due to coil along either east or west

direction.

2. What is the direction of the magnetic

field produced by the coil?

Along East or West, i.e. perpendicular to

the plane of the coil.

3. Why do we adjust the maximum

deflection at 60° ?

To restrict the error in the measurement of

θ and hence in the tan θ to less than 5%, we

always adjust the maximum deflection to

60°.

4. State Biot-Savart’s law.

Refer to text.

5. Define magnetic meridian.

It is the plane containing the axis of the

earth’s hypothetical bar magnet.

6. Why the ammeter should be placed far

away from the coil?

If it is sufficiently close to the coil, its horse

shoe magnet will influence the resultant

deflection of the compass which is an

undesirable effect.

7. What is the function of rheostat in this

experiment? To vary the current in the circuit and to

bring the deflection to desired value.

8. Can you determine the radius of the coil

without measuring it with a scale?

Yes, consider the tan θ vs. position graph.

Maximum value of tan θ is obtained at the

centre. Calculate the value of

√ .

Draw a horizontal line intersecting the tan θ

axis at this value. The line intersects the

graph (curve) at two different points. The

graphical distance between these two points

will give the diameter of the coil and half

of it will give the required radius of the

coil.

REFERENCES:

1. Advanced level physics, Nelkon and parker, magnetic fields due to conductors, p.935 2. Fundamentals of physics, Resnick, Halliday, Walker, 7

th ed, Example 30.3, p.942 (for fig).


TP 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

TORSIONAL PENDULUM THEORY DESCRIPTION OF PENDULUM:

It consists of uniform metal disk suspended by

a stainless steel wire whose rigidity modulus is

to be determined. The lower end of the wire is

gripped to a chuck nut fixed to the disk and the

upper end to another chuck nut fixed to a rigid

support. When the disk is turned through a

small angle (less than 50) in the horizontal

plane so as to twist the wire and released, the

pendulum executes torsional oscillations about

the axis of the wire.

The period of the oscillation is given by

√

Where,

I = Moment of inertia of the Disk about its

axis of rotation

C = Couple acting per unit twist of the wire

l

aC

2

4

a = Radius of the wire

l = Length of the pendulum

=

Rigidity modulus of material of

wire

The period of oscillation is expressed by,

√

Therefore,


PRINCIPLE: If we measure the time period of oscillation of the pendulum with various lengths of

suspensions, we can estimate the “η” of the material of the wire.

1. What is the pendulum?

A brass disk, of about 6 cm radius and about 1kg

mass, with a chuck nut at its centre to suspend it

with a wire. Suspend this disk to a wall bracket

that carries another chuck nut to hold the wire.

L, the length of the pendulum is the length of the

wire suspended between the two chuck nuts.

2. How to measure time period T ?

First focus the telescope on the pendulum. You

can make a mark on the edge of the pendulum

either by a marker or by attaching a pin to it with

wax. Use a stop clock to count the time taken for

say 20 oscillations and hence find out the period.

The amplitude of oscillation must be less than

5°.

Graph: Plot a graph between length of the pendulum (L) and the

square of the corresponding time period of oscillation (T2). It

will be a straight line passing through origin.

Choose 1 div = 5 cm on L axis and 1 div = 5 sec2 on T

2 axis.

REFERENCES:

1. Advanced practical physics for students, Worsnop and Flint, Methuen publications, p.100 –

102

2. Laboratory Physics, 3rd

Ed, J.H. Avery, A.W.K. Ingram, Heinemann publications, p.73

L

T2



TORSIONAL PENDULUM EXPERIMENT

AIM:

To determine the rigidity modulus of the material of the wire using Torsional pendulum.

APPARATUS:

Torsional Pendulum, Reading Telescope, Pin, Steel wire, Meter scale, Screw Gauge, Vernier

Calipers and Stop Clock.

FORMULA:

Where η = Rigidity Modulus of the material of the wire

a = Avg. radius of the wire

M = Mass of the Disk

R = Radius of the Disk

L = Length of the Pendulum

T = Time Period

PROCEDURE:

1. Fix the metal wire whose rigidity modulus is to be determined (without kinks) to the Wall

bracket with the help of chuck nut.

2. Carefully suspend the disk is from the other end of the wire.

3. Adjust the length between the two chuck nuts to say 40 cm using a meter scale.

4. Attach a pin vertically to the edge of the disk. Or equally you can make some reference line with

permanent marker.

5. Watch through the telescope and focus it on the pin. Make the vertical cross wire to coincide with

the reference line or pin.

6. Give a small twist to the wire by turning the disk slightly about the vertical axis.

7. Take proper care to avoid any up & down and lateral movements.

8. Let the mark come to one extreme of the vertical cross wire. From here start counting of

oscillations by turning on the stop watch.

9. When it executes torsional oscillations, count the time taken for 20 oscillations in two trials, trail

one and two. Calculate the time period ‘T’.

10. Now adjust the length of the wire to another position say 50cm. repeat the experiment two more

lengths of the wire in the intervals of 10 cm and calculate T in each case.

11. Calculate avg. L/T2.

12. Measure the mass of the disk and then its radius using rough balance and Vernier calipers

respectively.

13. For the radius of the disk, take at least three observations.

14. Use screw gauge and measure the mean radius of the wire by taking five observations at different

positions of the wire.

15. Determine the rigidity modulus by using the formula.

16. Plot a graph between L and T2. It gives a straight line passing through the origin. Calculate η also

from the graph.

Least count of Vernier calipers:

Least count (LC) =

Least count of Screw Gauge:

Pitch of the screw =

LC =



PRECAUTIONS:

1. The pendulum must be oscillated only in the Horizontal plane with small amplitude (< 5°)

and without any wobbling.

2. Wire must be free from kinks.

VIVA-VOCE QUESTIONS

1. What is meant by rigidity modulus?

The ratio of shearing stress applied on the

body to the corresponding shearing strain

developed in the body (Shear = tangential)

2. What is the moment of inertia of the

disk about an axis through its chuck

nut?

3. What happens to the time period of

oscillation of the disk when the length of

the suspended portion of wire is

increased?

, hence increase in l increases T

4. What is the least count of vernier

calipers?

0.01 cm

5. What is the least count of screw gauge?

0.01 mm

6. What is the zero error for a screw

gauge?

The zero of head scale usually doesn’t

coincide with the index line on the pitch

scale. If the zero of the head scale lies

above the index line, it will be negative

error equal to the number of divisions

between zero and index line. Similarly if

the zero lies below the index line it will be

positive error by the same divisions. For

positive error the correction should be

negative and vice versa.

7. What is the unit for rigidity modulus in

C.G.S. system?

Dyne/cm2

8. If we change the radius of the wire from

a to a/2, what will be the new rigidity

modulus of the material of the wire?

Does not change. η does not depend on the

physical dimensions of the wire. It is a

material constant. If we change the radius,

the new l/T2 will adjust in such a way to

compensate this, i.e. l/T2 decreases.


NR 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

t

rn

R

A

B

NEWTON’S RINGS THEORY DESCRIPTION:

When a Plano – convex lens with its convex

surface placed on an optically plane glass plate is

observed for interference fringes with an

extended monochromatic source, it will produce

concentric bright and dark rings of variable

radius. The pattern was first observed

independently by Hooke and Boyle. But the radii

of the rings were first measured by Sir Isaac

Newton and the name was given to him. The

correct mathematical explanation of these

fringes was given Thomas Young in later years.

Plano – convex lens encloses an air gap

with the glass plate that is a non parallel thin

film of variable thickness. When a beam of

parallel rays fall normally on the lens they will

undergo reflections from the top and bottom

layers of this Plano – concave shaped air film.

