phys 102 general physics ii labbook - koç...

PHYS 102

General Physics II Labbook generalphysics.ku.edu.tr

Electromagnetics (E&M) Spring 2020

KOÇ UNIVERSITY PHYSICS DEPARTMENT

ISTANBUL - TURKEY

www.ku.edu.tr

Name of the Student : ……………………………...............................................

ID Number : ………...………................................................................

Signature : …………………………...................................................

Department : ...........................................................................................

Name of the Laboratory Instructor : …………………………………………..........................

Name of the Laboratory Session : …….………………………………………….................

Date/Time of the Laboratory Session :………………………………………………...................

2

Contents Lab Rules, Regulations and Procedures ...................................................................................................... 4

Basic Measurements and Ohm’s Law .......................................................................................................... 6

Electric Field Lines ........................................................................................................................................ 13

Kirchhoff’s Laws and Wheatstone Bridge ................................................................................................. 20

Charging and Discharging of a Capacitor ................................................................................................. 28

Lorentz Force ............................................................................................................................................... 35

RC and RL Circuits ..................................................................................................................................... 42

Transformers and Rectifiers ....................................................................................................................... 50

Appendices .................................................................................................................................................... 59

4

Attendance

Attendance to all laboratory sessions is compulsory. Makeup laboratory sessions are eligible only by a

medical excuse approved by Koc University, dated at most one day later then the missed laboratory session’s

date.

Before The Laboratory-Session

IMPORTANT! Make sure that your own copy of the labbook and a scientific calculator is present

when you attend the laboratory session. Students without their own labbook are not allowed to

participate in the lab-session.

The experiment has to be studied from the labbook thoroughly before the lab-session. The

introduction and theory sections are essential to understand the objectives of the experiment and its

theoretical background. Consulting to external references is strongly recommended.

Reading the experimental procedure is extremely important to familiarize yourself beforehand with

the setup, equipment and measurement techniques to conduct an efficient laboratory session.

During The Laboratory Session

Follow the announcements of the laboratory Instructor at all times.

The laboratory session starts as scheduled. There is a grace period of 15 minutes after which admitting

the session is not allowed.

The total duration of the laboratory session is 165 minutes which includes the following sub sessions:

o Setting up the experiment

o Performing the experiment and recording data to the databook

o Processing and analyzing the data, plotting graphics

Answering the questions in the labbook for the current experiment.

o Preparing an experiment report as follows:

Experiment report must be hand written in the indicated space of the labbook and

handed to the lab TAs at the end of the laboratory session.

Make sure to fill in the following data in the data-book: Semester, Course, Title of

the experiment, Date, ID number, name of the labbook owner, name of the lab-

session partner, laboratory section.

Time extensions are not given unless an exceptional case acknowledged by the lab-instructor (e.g.

power outage, malfunctioning equipment) is present.

Finishing The Laboratory Session

All labbooks must be checked and approved by the laboratory instructor at the end of the lab session.

Leaving the laboratory without the instructor’s check will render your lab session void.

PHYS 102 /

Introduction

Lab Rules, Regulations and Procedures

5

The experiment setup must be disassembled, cleaned up and all the electrical and electronic

equipment including the computers must be turned off properly. Each setup will be inspected and

approved by the instructor. Ignoring these steps will result in a significant penalty to the lab grade.

Taking equipment out of the laboratory is prohibited and may result in disciplinary action and

prosecution.

Physics Laboratory Safety Rules

Koç University emergency dial 1122.

1. Physics Laboratory equipment include metal, plastic, wood, glass hardware, rotating/moving

machinery, electrical, electronic devices. If not properly used, the equipment may cause an accident,

fire, explosion, resulting in injuries ranging from minor to lethal.

2. Always wear appropriate clothing during the laboratory session. Hair, clothing parts or jewelry may

get caught in the equipment, causing mechanical or electrical injury.

3. Eating, drinking or smoking in the laboratory is prohibited.

4. Follow the instructor’s announcements at all times.

5. If instructed, wear protective equipment (gloves, googles) during the experiment. Protective

equipment will be supplied in the laboratory.

6. Inspect the equipment carefully before setup against broken, malfunctioning parts. If there is any

problem, inform the lab instructor immediately.

7. Any electrical device must be used in the following sequence:

a. BEFORE PLUG IN:

i. Inspect the outlet cable and its ends against wear and tear.

ii. Make sure the device is not connected to anything else.

iii. Make sure the main switch of the device is at “OFF” position.

b. BEFORE TURN ON: Make sure that output/adjustment knobs of the device are all at off or

minimum position.

c. Turn on the device and check that it operates properly.

d. Turn off and make the necessary connections to the device in the setup.

e. Turn on and use the device.

f. Set all the output/adjustment knobs of the device to off or minimum position.

g. Turn off the device.

h. Disconnect from the setup.

i. Unplug the device.

6

Introduction

In this experiment, you are going to learn how to use voltmeter, amperemeter (ammeter), ohmmeter

and to test the validity of Ohm’s Law.