These rays satisfy the conditions for coherent

sources and hence they produce sustained

interference pattern in the field of view of the

microscope (observer).

Nature of fringes:

These fringes are called the fringes of equal

inclination or Fizeau fringes. They are

concentric rings with variable diameters.

MATHEMATICAL TREATMENT: Consider a Plano-concave shaped thin film

formed by a medium of refractive index µ. Let

the radius of curvature of this Plano-concave

shaped film be R. Consider a parallel beam of

light rays incident normally (r, the angle of

refraction = 0) on this film. The ray reflected

from the upper surface of the film, at A will not

suffer any phase change due to reflection. But

the ray from B suffers a phase change of π due

to reflection from an optically denser boundary.

Path difference created between these

two rays at a location where the thickness is “t”

is,

From the figure, if the point of observation

(thickness = t) lies at a distance rn away from

the center of the lens, using Pythagoras theorem

for the right angled triangle implies,

For a thin Plano-convex lens usually the

thickness (t) will be small compared to its R.

Hence t2 will be much smaller than R and can

be neglected.

Or,

Using this in the expression for path difference

implies,

Replacing rn with Dn the diameter (Dn=2. rn)

gives,

For maxima, with

“n” representing the order of the bright fringe,

(

) With .

for bright fringes (rings).

For minima, the dark ring,

With “n”

representing the order of the dark fringe,

Rays move towards the microscope

oe



Ring order (n)

Dn2

(

) With . For Dark

fringes (rings).

If we consider air as the medium between lens

and glass plate, µ = 1, then

For dark ring, , hence

for

dark rings.

Consider an mth

order dark ring. Then,

Combining both equations implies,

R = radius of curvature of the Plano – convex

lens

= Wavelength of the monochromatic source

= 5893 Å for sodium vapour lamp

The above equation is valid for dark rings

only. In this experiment we intentionally choose

dark rings because it is easy to locate the dark

fringes exactly than the brighter ones.


PRINCIPLE: If we measure the diameters of various dark rings with traveling microscope, we can

determine the radius of curvature of the Plano – convex lens by knowing the wavelength λ.

1. What is the traveling microscope?

It is a compound microscope with a graduated

carriage that enables the reading of motion of the

microscope in both horizontal and vertical

directions. it has a vernier to read the position of

the microscope.

2. How to achieve normal incidence on the

lens?

With the help of a beam splitter, a plane glass

plate inclined at an angle 45° with vertical we

can collimate the beam normally on the lens

system.

Graph:

A graph should be plotted by taking the values of versus

the order of ring n. It is a straight line passing through origin as

shown in the figure. Determine the radius of curvature of lens from

the slope of graph.

Applications:

1. To check the optical flatness of a plane glass surface

2. To check the quality of grinding or polishing of lenses by

opticians

3. In the study of polarized Laser beams.

REFERENCES:

1. Advanced practical physics for students, Worsnop and Flint, Methuen publications, p.67 – 71 2. Laboratory Physics, 3

rd Ed, J.H. Avery, A.W.K. Ingram, Heinemann publications, p.93



NEWTON’S RINGS EXPERIMENT AIM:

To determine radius of Curvature of a given convex lens by forming Newton’s Rings.

APPARATUS:

Sodium Vapour lamp, traveling microscope, reading lens, convex lens and plane glass plates,

retort stand.

FORMULA:

Where

R = Radius of Curvature of Plano-convex lens

Dn = Diameter of nth

dark ring

λ = Wavelength of the source used = 5893 Å

n, m = order of the rings (Number of the ring from the

Central dark spot)

Procedure:

1. Take a piece of paper (paper should not be completely white, it must contain some markings

or rulings so that they can be observed in the field of view) and place it below the microscope

on the platform of the travelling microscope (TM). Adjust the rack and pinion and focus the

microscope. (markings on the paper will become very clear)

2. Take the Plano-convex lens and locate which side is plane and which side is curved. Clean

the lens with cloth (handle it with care) and place it on the plane glass plate. Place the black

paper below the plane glass plate.

3. Keep them on the platform of the TM. Make sure that neither the lens nor glass plate comes

on track of the moving base of the microscope.

4. Use a retort stand to hold another plane glass plate at 450 with vertical as described in the

theory. Place the glass plate in between the microscope and the lens setup.

5. Observe through the microscope and tilt the clamp of retort stand to get maximum yellow

light. This ensures normal incidence of light on the lens surface.

6. Now move the lens carefully to observe the central portion of the ring pattern, i.e. dark

central spot surrounded by rings. Do not disturb the lens once after you reach the central dark

spot.

7. Turn the screw gauge dial of the TM and bring the vertical cross wire near the central dark

spot.

8. Turn the dial by counting rings (arcs) first towards your right hand side until you reach at

least 20th

dark ring on that side.

9. If there is no difficulty in reaching the 20th

on RHS, return back to the central dark spot by

turning screw gauge dial back. Now turn the dial towards otherside until you reach the 20th

ring on the left hand side.

10. If it gets struck in the middle, then carefully move the lens system such that the 20th

ring or

another higher order ring (say 24th

) comes and coincides with the cross wire in the position

where you had this struck. Steps 8 to10 will make sure that you can go through the diameter

of the 20th

ring.

11. Lock the base screw of the TM for horizontal motion and turn the screw gauge dial to

coincide the reference line of main scale with any one division on the main scale.

12. Release the base screw and adjust the screw gauge dial such that the “0” of it coincides with

its reference line. Then once again lock the base screw and never release it again throughout

the experiment. This calibrates your TM.

13. Now once again come back to the central dark spot and go towards one side (either left or

right) by carefully counting the dark rings only. Make the cross wire tangential to the dark

ring, say 20th

. Note down the reading of TM.



14. Rotate the dial back by counting the rings carefully in decreasing order. Make the crosswire

tangential to the ring, say 18th

and note the reading of TM.

15. Proceed in the same way in steps of two-two rings until you reach the central dark spot.

16. Now continue taking readings on the other side of the ring pattern until you reach the other

side 20th

ring. Tabulate the readings.

Least count =

Or

(For screw gauge dial type microscope)

Least count =

Precautions:

1. The lens should not be disturbed from the initial position while taking the readings at various

positions.

2. Readings of the Vernier must be noted without parallax error.


1. What is cosine law?

2. What is the medium that is responsible

for the formation of Newton’s rings?

Air film in Plano – concave shape.

3. What is the shape of the thin film

forming the rings?

4. What happens to the ring pattern when

the refractive index of Plano convex lens

is changed? (either increased or

decreased)

No changes will take place.

5. What happens when a liquid is poured

in between the lens and glass plate?

Fringe pattern shrinks as µ for liquid is

greater than 1.

6. What happens to the fringe pattern

when the yellow light is changed to

1) Red light 2) violet light

7. Can you determine the refractive index

of a transparent liquid by using this

method? If yes, describe a method. If

no, why?

8. What happens to the fringe pattern if

we replace the sodium vapour lamp

with a mercury vapour lamp?

Few fringes are seen near the center and

after that there will be uniform

illumination.

9. What is back-lash error?

It is the error caused in the measurement

of vernier due to improper calibration of

the screw controlling the motion of the

microscope. Once if the screw is made

tight in one direction it gets calibrated and

afterwards the readings will be good. If we

change the direction of motion of the

microscope once again it needs to be

calibrated by a fraction of rotation in the

new direction.

10. Why do we get circular interference

fringes in this experiment? Why not

straight edge fringes?

They are fringes of equal thickness, i.e.

they are formed by the film of constant

thickness. The locus of constant thickness

of film will decide the shape of fringes. In

this case the locus will be circle and hence

fringes are rings. In the case of wedge

method the locus will be a straight line and

hence they are straight edge fringes.

11. What is the least count of the travelling

microscope that you have used? Write its

formula.

12. Why do we keep a black paper at the

bottom of the plane glass plate?

To avoid the light coming from the

platform of traveling microscope.


MD 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

Direction of vibration of prongs

Direction of propagation of waves

Longitudinal mode

String direction

T

l

l

MELDE’S EXPERIMENT

DESCRIPTION OF TUNINIG FORK:

The prongs of the tuning fork are vibrated

with an electromagnet. It is fitted with a metal

plate with an adjustable screw. An

electromagnetic coil is placed in the middle of

the prongs which has a make and break type

arrangement. The electromagnet is powered by

the variable voltage D.C. power supply. Once

power is turned on to the electromagnet, it pulls

(attracts) the prong inward. As the prong moves

towards the electromagnet the circuit breaks with

the help of the make and break key connected to

the prong along with the electromagnet coil.

Then the prong turns back and the circuit

gets completed again. This process repeats

continuously and we obtain continuous

vibrations in the tuning fork.

An electrically maintained tuning fork is

taken and to one end of its prongs a thread of

about one and half metre is attached. The

other prong of this electrically driven fork is

connected to the light and flexible string having

a light weight pan on the other end. This string

passes over a frictionless pulley. We can vary

the tension in the string by adding weights to the

pan. With a definite tension applied to the string

we can obtain a number of well defined loops in

the string.

LONGITUDINAL MODE:

In this mode the fork is adjusted until the

displacement of the prong is parallel to the

length of the string.

TRANSVERSE MODE:

In this mode the fork is adjusted until the

displacement of the prong is perpendicular

to the length of the string. This mode is

perpendicular to the longitudinal mode.


PRINCIPLE: If we measure the length of the loop of the standing wave in both longitudinal and

transverse modes we can estimate the frequency of vibration of the tuning fork by knowing the linear

density and tension applied to the string.

1. How much voltage is required?

4 to 6 Volts DC is suitable to vibrate the

fork.

2. How to apply tension to the string?

By adding known weights to the scale pan.

Tension will be the product of mass added

to the string including the mass of pan with

the free fall acceleration 980 cm/s2.

3. How to measure the linear density of

thread?

By taking a string of length roughly 5 to 10

meter and by weighing it in a sensitive

balance we can measure the linear density.

Graphs:

Plot a graph between √ and l on horizontal and vertical axes

respectively. Choose the horizontal axis with scale 1 div = 20

√ and on vertical axis choose 1 div = 10 cm or 5 cm.

Plot separate graphs for both Longitudinal and Transverse modes.


MD 2 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

MELDE’S EXPERIMENT AIM:

To determine the frequency of vibration of the electrically driven tuning fork.

APPARATUS:

An electrically driven tuning fork, light weight pan, soft and flexible thread, variable voltage

D.C. power supply, connecting wires, meter scale.

FORMULA:

√

For transverse mode

√

For longitudinal mode

Where, n = frequency of vibration of the tuning fork in Hz.

T = Tension applied to the string in dyne.

m = Linear density (mass per unit length) of the string. l = Length of each loop in cm.

PROCEDURE:

1. Set the apparatus in transverse mode, i.e.

the displacement of prong is perpendicular

to the length of the string.

2. Switch on the power supply and adjust the

screw until steady vibrations are obtained

with the fork.

3. Adjust the distance between pulley and the

prong of tuning fork until you get some

number of well defined loops, i.e. nodes and

antinodes.

4. Measure the total length of vibrating part of

the string. Then divide it by the number of

loops and obtain the length of each loop.

5. Add weights in steps to the pan and change

the tension in the string. In each step, measure the number of loops and total length of

vibrating segment. Then obtain the length of each loop for each case and tabulate the

readings.

6. Repeat the same process by adjusting the fork in Longitudinal mode, i.e. the displacement of

fork is parallel to the length of the string. Tabulate the observations.

7. For the same tension and same length of thread between the pulley and prongs, you will get

approximately double number of loops in transverse mode than in longitudinal mode.

PRECAUTIONS:

1. The displacement at the nodes on the thread must be completely zero.

2. Do not give very large amplitude to the vibrations of the tuning fork.

VIVA-VOCE QUESTIONS

1. What is meant by transverse wave?

2. What is meant by longitudinal wave?

3. If the linear density of the thread in this

experiment is doubled, what happens to

the frequency of the fork?

Does not change, remains constant.

4. If tension applied to the string is

decreased by four times of its initial

value, what happens to the length of the

loop?

Gets doubled.


D.G. 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

DIFFRACTION GRATING THEORY DIFFRACTION GRATING:

Plane diffraction grating consists of very large

number of parallel slits (open and opaque

portions) drawn on its surface. When the light

rays coming from collimator fall on the surface

of the grating normally (perpendicularly) it is

called normal incidence. Or, if the light rays fall

on the surface of the grating with an angle of

incidence ZERO, it will be normal incidence.

The following figure shows the diffraction of

plane waves under normal incidence at the

surface of a plane transmission grating.

The interference of secondary wavelets

generated from each of the open portions on the

grating is shown in the figure.

MATHEMATICAL TREATMENT:

If we calculate the resultant disturbance caused

due to the superposition of the spherical waves

(Huygens secondary wavelets) we will the

resultant intensity on the screen will be,

(

)

(

)

Where,

and

And d, e are representing respectively the slit

width and slit separation of the grating slits.

Here d is the width open portion of the slit and e

is the distance between the centers of two

successive opaque portions of the slit.

The above said expression has its maximum

value when both terms in the braces are

maximum. Clearly, the first Sinc function has a

maximum value of 1 at α = 0. The second Sinc

has maximum value of N at β = ± nπ, with n

taking natural numbers.

Hence, for maximas,

Or,

Here n represents the order of the spectrum.

(n = 0, 1, 2,….)

With N = 1/e, the number of slits per unit width

of the grating surface. (e, is the distance between

the centers of two neighboring opaque portions

and hence it tells the extent over which one slit

occupies, so 1/e tells the number of such slits

within unit width). Clearly there will be no

spectrum for zero order n. From n = 1 onwards

we can see the spectrum. This is because for n =

0 all wavelengths λ will fall at θ = 0, so no

splitting. But for n = 1 onwards different

wavelengths have different corresponding θ’s

and hence a spectrum of colours.

APPLICATIONS:

1. For the analysis of spectrum of various

gases (discharge process)

EXAMPLES IN DAY – TO – DAY

EXPERIENCE:

1. The colours seen on a compact disk(CD) or

a DVD (digital versatile disk) is an example

for reflection grating

2. The colours on the peacock feather.

3. The colours of the wings of a fly (insect).

4. Wire mesh in front of a loud speaker is an

acoustic transmission grating.

PLANE DIFFRACTION GRATING




PRINCIPLE: If we measure the angle θ of diffraction for maximas in a particular order of spectrum

say for n = 1, we can calculate the wavelength of the corresponding spectral line by knowing the

number of rulings over the grating per unit width, N.

1. What is the Source of light?

A mercury vapour lamp. 2. How to measure θ ?