Equipment needed

- PC and Universal Interface

- Circuit Experiment Board

- Resistors (1k, 100)

- Digital Multimeter (DMM)

-----------------------------------------------------------------------------------------------------------------------

Important note !

-----------------------------------------------------------------------------------------------------------------------

The voltages used in this experiment are not dangerous to you, but are potentially damaging to the

equipment and the electronic components. Please read and follow the warnings given below, work very

carefully, observe correct polarities when connecting equipment, avoid short circuits, and always have

an instructor check your circuit before energizing. If you do not understand something or are not sure

exactly what you are doing, then consult your instructor. You will be held financially responsible for

any damaged equipment!

-----------------------------------------------------------------------------------------------------------------------

Basic Measurements The most commonly used equipment in the electric laboratories are ampere meters, voltmeters, and

ohmmeters. These devices are combined into one instrument called a multimeter or AVOmeter

(ampere-volt-ohm meter). Thus, we need some information about their principles and method of

usage.

Ampere meter is used to measure the current flowing through a conductor. To measure the

current we have to connect the ampere meter in series, thus its internal resistance causes to

increase the total resistance of the circuit. Therefore, a good ampere meter should have a very

low internal resistance, ideally zero. A device which has such a low internal resistance can be

easily damaged if it is subjected to a potential difference directly. Even a very small potential

difference will lead to a high current flowing through the ampere meter which can damage the

device.

PHYS 102 /

Experiment 1

Basic Measurements and Ohm’s Law

a) b)

Figure 1. a) True connection for current measurement b) True connection for potential

measurement ,

7

Voltmeter is used for measuring the potential difference between the two points in any circuit. It is

connected to the circuit in parallel. The internal resistance of a voltmeter should be very high, ideally

infinite, so that no current can flow through it when it is connected to the circuit.

To make measurement, first we set the device in its largest unit, and then make a measurement. If

the change on the scale is too small to realize, we decrease the unit one by one until the change is

readable. If it is still unreadable in the smallest unit of the device, we say that the magnitude of the

measured unit is out of range of this device.

Ohmmeter is used to directly measure the resistance of a resistor. This equipment is based on the

Ohm’s Law. No external power source is needed for measuring the resistance.

1. LCD Display

2. Data Hold Button

3. Transistor Jack

4. COM Input Terminal

5. Other Input Terminals

6. mA Input Terminal

7. 20A/10A Input Terminal

8. Capacitance Jack

9. Rotary Switch

10. Power

Figure 2. Structure of digital multimeter

Theory for Ohm’s Law

Ohm’s Law is a very useful relationship in circuit theory which relates the potential difference, V

across a device to the current, I through the device and the resistance, R of the device. Ohm’s Law

states simply that;

𝑉 = 𝐼𝑅 (1)

This relationship is true for many devices (such as resistors) but is not true for many others

(capacitors, diodes, transistors, etc.). If the device obeys Ohm’s Law, it is chategorized as “ohmic”;

and if it does not, it is said to be “non-ohmic”

Experimental procedure

In this experiment, you will measure the voltage versus current across a 100 resistor to see if it

obeys Ohm’s Law.

1. Place the resistor on the breadboard between two junctions.

8

The breadboard as shown in the Figure 2.4, consists of small junctions into which wires and

components can be connected. It also has a – and + row for connection to external power source.

Connect the positive lead of the Signal Generator to one lead of the resistor. At the other lead,

connect the positive lead of the DMM set up to measure the current through the resistor. Be sure to

use the correct jacks for a current measurement on the DMM. The DMM should be on the 200 mA

range. The negative lead of the DMM should be connected to the other lead of the resistor to

complete the circuit. Connect the leads of the voltage probe to measure the voltage across the

resistor, using the Digits-Displays function of the software. You are now ready to take data.

Figure 3. The Breadboard

2. Set the Signal Generator to 0 V DC and turn it on. You should have nearly 0 V and 0 mA. Increase

the voltage in 1 V steps and record the voltage and current at each step. Proceed to 8 V across the

resistor. When finished, return the voltage to zero and turn OFF the Signal Generator. Record the

voltage-current values in Table 1.

3. Disconnect the voltage supply and the voltage probe from the resistor. Remove the DMM from

the circuit and set it up as an ohmmeter. Be sure to use the correct jacks for the leads. Short the two

leads together and verify that it reads zero resistance.

1. Directly measure and record the resistance of your 100 resistor and record the value in Table1.

2. Repeat the procedure for 1 k resistor and record the values in Table 2.

9

TABLE 1. (10 PTS) VOLTAGE-CURRENT AND RESISTANCE VALUES FOR 100 OHM

RESISTOR

Voltage(V) 1 2 3 4 5 6 7 8

Current

𝑅1 =____________

TABLE 2. (10 PTS) VOLTAGE-CURRENT AND RESISTANCE VALUES FOR 1000 OHM

RESISTOR

Voltage(V) 1 2 3 4 5 6 7 8

Current

𝑅2 =____________

Report

1. (20 pts) Plot a graph of V versus I for the 100 resistor.

2. (5 pts) Find the slope which gives the resistance of the resistor.

3. (10 pts) Compare it with your directly measured value.