With a spectrometer. (Refer Appendix)

REFERENCES:

1. Advanced practical physics for students, Worsnop and Flint, Methuen publications, p.362 –

365 and p.279-282 for spectrometer description. 2. Laboratory Physics, 3

rd Ed, J.H. Avery, A.W.K. Ingram, Heinemann publications, p.218-220

DIFFRACTION GRATING – NORMAL INCIDENCE EXPERIMENT AIM:

To determine the wavelength of spectral lines in the mercury spectrum using diffraction grating

under normal incidence of light.

APPARATUS:

Spectrometer, Plane diffraction grating, spirit level, reading lens and mercury vapour lamp source.

FORMULA:

Where

λ = wavelength of the spectral line.

Θ = Angle of the diffraction of a spectral line

n = order of the spectrum

N = number of lines on the grating per unit width.

= 15000 LPI = (

) = 5905.6 lines/ cm (LPI = lines per inch)

PROCEDURE:

STEPS 1 TO 7 ARE KNOWN AS PRELIMINARY ADJUSTMENTS

1. Assuming that the mercury vapor lamp is switched on, adjust the collimator of the spectrometer

in front of the lamp such that its slit faces opposite to the lamp.

2. Turn the telescope towards a distant object, a building at far seen through the window of your

dark room. Watch through the telescope and adjust its rack and pinion until you see the clear

inverted image of the building.

3. Turn the telescope back and try to see the light coming from the lamp through the collimator. In

this position both telescope and collimator will come on a straight line, i.e. collinear.

4. Initially, the view of the slit of collimator need not be clear, you may see a blurred image, i.e.

some diffused white light. Continue watching through the telescope and adjust the rack and

pinion of collimator (but not the rack and pinion of telescope) until you see the sharp image of

the slit of collimator. Now adjust the width of the slit (an adjustable screw is fitted with the slit)

and make it very thin.

5. Look at the base of the telescope, you will find two screws attached with the rotating platform.

One screw locks the telescope from moving, known as locking screw and the other screw, known

as tangential screw moves the telescope very slowly when it is locked by the locking screw.

Remember tangential screw will operate if and only if the telescope is locked. You will also find

another pair of screws attached with the base of prism table. Their action is also similar. They

lock the prism table and allow fine adjustments to it.

6. Coincide the telescope’s vertical crosswire with the slit and lock the telescope.



7. Release the prism table base screw and adjust it until you see in both verniers the zeros getting

coincided with 0 and 1800 divisions of main scale. Now lock the prism table base screw and then

release the telescope. This adjustment calibrates the telescope

8. Fix the grating holder to the prism table. Insert the grating in the holder. Do not make scratches

on the grating surface as it reduces the life of grating.

9. Rotate the telescope through 900 either clock-wise or counter clock-wise and lock it.

10. Free the prism table (not its base, but the long metal screw below the prism table platform and

make it free to rotate). With one hand slowly turn the prism table and watch through the

telescope until you see the reflection of the slit in the telescope.

11. Bring the reflection of slit exactly onto the vertical cross-wire only by turning the prism table.

(Do not adjust the telescope with its tangential

screw to bring the slit on cross wire)

12. With one hand carefully hold the grating, in the

position where the reflection coinciding with cross

wire, and with the other hand lock the metal screw

below the prism table carefully. This makes grating at

450 with the incident beam.

13. Release the base screw of prism table and turn the

entire prism table through further 450 until the plane

of grating makes 900 angle with the incident beam.

You can do this by looking at the initial reading of

telescope. If the reading in one vernier is say 900,

then, after rotating the prism table it may become

either (90+45=1350) or (90-45=45

0). Use your

commonsense to decide whether to rotate to 450 or

1350 to make the plane of grating normal (90

0) with

the incident beam.

14. In this position lock the prism table and release the

telescope.

15. Go though both sides of direct position to observe the spectrum.

16. Concentrate first on left hand side spectrum of the direct position. Rotate the telescope and

coincide each spectral line with cross wire and then lock it. In each case note down the vernier

readings (both vernier 1 and 2).

17. After completion of readings on left hand side go to the right hand side and repeat the same

process and obtain the readings.

Precautions:

1. Plane of the Grating must be vertical to the prism table. If the holder is not perfectly

perpendicular then use paper padding to make the plane of grating perpendicular to the rays.

2. Grating should not be disturbed after fixing it for normal incidence.

3. Readings of the spectrometer must be noted without parallax.

VIVA-VOCE QUESTIONS

1. What is normal incidence?

2. How do you keep the grating for normal

incidence using spectrometer?

3. When you see the reflection of slit in the

telescope by tilting the plane of the

grating, What will be angle of incidence

on the grating for the incident rays

(slit)?

45°

4. What is the least count of spectrometer?

5. Describe the construction of collimator.

Refer appendix.

6. Describe the construction of telescope.

7. What kinds of waves (shape) are

emitted by the mercury vapour lamp?

Spherical waves.

8. What serves as object in this

experiment?

Rectangular slit.

9. What is the function of mercury vapour

lamp in the prism experiment?

Just to illuminate the slit.

Telesco-pe direct position

Telescope rotated through 90

COLLIMATOR

450

450

450

450



10. What kinds of waves (shape) are

emitted through collimator?

Plane waves.

11. I will hide the object placed on the

prism table by using suitable box and

show you the spectrum alone through

telescope. If I ask you whether the

object inside the box is prism or

transmission type diffraction grating,

how will you decide it?

In the spectrum seen, if the red line comes

at a smaller angle with respect to the direct

position than the violet line, it is due to

grating. If the violet comes at smaller

angle than the red line, it will be due to

prism.


CP 1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

X

IG = mk2 I

S IS = mx2 + IG

m = mass of pendulum

Centre of mass

COMPOUND PENDULUM THEORY DESCRIPTION OF PENDULUM:

Compound pendulum consists of a uniform

rectangular bar made up of iron or brass with a

number of holes drilled along its length at equal

distances symmetrically on either sides of the

center of gravity (CG). The pendulum can be

suspended vertically by means of a horizontal

knife edge passing through one of the holes.

Suppose that the mass of the pendulum bar be m.

Let “x” be the distance of the point of suspension

of the pendulum (from where it is suspended

with the axle) to the center of mass of the

pendulum, i.e. at the midpoint of the pendulum

(50 cm location). Let θ be the angle made by the

axis of the pendulum with respect to the vertical.

If “I” represents the moment of inertia of the

pendulum bar about the point of suspension,

then the equation of motion (torque) governing

the pendulum will be,

Where α represents the angular acceleration of

the pendulum bar about the axis of suspension.

Force is the weight mg.

In this case from the figure, the perpendicular

distance will be x sin θ. Hence

Here we make the approximation that the

oscillations are very small so that the angular

amplitude θ is less than 50. Then,

(

)

With

, where ω representing the

angular frequency of the oscillations, it is clear

that the pendulum executes simple harmonic

motion.

Moment of inertia I is given as, . k is called the radius of gyration of the

compound pendulum about an axis passing

through the center of mass point. Here we have

used the parallel axes theorem which states that

the moment of inertia of the pendulum about the

point of suspension is equal to sum of the

moment of inertia of the pendulum about its

center of mass and m x2.

√

OR

θ

mg

Centre of mass

Point of suspension

x

θ

Point of suspension

x

xsin θ



Center of suspension

Center of suspension

Center of suspension Center of suspension

l

l

√( )

Putting ( )

, where l represents the

effective or equivalent length of a simple

pendulum which has the same time period as

that of the compound pendulum. Then

If we plot the graph of ( )

with time t

on vertical axis and position x on horizontal axis,

we will get the following graph. If we fix the

value of t, then it will represent a horizontal

straight line (dotted) on this graph.