4. (20 pts) Plot a graph of V versus I for the 1 k resistor,

5. (5 pts) Find the slope which gives the resistance of the resistor.

10

6. (5 pts) Compare it with your directly measured value.

7. (5 pts) Is the resistor an ohmic component? Explain.

Conclusion (10 pts)

(Summarize what you have learned from the experiment in a few sentences and discuss the main errors you

encountered and possible measurement improvements.)

11

Completed by:

Name, Surname and ID of Lab partner(s):

Department of Lab partner(s):

Verified by:

12

Completed by:



Verified by:

13

Introduction The aim of this experiment is to investigate the electric field lines for a uniform electric field and

equipotential surfaces surrounding a two dimensional charged conductor.

Two point charges, one point charge and a parallel plate, two parallel plates and concentric placed two

rings will be used as the charged conductors.

Equipment Semi conductive paper

Silver conductive ink pen

Corkboard working surface

Metal push pins

Power supply

Connecting leads

Multimeter

Pen and paper

Theory Physical quantities are classified in two main groups; scalar and vectorial. Vectorial quantities such as

the electric field are completely specified by both magnitude and direction and scalar quantities

completely specified by a number. The electric field caused by a charge distribution can be found by

placing a test charge at that point and measuring the force acting on that test charge. (F=qE, where F is

the force, q is the test charge and E is the electric field.)

The electric field lines for a positive point charge and a negative point charge is shown in Figure

1. Electric field lines can be visualized by drawing lines pointing in the same direction as the electric

field vector at any point. At each point on these lines the electric field vector is tangent to the electric

field line. The strength of the electric field depends on the number of lines per unit area through a

surface perpendicular to the lines in that region.

Thus the magnitude of the electric field, E is large when the field lines are close together and small

when they are apart.

The lines begin on positive charges and terminate at negative charges or at infinity. The electric

field in either case becomes more intense near the charge since the lines are close to each other.

Figure 1. The electric field lines are radially outward for a positive point charge and radially inward

for a negative point charge.

PHYS 102 /

Experiment 2

Electric Field Lines

14

Electric Potential Electric potential is a scalar function of position therefore electrostatic phenomena can be described

in a simpler way-instead of dealing with the components of a vectorial quantity, one deals with only

the magnitude. The concept of electric field has a practical value when one needs to measure the

voltage between any two points in an electrical circuit. The potential difference between two points is

directly related to the work done against the electric force in order to push a test charge from one point

to the other.

A set of points of which the potential has the same value is called an equipotential surface. Fig.

2(a) shows electric field lines (solid lines) and equipotential lines (broken lines) for a very large sheet

with a uniform charge distribution. The equipotential surfaces are parallel planes. Fig. 2(b) shows electric

field lines (solid lines) and equipotential lines (broken lines) for a positive point charge. The

equipotential surfaces are concentric spheres.

- - - - - - - - - -

E

E

+ + + + + + +

(a) (b)

Figure 2. Electric field and equipotential lines a)for a sheet charge distribution, b) for a positive

point charge.

Gauss’ Law

Gauss’ law shows a relationship between a net charge within a volume and the electric flux through the

closed surface of this volume. The electric flux through the surface is defined as the product of the area

by the magnitude of the normal component of the electric field.

Gauss’ law represents the total electric field due to the charges inside the Gauss surfaces. It

states that the net electric flux through any closed Gauss surface is proportional to the net charge inside

this surface, 0

insideQSdE

, where 0 is the dielectric permittivity of vacuum. Net charge is the

sum of negative and positive charges within the closed surface.

A good electrical conductor such as silver, copper, aluminum contains free electrons. These

electrons can move without restraint within the volume of the metal. If such a conductor immersed in

an electric field, the free electrons move in a direction opposite to the direction of the electric field and

they continue moving until they reach the surface of the metal. When there is no net motion of charge

within the conductor, the conductor is said to be in electrostatic equilibrium. A conductor in electrostatic

equilibrium has the following properties.

1. The electric field is zero anywhere inside the conductor.

2. All the extra electric charge resides on the surface of the conductor.

3. The electric field at the surface of a conductor is normal to the surface.

4. If the conductor is irregularly shaped, charge tends to accumulate at sharp points. Since they want

to repel each other far away as far as possible.

+

15

Experimental Set up

Sketching the Electrodes

1. Draw the electrodes on the black paper. Please note that the silver conductive ink reaches its maximum

conductivity after at least 10 minutes of drying time.

Follow these steps carefully:

2. Place the grid conductive paper printed side up, on a smooth hard surface. Do not attempt to draw the

electrodes while the paper is on the corkboard.

3. Vigorously shake the conductive ink pen (with the cap on) for 10-20 seconds to disperse any particle matter

suspended in the ink.

c) Remove the cap. On a piece of scrap paper, press lightly down on the spring-loaded tip while squeezing

the pen barrel firmly. This starts the ink flowing. Slowly drawing the pen across the paper produces a solid

line. Drawing speed and exerted pressure determines the path width.

d) Once a satisfactory line is produced on the scrap paper, draw the electrodes on the grid of the black

conductive paper. If the line becomes thin or spotty, draw over it again. A solid line is essential for good

measurements.

e) Place the plastic template on the conductive paper and draw the circles with the conductive ink pen.

3. Mount the conductive paper on the corkboard using one of the metal push pins in each corner.

Connecting the Electrodes to a Power Supply and Checking their Potential

1. Using the supplied connecting wires, connect the electrodes to the DC power supply.

Figure 3. Experimental set up

2. Place the terminal of a connecting wire over the electrode, then stick a metal push pin through its terminal

and the electrode into the corkboard. Make certain the pin holds the terminal firmly to the electrode as in

below figure.

Figure 4. Electrode with connecting wire

16

NOTE: Check to see that the terminal which touches the electrode is clean. A dirty path may result in a bad

contact.

3. Connect the other end of the wire to the power supply.

4. To check the electrodes for proper conductivity, connect one voltmeter lead near the push pin on an

electrode. Touch the voltmeter’s second lead to other points on the same electrode. If the electrode has been

properly drawn, the maximum potential between any two points on the same electrode will not exceed 1% of

the potential applied between the two electrodes. If not, remove the paper from the corkboard and draw over

the electrodes a second time with the conductive ink.

Procedure

1. Mount the semi conductive paper on the corckboard using a metal push pin in each corner.

2. Stick one metal puch pin onto each electrode.

3. Make sure the puch pin completely pierces the paper through the electrode and is held

firmly on the corcboard.

4. Use connecting leads and alligator clips to connect the positive and negative terminals on

a power supply to the push pins in the electrodes, positive to one electrode and negative to

the other.

5. Use connecting leads and alligator clips to connect the positive and negative terminals on

a voltmeter. Then connect the voltmeter’s ground terminal (black lead) to the negative

electrode.

6. Use a pointy end lead on the other voltmeter terminal to use it as aprobe.

7. Turn the power supply and adjust it to 8 V.

8. Touch the probe to the paper to measure the potential difference between the negative

electrode and the probe location.

9. Move the probe until the desired potential difference is measured and mark the paper at

this point.

10. Continue to move the probe and identify other locations on the paper with the same

potential difference and mark these points.

11. After a sufficient number of points have been marked, connect them with a pen to produce

an equipotential line.

12. Draw an electric field line as an arrow, starting from any point on the surface of the positive

electrode. Exted it to the nearest equipotential line. Draw the line so that it leaves the

electrode at the right angle and intercepts the nearest equipotential line also at a right angle.

13. Draw another electric field line next to the first one with the same way electrode to one

equipotentila line to the next until you reach the electrode or the edge of the paper. The

line extends on the edge of the paper may also reenter the paper at anouther location. Use

the equipotential lines as your guide drawing arrows from the higher potential to lower

potential.

14. Draw as many field lines as possible originating from the positive electrode, to demonstrate

the shape of the electric field.

Use the steps above to measure the equipotential surfaces and electric field lines for below

configurations. And attach them your conductive papers to your Labbook.

17

1. (20 pts) Draw the electrodes in the conductive paper as shown below, measure the equipotential

surfaces and draw the electric field lines for two point charges.

2. (20 pts) Draw the electrodes in the conductive paper as shown below. Measure the equipotential

surfaces and draw the electric field lines for a point charge and one plate.

3. (20 pts) Draw the electric field lines for a circular conductor.

18

Report

1. (3 pts) What is the relation between the electric field lines and the magnitude of the electric field?

2. (3 pts) What are the properties of the electric field lines?

3. (3 pts) Is electrical potential a scalar or a vectorial quantity?

4. (3 pts) What is the voltage?

5. (3 pts) What is the equipotantial surface?

6. (3 pts) How can we obtain electric field lines using equipotential surfaces?

7. (3 pts) Explain the relation between the results obtained for (1) and (2).

19

8. (6 pts) Explain your results of electric filed lines of circular conductor by Gauss law.

9. (9 pts) How the electric field lines would change if we used an AC source?

Conclusion (10 pts)

Completed by:



Verified by:

20

Introduction

The purpose of this experiment is to discover the laws governing resistance, voltage and current in

circuits, investigate Kirchhoff’s Laws and Wheatstone bridge.

Equipment needed



- Resistors (3x1k, 1x2.2k, 2x100)

-Variable Resistor (0-33 )

- Digital Multimeter (DMM)

Theory for Kirchhoff’s Laws

Every element used in an electric circuit is called as a circuit element. Each conducting end coming

out from a circuit element that provides an external connection is called a terminal. If two or more

circuit elements meet in a terminal, it is called node. For example, in the Fig. 1, points B and E are

the nodes.

Figure 1. An electrical circuit composed of a battery and resistances.

Any closed conducting path is called a loop. In Fig. 1, ABEFA and BCDEB paths are loops. To

measure the resistances in the Fig. 1, one can use the Ohm's Law.

I

VR (1)

This states that the voltage (V) between the two points of a resistance, divided by the current (I)

passing through the resistance, will give the value of the resistance (R).