If we solve the equation ( )

for

solutions,

And hence if x = x1 is a

solution to the above equation, obviously x2= (l-

x1) will also be a solution. Because the sum of

roots of a quadratic equation ax2+bx+c=0 with

roots α1 and α2 is (α1 + α2 = - b/a).

So,

Hence, on the horizontal straight line, there will

be four points with same time period of

oscillation t. These points form a set of

conjugate points. The first point from the left is

called the Center Of Suspension and its

corresponding conjugate point is the Center Of

Oscillation which is the third intersecting point

on the same line. Observe the two more set of

conjugate points on the same line. Distance

between the center of oscillation and center of

suspension of the compound pendulum is called

the Equivalent length of simple pendulum (l)

What is Center of suspension and center of

oscillation?

When a compound pendulum is

suspended freely at any arbitrary point (any

hole), it will be the Center Of Suspension.

If we consider a simple pendulum whose

bob has the same mass as that of the compound

pendulum with length (l)equivalent to the

effective length (as said above), it will have an

equal time period as that of the suspended

compound pendulum.

By putting x = k in ( )

, we

obtain k =l/2.

We can get two such k’s from the graph. Either

by taking their average or by taking the square

root of their product we can obtain the value of

radius of gyration of the compound pendulum

about an axis passing through its center of mass.

We can calculate the same by using the

theoretical formula,

L and B are respectively the length and breadth

of the compound pendulum. As the breadth is

comparatively small in comparison to its length,

k is approximately equal to

√ .

√(

)




PRINCIPLE: If we measure the time period of oscillation of the pendulum at various points of

suspension (holes) we can estimate the “g” and “k” from graphs.

3. What is the pendulum?

A metal bar of one meter long and about 5 cm in

width having holes drilled at every 5 cm of its

length.

4. How to measure T?

Use a stop clock to count the time taken for say

20 oscillations and hence find out the period.

The amplitude of oscillation must be less than

5°.

Graphs:

If we plot the graph of vs. , with on y – axis and on x – axis, it will give a straight

line with a slope of (

) and a y – intercept of (

). We can estimate the average ‘g’ value

from the slope of the graph by using,

And the value of the radius of gyration k can be obtained by using,

You may use the standard g value of 980 cm/s2 in the above expression to find the value of k.

1. Plot a graph with x – axis as point of suspension (1 division = 5cm) and y – axis as time period T

(1 division = 0.1 sec) of the oscillation. Take at least three horizontal lines in the valley region

with T = constant. Locate the points D, F, A and E as described in theory for each line. For each

line calculate (AD+FE)/2 and hence calculate the l/T2. Take the average of the l/T

2. Use this to

find out the g. Locate the minimas M and on the curve. Half the average distance M gives K,

radius of gyration.

2. Plot the graph of vs. , with on y – axis (1 division = 10cm.s2) and on x – axis

(1division = 200 cm2), it will give a straight line with a slope of (

) and a y – intercept

of (

). Estimate the average ‘g’ value from the slope of the graph.

REFERENCES:

1. Advanced practical physics for students, Worsnop and Flint, Methuen publications, p.67 – 71 2. Laboratory Physics, 3

rd Ed, J.H. Avery, A.W.K. Ingram, Heinemann publications, p.93

0

20

40

60

80

100

120

140

-3000 -2000 -1000 0 1000 2000 3000

√

(

) (

)



< 5° < 5°

Compound pendulum

Knife edge

G clamp holder

B

A

COMPOUND PENDULUM EXPERIMENT AIM:

1. To determine the acceleration due to gravity at the location of the laboratory.

2. To determine the radius of gyration about the center of gravity of compound pendulum.

APPARATUS:

Compound pendulum (CP) of about 1 meter long, knife edge suspension, stop watch,

telescope and meter scale.

PROCEDURE:

1. Notice the centre of mass “hole” on the

pendulum.

2. Suspend the pendulum through the hole

that is next to centre of mass hole, i.e. 5cm

away from C.O.M. On left hand side of

the pendulum. if you have any confusion

regarding the left and right hand sides,

make a mark on the pendulum with one

end as side A (left hand side) and the other

end as side B(right hand side)

3. Focus the telescope on the mark made at

the end of the pendulum.

4. Give a small displacement to the pendulum such that it si less than 50 with the vertical. Avoid

wobbling of the pendulum.

5. Count the time taken for, say 20, oscillations or more in two trials and tabulate them. Take their

average (t).

6. The time period of oscillation (T) can be obtained from (t/20).

7. Go to the next hole (10 cm away from C.O.M.) and repeat the above said process to obtain the

time period of oscillation (T). Count the time periods at all these points of suspensions until you

reach the end A.

8. Now come back to C.O.M. and suspend the pendulum in hole that is next to the C.O.M. but on

right hand side (i.e. towards side B).

9. Start counting the time for twenty oscillations as said above for each hole until you reach the

other end B. Tabulate the readings in the data sheet provided at the end of this book.

Precautions:

1. The pendulum must be oscillated only in the vertical plane with small amplitude and without

any wobbling.

2. The knife edge should be horizontal.


1. What is the basic difference between a

simple pendulum and a compound

pendulum?

Mass of pendulum is concentrated in the

bob in case of simple pendulum. But it is

uniformly distributed in the case of

compound pendulum.

2. What is moment of inertia for a body?

It is a rotational analogue of mass in linear

motion. It comes from the equivalence of

kinetic energy in both linear and rotational

motions. I = MK2

3. What is radius of gyration?

In the above formula M represents the

total mass of the body and K represents

the radius of gyration.

4. State parallel axes theorem.

5. State perpendicular axis theorem.

6. What is the maximum allowed angular

displacement for this pendulum?

5°

7. Define torque.

τ = Moment of inertia × angular

acceleration

8. A pendulum bar has length L and breadth

B. what is the moment of inertia of the

pendulum about an axis,



a) Parallel to and about one of its edge and

perpendicular to its length.

b) Parallel to and about one of its edge and

perpendicular to its breadth.

c) Perpendicular to its length and through

its centre of mass

d) Perpendicular to its breadth and through

its centre of mass

e) Perpendicular to both its length and

breadth, through its centre of mass

9. What is center of oscillation?

It is a significant point on the pendulum. If

we make a simple pendulum with a bob

whose mass is same as that of the entire

compound pendulum, it will have the same

time period when suspended by a mass

less thread of length exactly equal to the

distance of this center of oscillation from

the centre of mass of compound

pendulum. (Center of oscillation is totally

different from center of mass of

pendulum)

10. What is center of suspension?

It is the point where the pendulum is

suspended with the help of the axle.

11. What is equivalent length of simple

pendulum?

Refer center of oscillation

12. What is the nature of graph plotted

between T2x vs x

2.

Straight line.

13. For what value of position ‘x’ the time

period will be minimum?

When x = k.

14. For what value of position ‘x’ the time

period will be maximum?

Infinity at the center of mass.


WM1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

t

l

t

l

α A

B

C

y

xn

α

α α

i

r r+α

r+α

y

i

S Q

P

B

F

D

C

E

r

α r

WEDGE METHOD THEORY:

The set up is similar to Newton’s rings

experiment. The Plano-convex lens is replaced

with an air wedge formed by a pair of plane

glass plates.

The path difference between rays reflected at B

and transmitted from D can be calculated as

follows.

Due to reflection at C an extra phase of π

(path

) is added.

For dark line,

For nearly normal incidence, we can put r=0.