Kirchhoff’s Laws

Current Law: In an electric circuit, the sum of the incoming currents to a node is equal to

the sum of the outgoing currents from that node. For the point B in the Fig. 1

PHYS 102 /

Experiment 3

Kirchhoff’s Laws and Wheatstone

Bridge

21

321 III (2)

and for the point E

546 III (3)

is satisfied.

Voltage Law: Summation of all voltage differences in a given loop is zero. For loop 1 in the

Fig. 1

0V VVV FAEFBEAB (4)

and for loop 2

0V VVV EBDECDBC (5)

is satisfied.

Wheatstone Bridge

An accurate method for measuring a small resistance is the method of “Wheatstone Bridge”. In

practice, this method is used for measuring very small resistances. One of the four resistances

R1, R2, R3, and Rx, shown in Fig. 2 will be measured in this experiment.

Figure 2. Wheatstone Bridge Circuit.

The power supply is connected to the circuit with a resistance R4 in series to protect the rest of

the circuit from excessive currents. At least one of the known resistances must be variable. This

variable resistance is adjusted to zero the current passing through the amperemeter. Then the

points M and N must be at the same potential. If this condition is true, the circuit is

balanced. At the balance, the potential drop from K to M is the same as that from K to N, or

𝐼1𝑅1 = 𝐼2𝑅2 and 𝐼𝑥𝑅𝑥 = 𝐼3𝑅3 (6)

Eq. 6 yields

𝐼1𝑅1

𝐼𝑥𝑅𝑥=

𝐼2𝑅2

𝐼3𝑅3. (7)

However, if there is no current passing through the ampermeter, 𝐼2 = 𝐼3 and I1 = Ix. As a result the

22

equation reduces to

𝑅3 = 𝑅1𝑅𝑥

𝑅2. (8)

Experimental procedure for Kirchhoff’s Current Law

1. Connect the circuit in figure 2 on the board.

Figure 3. Experimental circuit for Kirchhoff’s Laws

2. Draw the circuit on a sheet of paper and show all current and voltages with their directions and

polarities on the circuit by assigning a reference direction to each current and voltage before going

on the experiment.

3. Use node B to apply the Kirchhoff’s current law.

4. Set the Signal Generator to 5 V DC and turn it on measure and record all the currents entering (or

leaving) node A in Table 2 by using current directions you determined. To measure currents, set the

DMM to the current measurement and connect it in series to the circuit. The currents should be

measured from + to – polarity of the DMM even if the determined current directions give a negative

Ampere value.

5. Record your readings in Table 1.

6. Use Node E and repeat step 4 to apply the Kirchhoff’s current law and record your readings in

Table 2.

7. Turn off the Signal Generator.

Experimental Procedure For Kirchoff’s Voltage Law

1. Set the Signal Generator to 5 V DC again and turn it on to measure and record all voltages on

loop 1 (VAB, VBE, VEF and VFA). To measure voltages, connect the DMM parallel to the resistor. Measure

voltages by using your determined polarities.

2. Measure and record all voltages on loop 2 (VBC, VCD, VDE and VEB). To measure voltages, connect the

DMM parallel to the resistor. Measure voltages by using your determined polarities.

3. Turn off the Signal Generator.

23

Experimental Procedure For Wheatstone Bridge

1. Build up the circuit given in Fig. 4.

Figure 4. Experimental circuit for Wheatstone Bridge

2. Turn on the power supply and connect the multimeter to measure the potential difference

between the points M and N.

3. Slowly change the value of the variable resistor, Rx by varying the knob until the voltage

reading on the multimeter is zero.

4. Measure the resistance of Rx and record the value in Table 4.

5. Measure the resistance of R3 and record the value in Table 4.

24

TABLE 1. (5 PTS) CURRENT MEASUREMENTS FOR KIRCHHOFF’S LAW FOR NODE B.

I1 (…....) I2 (…....) I3 (…....)

TABLE 2. (5 PTS) CURRENT MEASUREMENTS FOR KIRCHHOFF’S LAW FOR NODE E.

I4 (…....) I5 (…....) I6 (…....)

TABLE 3. (5 PTS) VOLTAGE MEASUREMENTS FOR KIRCHHOFF’S LAW for LOOP 1.

VAB (…....) VBE (…....) VEF (…....) VFA (…....)

TABLE 4. (5 PTS) VOLTAGE MEASUREMENTS FOR KIRCHHOFF’S LAW for LOOP 2.

VBC (…....) VCD (…....) VDE (…....) VEB (…....)

TABLE 5. (5 PTS) RESISTANCE MEASUREMENTS FOR WHEATSTONE BRIDGE

Rx R3(measured)

25

Report

Questions for Kirchhoff’s Current Law 1. ( 3 pts) Write the Kirchhoff’s current law for node B by using determined current directions.

2. (5 pts) Take the algebraic sum of measured current values of I1, I2 and I3. Is the Kirchhoff’s

current law verified? Explain.

3. (5 pts) Calculate theoretical values of I1, I2 and I3.

4. (3 pts) Write the Kirchhoff’s current law for node E by using determined current directions.

5. (5 pts) Take the algebraic sum of measured current values of I4, I5 and I6. Is the Kirchhoff’s

current law verified? Explain.

6. (5 pts) Calculate theoretical values of I4, I5 and I6.

7. (3 pts) Compare your experimental results with the theoretical values. Do they agree or not?

If not explain why?

26

Questions for Kirchhoff’s Voltage Law

1. (3 pts) Write the equation expressing the Kirchhoff’s voltage law for loop 1.

2. (5 pts) Take the algebraic sum of measured voltage (V) values around the loop. Is the

Kirchoff’s voltage law verified or not?

3. (5 pts) Calculate theoretical values of VAB, VBE, VEF and VFA.

4. (3 pts) Write the equation expressing the voltage law for loop 2.

5. (5 pts) Take the algebraic sum of measured voltage (V) values around the loop . Is the

Kirchoff’s voltage law verified or not?

6. (5 pts) Calculate theoretical values of VBC, VCD, VDE and VEB.

7. ( 3 pts) Compare your experimental results with the theoretical values. Do they agree or not?

If not explain why?

27

Questions for Wheatstone Bridge

1. (5 pts) Use equation (8) to find the value of R3.

2. (5 pts) Directly measure the resistance of R3 using a multimeter. Find percent error of your

measurement.

Conclusion (7 pts)



28

Introduction

The purpose of this experiment is to observe the charging and discharging of a capacitor in a simple

RC circuit and find the time constant of a capacitor.

Equipment needed



- 100 k𝛺 Resistor

- 470𝜇𝐹 Capacitor

- Voltage Sensor

-----------------------------------------------------------------------------------------------------------------------

Important note !

-----------------------------------------------------------------------------------------------------------------------

The voltages used in this experiment are not dangerous to you, but are potentially damaging

to the equipment and the electronic components. Please read and follow the warnings given

below, work very carefully, observe correct polarities when connecting equipment, avoid short

circuits, and always have an instructor check your circuit before energizing. If you do not

understand something or are not sure exactly what you are doing, then consult your instructor.

You will be held financially responsible for any damaged equipment!

-----------------------------------------------------------------------------------------------------------------------

Theory

In this experiment, you will investigate the times required for charging and discharging capacitors.

A capacitor is a device designed to store electric charge. The classic model of the capacitor is the

parallel-plate capacitor, in which a charge +Q is stored on one plate, and a charge –Q is stored on

the other.

The amount of charge that a capacitor can hold depends on the potential drop accress the plates of

the capacitor, and is given by Q = CV, where Q is the total charge in the capacitor of capacitance C

with unit of Farad, and V is the potential difference between the plates of the capacitor with unit of

Volt. Therefore, the capacitance C is a measure of how much charge can be stored in the device. The

accumulation of charge is not instantaneous, but it takes some time to build up from zero. Consider

charging a capacitor through a resistance R as shown in the circuit in figure 3.1:

PHYS 102 /

Experiment 4

Charging and Discharging of a

Capacitor

29

Figure 3.1. Series RC circuit.

Applying Kirchhoff law to this circuit;

0 / ab ax xbV V V V Q C IR (1)

can be written. The charge passing through the circuit in time dt will be dQ= Idt, here I is the

current with unit Ampere (A) . When this expression is substituted into Eq. (1), one can find the

differential equation.

00 0

Q dQ dQ Q VV R

C dt dt RC R (2)

By solving this equation with respect to time we get the stored charge on each of the plates at any

time ,

- /( )

0 1- t RCQ CV e (3)

Eq. (3) implies that Q approaches to CV0 as time elapses. For t=RC, the magnitude of the charge

reaches to the 1-(1/e) of its maximum value. Thus, the time at which the charge reaches almost its

maximum value depends on the capacitance and the resistance. The magnitude of the current passing

through the circuit at this time (t=RC) can be found by taking the derivative of Eq. (3).

- /0 t RCV

I eR

(4)

As can be seen from the equation above, the current decays exponentially within time.

Discharging of a Capacitor Over a Resistance

The power supply should be removed, because the charged capacitor will perform like a power

supply. A charged capacitor with capacity C has a potential difference between the plates V=Q/C.

Therefore, if a resistance is connected at the ends of the charged capacitor, the capacitor discharges

over the resistor. In this case, the potential difference between the capacitor plates is given to be VC

=VR, and since VR =IR, the differential equation can be written as;

Figure 3.2. Discharge of a RC circuit

V R

C

30

𝑄

𝐶− 𝑅𝐼 = 0 or

𝑄

𝐶+ 𝑅

𝑑𝑄

𝑑𝑡= 0 (5)

where I= -dQ/dt since the capacitor is discharging in this case.

From the solution of this equation, the charge on the capacitor can be found to be,

- /

0 t RC

Q CV e (6)

If we take the time derivative of Eq. (6) we can get the current at any time t

- /0 t RCV

I eR

(7)

The minus sign here shows that the direction of the current is opposite to that of the capacitor is

being charged. The expression RC, is the “time constant” of the circuit.