From the ∆ ABC,

y = xn tanα

Combining implies,

For air medium as thin film, µ =1

Or

Fringe width β (the distance between successive

dark fringes) is

As α is small, sin α can be replaced with tan α.

From the above triangle,

or,

Where, t = is thickness of the object (the

diameter of a hairline or thin wire).

Nature of fringes: The fringes formed here are

bright and dark straight edge fringes with equal

fringe spacing independent of the order. This is

in sharp contrast with the fringes obtained in

Newton’s rings where the diameter of fringe

depends on the order of fringe n.


PRINCIPLE: If we measure the fringe width β for dark fringes and the distance l experimentally we

can estimate the thickness of the object.

1. How to measure β?

By using a traveling microscope.

2. How to measure l ?

By using a scale.



3. How to set up the fringe pattern?

Take a pair of optically plane glass plates

(Clinical glass slides will serve good) make

triangular wedge (air gap) by inserting a piece of

paper or a thin wire. Use cellophane tape to hold

the glass slides together if necessary.

4. How to illuminate the wedge shaped air

film?

By using sodium vapor lamp and a plane glass

plate along with a retort stand (to reflect the

incident light on the wedge).

APPLICATIONS OF WEDGE METHOD:

1. To measure the thickness of thin objects like hairlines, wires, thin paper foils etc.

2. To check the optical flatness of a given transparent dielectric slab

WEDGE METHOD EXPERIMENT Aim:

To determine the thickness of the given hairline or paper by forming interference fringes due to

wedge shaped air film.

Apparatus: Sodium Vapour lamp, traveling microscope, reading lens, optically plane glass plates (clinical

slides), plane glass plates, retort stand.

Formula:

Where

t = thickness of the hairline or paper (object placed between glass plates to form the wedge).

= Fringe width, the gap between successive dark fringes

λ = Wavelength of the source used = 5893 Å

l = Distance between point of contact of glass slabs, forming the air wedge, to the point where

the thin wire or paper is placed.

Procedure:

1. Take a piece of paper (paper should not be completely white, it must contain some markings or

rulings so that they can be observed in the field of view) and place it below the microscope on

the platform of the travelling microscope (TM). Adjust the rack and pinion and focus the

microscope. (markings on the paper should be very clear)

2. Take the wedge formed by the pair of optically plane glass plates and clean the surface with

cloth (handle it with care). Observe the position of the thin wire and make sure that it is near the

edge of the wedge. Measure the distance between the point where you have placed the thin

wire from the other end of the wedge and note it as l.

3. Place this wedge on a plane glass plate. Place the black paper below the plane glass plate.

4. Keep this set up on the platform of the TM. Make sure that glass plate does not come on the

track of the moving base of microscope.

5. Use a retort stand to hold another plane glass plate at 45° with vertical. Place the glass plate in

between the microscope and the wedge setup.

6. Observe through the microscope and tilt the clamp of retort stand to get maximum yellow light.

This ensures normal incidence of light on the wedge shaped air film. If you are using a vernier

type TM, then leave the steps 7 and 8, directly go to 9.

7. Lock the base screw of the TM for horizontal motion and turn the screw gauge dial to coincide

the reference line of main scale with any one division on the main scale.

8. Release the base screw and adjust the screw gauge dial such that the “0” of it coincides with its

reference line. Then once again lock the base screw and never release it again throughout the

experiment. This calibrates your TM.

9. Coincide the vertical cross wire with any one of the dark fringe. Assume that the fringe is of nth

order.



10. Move the traveling microscope (either left or right but only in one direction) by carefully

counting the dark rings only. Coincide the cross wire with the fifth fringe after your nth

fringe,

i.e. (n+5)th

fringe. Note down the reading of TM.

11. Now go to the next fifth, i.e. (n+10) and repeat the process at least up to (n+35)th

fringe and

tabulate the readings.

12. The difference of successive readings of microscope gives five times the fringe width (5β). T.R. Total Reading = MSR + [V.C. X L.C.]

Least count =

Or

(For screw gauge dial type microscope)

Least count =

Precautions:

1. The wedge should not be disturbed from the initial position while taking the readings at

various positions.

2. Readings of the Vernier must be noted without parallax error.


1. What happens to fringe pattern as we

move the wire (or paper) so as to

increase the angle of the wedge? If the wedge angle increases, the fringe

width decreases. Hence the fringe pattern

will shrink. If we move wire to other side

(decreasing the wedge angle) the fringe

pattern expands due to increase in fringe

width.

2. What happens to the fringe pattern if we

replace the sodium vapour lamp with a

monochromatic red source? As β is proportional to wavelength λ, red

has more wavelength than yellow, the

fringe width increases.

3. What happens to the fringe pattern if

increase the refractive index of the glass

plates forming the wedge? No changes. Interference is taking place in

the air film (wedge) and not in the glass

plates, so pattern does not change, of

course the intensity of the fringes may

change due to changes in the glass plate.

4. What is Normal incidence?

If the light rays fall on a surface

perpendicularly (normally) we say that it is

normal incidence. The angle of incidence

as well as angle of refraction will be zero in

this case.

REFERENCES:

1. Optics, 4 ed. Eugene Hecht, Addison Wesley publications p.404-407

APPENDIX ENGINEERING PHYSICS LABORATORY

G.V.P. COLLEGE OF ENGINEERING FOR WOMEN APP 1

BREAD BOARD: The figure shows sets of five holed boxes. Each hole in a five hole box has METAL CONTACT with the remaining four holes in that

box.

HORIZONTAL BUSES:

The series of holes on the top and bottom parts of the bread board are called horizontal buses. For indexing purpose they were named as A, B, C, D, E, F, G

and H in the figure. IN PRACTICAL BREAD BOARD YOU WILL NOT FIND ANY SUCH NAMING.

A bus: The five hole pairs are joined to each other by a metal strip on the back side of bread board. If you insert a battery positive lead in any of the holes in A

bus, the other holes will also have the same potential. Similarly the buses B, C, D, E, F, G and H also have the same hole connections. The above said eight

horizontal buses are independent of each other, i.e. A and B do not have any connection, similarly A and E ; B and F etc, are not connected.

USUALLY THE A BUS IS RESERVED FOR POSITIVE OF THE D.C. SUPPLY. SIMILARLY C BUS IS RESERVED FOR GROUND (NEGATIVE OF

D.C. SUPPLY)

A

B

A

B

C C

D D

E

F

E

F

G

H H

G

1 2 3 4 5 6 7…………………………………………………………………………………………………………………………………………………………………….56 57 58 59 60

……………………………………………………………………….

61 62 63 64 65 66 67………………………………………………………………………………………………………………………………………………………………………………. 120

……………………………………………………………………….

VER

TIC

AL

BU

SES V

ERTIC

AL B

USES



BATTERY/

D.C.

SOURCE

VARIABLE

VOLTAGE

D.C. SOURCE GROUND ZERO POTENTIAL

LIGHT EMITTING

DIODE (LED)

INDUCTOR

RHEOSTAT

Temperature

Sensitive Resistor

VERTICAL BUSES:

The five holed buses numbered as 1, 2,…29,30…58,59,60,….120 in the fig. are called VERTICAL

BUSES. There is a metal strip on the back side of five holes in each vertical bus. Hence there is no

connection between 1 and 2 buses. This is same for all other vertical buses. Hence if we insert any

component lead in a vertical bus, the remaining four holes will come in contact with the component.

There are two rows of such vertical buses in the middle of the bread board in between the horizontal

buses. Vertical buses are used for inserting the components like resistors, capacitors and IC’s.

A bus is reserved for +ve of the power supply. C bus is reserved for -ve of the power supply,

this is also known as ground bus. If the circuit is complex and has many more power

supplies, say, a circuit may run with 18 V, 12 V and 9V power supplies with common ground

(-ve), we can use the B, E, F, D, G, H buses for those power points. Sometimes many

connections are made with a single power point. In that case we can join the A and E buses

with a (jumper) wire to use the entire top line as power bus +VCC. Similarly we can join C

and G buses for having a long ground bus. If the circuit is much more complex, then we join

two or more bread boards together to provide more space for the extra components. But the

rule of making a circuit is that its layout must be very clear and understandable to any other

person and at the same time it should use minimum space on the

bread board. COMPONENTS AND THEIR CIRCUIT SYMBOLS:

ZENER

DIODE

CAPACITOR (NON-ELECTROLYTIC)

NO POLARITY,

CAN BE USED

IN BOTH WAYS

CAPACITOR (ELECTROLYTIC)

HAS POLARITY

AMMETER

A +

_

_ +

MICRO AND MILLI -

AMMETERS

µA mA + + _ _

GALVANOMETER

G

PN JUNCTION DIODE

RESISTOR

(FIXED RESISTANCE)

POTENTIOMETER

(VARIABLE

RESISTANCE)



i1

i2

i3

B

D

10V

C

i

A

KIRCHHOFF’S LAWS (KCL AND KVL):

1. CURRENT RULE OR JUNCTION RULE (KCL): The

algebraic sum of all currents meeting at any junction (node) of a

circuit is zero. The convention of current direction is that the

current is positive if it moves towards the given node or junction

and it will be negative, if it moves away from the junction. Here i1

is positive as the current is approaching the node and the other

currents i2, i3 are negative as they move away from the node.

2. VOLTAGE RULE OR LOOP RULE (KVL): The algebraic sum

of the voltage drops in any closed loop of the given

circuit is zero. It means, VAD+VBA+VCB+VDC = 0.

VAD means the potential at point A with respect to the

point D. So, VAD= +10. Similarly VDA= –10.

Convention: Assume an arbitrary direction in the given

loop, i.e. say ABCD. If you are travelling from A to

B, the potential drop will be VAB, equal to – VD, the

voltage drop across the diode in forward bias. This is

because the voltage at B is less than the voltage at A by a value equal to the forward cut – in

voltage of the diode (VD). Similarly from B to C, VBC=+ i RL (by using Ohm’s law). If you are

travelling from C to B, then it will be – i RL. Similarly, VCD= +VC, the voltage across the

capacitor. If the capacitor is charged, then the positive plate will be at high potential than the

negative plate by the value of applied voltage. Hence, the equation will be, +10 – VD – i RL+VC =

0. If we travel from D to A along DCBA path, then the equation will be, –VC + i RL+ VD –10 = 0.

Hence both equations are one and the same.

COLOUR CODES FOR CARBON RESISTORS



REFERENCE BOOKS:

1. ELECTRONIC DEVICES 9th

Ed; Thomas L. Floyd; Unit -2, Diodes and applications; Prentice

Hall publications. 2. ELECTRONIC DEVICES AND CIRCUITS; Jacob millman and Christos Halkias. Mc. Graw-

hill publications.

BROWN 1

BLACK 0

RED 2

Error: Gold ± 5%

Black - 0 Brown - 1 Red - 2 Orange - 3 Yellow - 4 Green - 5 Blue - 6 Violet - 7 Grey - 8 White - 9

Tolerance: (Error in the mentioned value of resistance) No colour : ± 20% Gold colour : ± 5% Silver colour : ± 10%

The first two colour bands represent the first two digits

Third colour band indicates the number of ZEROs.

Resistance of above resistor will be 10 with two zeros, i.e. 1000 Ω. Gold band indicates 5% error. i.e. ± 50Ω. Resistance will be (1000±50) Ω. If you measure the resistance you will find it lying between 950Ω and 1050Ω

B B R O Y of Great Britain has Very Good Wife



LEAST SQUARE FIT (FITTING THE DATA TO A STRAIGHT LINE)

To fit the given data to a straight line the following process is to be adopted.

Define a parameter called Residue

∑

The standard deviation S of the data point (xi, yi) from its average value ( , ) will be

∑

To minimize the deviation with respect to the constants m and c to have a best fit,

After solving the equations we get

∑ ∑ ∑

and

∑ ∑ ∑

After solving for m and c gives

And

Where, refers to the average values of all xi and yi respectively.

If the given function is a polynomial of the form y = xm

, then use natural logarithm to transform it in

to a linear equation containing logarithmic variables and proceed in the same manner as described

above.

θ error in θ

tan (θ) tan

(θ+0.5) tan

(θ- 0.5) % error in

tan θ

10 ±0.5 0.176327 0.185339 0.167343 5.103143

15 ±0.5 0.267949 0.277325 0.258618 3.490766

20 ±0.5 0.36397 0.373885 0.354119 2.715347

25 ±0.5 0.466308 0.476976 0.455726 2.278461

30 ±0.5 0.57735 0.589045 0.565773 2.015435

35 ±0.5 0.700208 0.713293 0.687281 1.857457

40 ±0.5 0.8391 0.854081 0.824336 1.772394

45 ±0.5 1 1.017607 0.982697 1.745506

50 ±0.5 1.191754 1.213097 1.17085 1.77249

55 ±0.5 1.428148 1.455009 1.401948 1.857676

60 ±0.5 1.732051 1.767494 1.697663 2.015844

65 ±0.5 2.144507 2.1943 2.096544 2.279222

70 ±0.5 2.747477 2.823913 2.674621 2.716881

75 ±0.5 3.732051 3.866713 3.605884 3.494454

80 ±0.5 5.671282 5.975764 5.395517 5.115662

∑

∑



SPECTROMETER

ADJUSTMENTS AND DESCRIPTION:

The Spectrometer mainly consists of

1. Telescope

2. Collimator

3. Prism table

SPECTROMETER

TELESCOPE:

The telescope is turned towards a distant object like a tree and the rack and pinion is adjusted until

the inverted image of it is seen very clear. This ensures that the light coming from infinity alone is

seen by the observer. Hence plane waves are received at the point of observation. After this the rack

and pinion of telescope should not be disturbed.

COLLIMATOR:

It consists of two hollow tubes which exactly fit into one another and can be moved in and out by

rock and pinion screw. The outer end of the hollow tube is fitted with an adjustable slit and inner end

with a convergent lens.

The slit is illuminated by a poly chromatic source like mercury vapour lamp. The adjustable

slit acts as the object.

After adjusting the telescope for distant focus, it is turned towards the slit of collimator and is

viewed through the telescope. In general the edges of slit are seen blurred with a diffused

background of light source. The rack and pinion of collimator is adjusted until the edges of slit are

seen very sharp. This is due to the fact that when we adjust the rack and pinion we bring the

rectangular slit in the focal plane (at the focus) of the convergent lens (at the end opposite to the slit

on the collimator). An object placed at the focus of the lens will form its image at infinity. I.e. the

waves coming out of the collimator travel towards infinity as PLANE WAVES. The slit is adjusted

as narrow as possible by adjusting the screw attached to the slit.

PRISM TABLE:

There are three leveling screws on the reverse side of the prism table. If the prism table has parallel

line markings, then place the spirit level parallel to the markings and by adjusting the two screws



which are parallel to the axis of the sprit level bring the bubble in the middle. Then turn the sprit

level and make it perpendicular to the lines. By adjusting the third (left over) screw; bring the bubble

in the middle. This makes the prism table flat.