- /0 t RCV

I eR

(7)

Equation (7) can be written

V = 𝑉0𝑒−𝑡(𝑅𝐶) (8)

Taking the natural logarithms on both sides of equation (8);

ln(𝑉) = ln(𝑉0) −𝑡

𝑅𝐶 (9)

Hence a graph of ln V vs. t will yield a straight line with slope equal to –1/RC = –1/τ.

Experimental procedure

1. Switch on the Interface and PC and Launch the Capstone software.

2. On the main Capstone window, click on Signal Generator and apply its settings as DC with an

amplitude of +5V.

3. Using the 2.2 k resistor and one 100mF capacitor, wire up the series RC circuit on the

breadboard. Keep the signal generator turned off while connecting it to the circuit.

2. Connect the leads of the DMM to measure the voltage across the capacitor. You are now ready to

take data.

9. Turn on the signal generator and start timer simultaneously.

10. Measure the potential difference across the capacitor for 5.5 minutes at given time intervals and

record your readings in Table 1.

11. In the next step, we will analyze the discharging of the capacitor. Set up the circuit shown in Fig.

3.2 by disconnecting the signal generator cables from the circuit.

12. Start timer simultaneously to take measurements for the discharge process.

13. Measure the potential difference across the capacitor for 5.5 minutes at given time intervals and

record your readings in Table 2.

14. Take the natural logarithms of the potential difference measurements in Table 2 and record the

results in Table 3.

31

Table 1. (10 PTS) Charging of a Capacitor

t (s) V (Volt) t (s) V (Volt) t (s) V (Volt)

0 75 210

15 90 240

30 120 270

45 150 300

60 180 320

Table 2. (10 PTS) Discharging of a Capacitor

t (s) V (Volt) t (s) V (Volt) t (s) V (Volt)

0 75 210

15 90 240

30 120 270

45 150 300

60 180 320

Table 3. (10 PTS) lnV in Discharging of a Capacitor

t (s) lnV (Volt) t (s) lnV (Volt) t (s) lnV (Volt)

0 75 210

15 90 240

30 120 270

45 150 300

60 180 320

32

Report 1. (20 PTS) Use the values in Tables 1 and 2 to plot the charging and discharging of the capacitor

on a graph paper.

2. (20 PTS) Using the values in Table 3, plot ln V versus t, draw the best fit line and find the slope.

3. (10 PTS) Calculate the capacitance of the capacitor using the time constant you found.

4. (10 PTS) The tolerance on capacitors is usually very bad, and 20% is normal. Do your

capacitance value agree with the stated value of 100 mF?

Conclusion (10 pts)



34

Completed by:



Verified by:

35

Introduction

Our aim in this experiment is to investigate the force exerted on a current carrying conductor inside

a magnetic field.

Equipment needed

-PC Signal Interface

-Power amplifier

-Precision balance

-Magnetic field sensor

-Permanent magnets (side polarity) & Magnet holder

-Stands, bosses & clamps

-Copper Rod

-Digital Multimeter (DMM)

-----------------------------------------------------------------------------------------------------------------------

Important note!

-----------------------------------------------------------------------------------------------------------------------







-----------------------------------------------------------------------------------------------------------------------

Theory When current carrying conductor lies in magnetic field, magnetic forces are exerted on the moving

charges within the conductor and the conductor as a whole experiences a force distributed along its

length. We can compute the force on a current-carrying conductor starting with the magnetic force

BvqF

(4.1)

The magnetic forces on the moving charges

on a single moving charge.

We can derive an expression for the total force on all the moving charges in a length l of conductor

with cross sectional area A. The number of charges per unit volume is n; a segment of conductor

with length l has volume Al and contains a number of charges equal to nAl. The total force F

on all

the moving charges in this segment has magnitude;

))(())(( lBAnqvBqvnAlF dd (4.2)

PHYS 102 /

Experiment 5

Lorentz Force

36

Current density is stated as dnqvJ . The product JA is the total current I so we can write the

equation (4.2) as;

lBF I (4.3)

If B

field is not perpendicular to the wire, but makes an angle with it, the component B

which

is perpendicular to the wire (and to the drift velocities of the charges) is .sin BB The magnetic

force on the wire segment is then;

sinIlBIlBF (4.4)

This force can be expressed as vector product, just like the force on a single moving charge. We

represent the segment of wire with a vector l

along the wire in the direction of current; the force F

on this segment is

BlIF

(4.5)

If the conductor is not straight, we can divide it into infinitesimal segments ld

. The force Fd

on

each segment is

𝑑𝐹⃗⃗ ⃗⃗ ⃗ = 𝑑𝑙⃗⃗⃗⃗ 𝐼 × �⃗⃗� (4.6)

Then we can integrate this expression along the wire to find the total force of a conductor of any

shape.

Magnetic field or magnetic flux density has units of N A-1 m-1 or tesla (T). A field of 1T is a very

strong field. One gauss (G) corresponds to 410 tesla (T) in SI. The Earth's magnetic field is about

10-5 T.

A Straight wire segment of length l

carries a current I in the direction of l

. The magnetic force on

this segment is perpendicular to both l

and the magnetic field B

as shown in Figure 4.1.

Figure 4.1: Right Hand Rule.