After the adjustments to telescope, collimator and slit, the telescope is focused on the slit and the

vertical cross wire is coincided with the slit. Telescope is kept in locked position. Prism table is

released and the verniers are adjusted to read 0- 180o and 0 – 0

o. Then the prism table is locked

and telescope screw is released.

EXPT. No……. COMPOUND PENDULUM ROLL No: Date: DATA SHEET

ENGINEERING PHYSICS LABORATORY - G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

TABULAR FORM FOR THE DETERMINATION OF TIME PERIOD (T)

DETERMINATION OF L/T2:

Sl.No.

Distance of point of

suspension from centre of

mass(X)

X2

ON LEFT HAND SIDE OF C.O.M. (side A)

Perio

d (T

) (I

n Se

c)

T2. X Of

Side A

ON RIGHT HAND SIDE OF C.O.M. (side B) Period (T)

(In Sec)

T2. X Of

Side B Time for 20 oscillations Time for 20 oscillations

Trial I Trial II Mean Trial I Trial II Mean 1 0 cm (C.O.M.) Theoretically Infinity Theoretically Infinity

2 5 cm

3 10 cm

4 15 cm

5 20 cm

6 25 cm

7 30 cm

8 35 cm

9 40 cm

10 45 cm

Sl.No AC

BD

Length of the equivalent simple pendulum L= (DA+FE)/2

T sec T2

Avg.

1

2

3

EXPT. No……. TORSIONAL PENDULUM ROLL No: DATE: DATA SHEET

ENGINEERING PHYSICS LABORATORY - G.V.P.C.E.WOMEN

Time period of the oscillations

S. No.

Length of the wire ‘L’ (cm)

Time ‘t’ for 20 oscillations (sec) T = t/20

(sec) T2 L/T2

cm/sec2 Trail 1 Trail 2 Mean(t)

1

2

3

Avg. L/T2= cm/s2

Radius (R) of the Disk using Vernier Calipers

S. No MSR (cm) VC LC (cm) Total= (MSR+VC x LC) cm

1

0.01

2

3 Avg. diameter = cm Avg. radius (R)= cm Radius of the wire using Screw gauge Least count of the Screw gauge = ………….. Zero error = …………… Correction = ………..

S. No PSR mm HSR CHSR PSR +CHSR x LC) mm

1

2

3

Average diameter= mm Average radius (a) = cm

RESULT: Rigidity Modulus η of the material of the wire determined as 1) From table = …………………………. dyne/cm2 2) From graph = ………………..……….dyne/cm2

EXPT. No……. MELDE’S EXPERIMENT ROLL No: DATE: DATA SHEET


LONGITUDINAL MODE: Mass of empty pan (mp) =

S.No Mass (m) added to pan (gm)

Tension T (m+mp)g

(dyne)

Number of loops

Total length of vibrating string

CM

Length of each loop

(l) CM

1

2

3

4

5

6

Average (Longitudinal mode) =

TRANSVERSE MODE: Mass of empty pan (mp) =

S.No Mass (m) added to pan (gm)

Tension T (m+mp)g

(dyne)

Number of loops

Total length of vibrating string

Length of each loop

(l)

1

2

3

4

5

6

Average (Transverse mode) =

RESULT: The frequency of vibration of the tuning fork is found to be

From table

Longitudinal mode :

Transverse mode :

From graph Longitudinal mode :

Transverse mode :

EXPT. No……. WEDGE METHOD ROLL No: DATE: DATA SHEET


TABULAR FORM FOR MEASUREMENT OF FRINGE WIDTH β:

S.No.

Order of fringe

T.M. Readings 5β

(Difference between successive T.R.)

M.S.R. V.C. T.R.cm

1 n

2 n+5

3 n+10

4 n+15

5 n+20

6 n+25

7 n+30

8 n+35

9 n+40

Average5β = Calculations: Length of the wedge l = cm RESULT:

The thickness of given object is found to be ………….

EXPT. No……. NEWTON’S RINGS ROLL No: DATE: DATA SHEET


From graph of Dn2 vs. n: Slope = Radius of Curvature of lens:

From table

RESULT: The radius of curvature of the lens is found to be From graph From table : ………….

S.No Order of ring

( xi )

T.M. Readings (Left side)

T.M. Readings (Right side)

Diameter of ring

Squared diameter

M.S.R V.C Total (L) M.S.R V.C Total

(R) Di

(L ~ R) Di

2

( yi )

1

2

3

4

5

6

7

8

9

10

EXPT. No……. NEWTON’S RINGS ROLL No: DATE: DATA SHEET


DETERMINATION OF ANGLE OF DIFFRACTION (Θ):

Spec

tral l

ine Readings of the spectrometer with telescope on Difference of

two readings (2Θ) Θ

Å

Left hand side spectrum Right hand side spectrum

V1 V2 V1 V2 V1~ V1

(2Θ1)

V2~ V2

(2Θ2) MSR VC Total MSR VC Total MSR VC Total MSR VC Total

Result: The wavelengths of following spectral lines are found to be


G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

REGD. NO:……………………………… Expt. No…………… Date: ……………….. BAND GAP OF EXTRINSIC SEMI CONDUCTOR USING PN JUNCTION DIODE Observations and Calculations: Temperature In 0 C (TC)

T (Kelvin) = TC+273

Current (I) ( ×10 -6A)

= ln(I)= ( )2

Total number of observations of made N =

= =



REGD. NO:……………………………… Expt. No…………… Date: ………………..

THERMISTOR CHARACTERISTICS Observations and Calculations: Temperature

in 0 C Resistance

in Ω Temperature

in K Xi=

1/T (K-1) Yi= ln R

Average =

Average

A =

From graphs:




ZENER DIODE V – I CHARACTERISTICS

FORWARD BIAS Current limiting resistor RS=

REVERSE BIAS Current limiting resistor RS=

S.No Voltage across diode (in volt)

Current through the diode (mA)



FROM GRAPH: FORWARD BIAS CHARACTERISTICS: CUT – IN VOLTAGE (Vγ) : SLOPE OF V – I GRAPH IN FORWARD

BIAS FORWARD DYNAMIC RESISTANCE

Make of diode may be

REVERSE BIAS CHARACTERISTICS: BREAK – DOWN VOLTAGE OR ZENER VOLTAGE (VZ): SLOPE OF V – I GRAPH IN BREAK –

DOWN REGION ZENER RESISTANCE IN BREAK – DOWN

REGION




PN JUNCTION DIODE V – I CHARACTERISTICS

FORWARD BIAS Current limiting resistor RS=

REVERSE BIAS Current limiting resistor RS=




Current through the diode (µA)

FROM GRAPH: FORWARD BIAS CHARACTERISTICS: CUT – IN VOLTAGE (Vγ) : Make of diode may be SLOPE OF V – I GRAPH IN FORWARD

BIAS FORWARD DYNAMIC RESISTANCE

REVERSE BIAS CHARACTERISTICS: SLOPE OF V – I GRAPH IN REVERSE

BIAS IS JUNCTION DIODE RESISTANCE IN REVERSE BIAS IS



REGD. NO:…………… Expt. No…………… Date: ……………….. Observations: Current through the coil i = ……….. Ampere Horizontal component of earth’s field H = 0.38 Oersted Circumference of the coil = radius (a) =

S.No Distance

x

Deflection magnetometer readings

Θ = tan θ

Bexp=

H tan θ BTh East West

Θ1 Θ2 Θ3 Θ4 ΘE Tan θE Θ5 Θ6 Θ7 Θ8 Θw Tan θW