37

Experimental Set up

1- A magnet holder is placed on the precision balance. Place two permanent magnets on the

magnet holder, north and south poles of the magnets facing each other. Turn the balance on,

take the reading.

2- Clamp a copper rod to two stands on the sides of the balance so that the rod crosses between

and equal distance to the magnets.

3- You will use the PC and Capstone software to generate the source voltage. The interface and

the power amplifier should have already been connected, and you should verify that the

power amplifier is connected to Analog Output A of the Interface. Also verify that connected

to Analog Output B of the Interface is “Magnetic Field Sensor”, which is in “radial” mesuring

mode. If not already done for you, you should connect a red and black banana plug lead to

the output jacks of the Power Amplifier. These leads will be connected to the points in the

circuit where you wish to apply the voltage. Turn on the Interface and Power Amplifier.

4- Launch The Capstone software. Then introduce Power Amplifier (output signal) by double-

clicking on it. Open the Graph window. Introduce the Magnetic Field sensor by double-

clicking on it.

Procedure for the effect of the current on the force

1- Set sample rate for the Magnetic Field Sensor to “Tesla”. Click Start to acquire data. Open

“graph” window.

2- Zero the reading on the Sensor, and then measure “the magnetic field strength” between the

magnets.

3- You will need to measure the magnetic field strength at one end, and in the middle of the

magnets. The average of the two values will be the approximate magnetic field strength

applied to the Copper rod by the magnets.

4- Click Stop. Record the data as MeasuredB .

5- Set Power Amplifier to DC with an amplitude of +0.01V.

6- Output jacks of the Power Amplifier are connected to the copper rod and a DMM, in series.

Set DMM range to current (10A).

7- Click in the Signal Generator window to activate it, and then click ON the Signal Generator.

On the DMM, you will read the current passing through the copper rod, and on the precision

balance, you will read the force exerted on the copper rod by the magnetic field. The length

of the wire which is in the magnetic field is equal to the length of magnets.

8- Increase the voltage setting in steps of 0.01 V on the signal generator to achieve the current

readings from +0.1A to +0.9A. Record the values on Table 1.

Procedure for the effect of the magnetic field strength on the force

1- Add two more magnets to the magnet holder.

2- Check the polarity of the magnets.

3- Repeat steps 1 to 4 and record the values on Table 2.

38

Procedure for the effect of the wire length on the force

1- This time join the magnets side by side, increasing the length of the rod inside the magnetic

field.

2- Check the polarity of the magnets.

3- Zero the reading on the Sensor, and then measure “the magnetic field strength” between the

magnets.

4- You will need to measure the magnetic field strength at one end, and in the middle. The

average of the two values will be the approximate magnetic field strength applied to the

copper rod by the magnets.

5- Click Stop. Record the data as MeasuredB .

6- Repeat steps 2 to 4 and record the values on Table 3.

Table 1. The effect of the current on the force (10 pts)

L (m):__________ MeasuredB (T):__________

I (A) m (kg) F (N)

0.1

0.2

0.3

0.4

0.5

Table 2. The effect of the magnetic field strength on the force (10 pts)

L (m):_________ MeasuredB (T):__________

I m (kg) F (N)

0.1

0.2

0.3

0.4

0.5

Table 3. The effect of the wire length on the force (10 pts)

L (m):___________ MeasuredB (T):__________

I (A) m (kg) F (N)

0.1

0.2

0.3

0.4

0.5

39

Report

1. (15 pts) Sketch the experimental set up below and indicate;

a) The polarity of the magnets, b) The direction of the magnetic field lines, c) The direction of the

current passing through the cupper rod, d) The direction of the magnetic force acting on the rod.

2. (6 pts) How does the magnetic force on the conductor vary with the

a) Current passing through the conductor? b) Magnetic Field Strength? c) Length of Conductor

inside the Magnetic Field? Explain.

2. (30 pts) Plot a graph of F versus Il for each Part. Find CalculatedB from the slope of the graphs.

40

3. (9 pts) Compare MeasuredB and CalculatedB for each part. Do you expect them to be equal? Explain.

Note: % error for B= 100

calculated

calculatedmeasured

B

BB

Conclusion (10 pts)



41

Completed by:



Verified by:

42

Introduction

The purpose of this experiment is to investigate the response to an abrubt of simple RC and RL

circuits, calculate their time constants and determine capacitance and inductance.

Equipment needed



- one 100 Resistor

- one 470 F Capacitor

-22 mH Inductor

- Voltage Sensor

-----------------------------------------------------------------------------------------------------------------------

Important note !

-----------------------------------------------------------------------------------------------------------------------







-----------------------------------------------------------------------------------------------------------------------

Theory for RC circuits

In this experiment, you will investigate the times required for charging and discharging

capacitors, and you will also discover how capacitors combine in series and parallel. A capacitor

is a device designed to store electric charge. The classic model of the capacitor is the parallel-

plate capacitor, in which a charge +Q is stored on one plate, and a charge –Q is stored on the

other. The capacitor has many uses, not just as a simple charge storage device, but also for

filtering and smoothing of time-varying waveforms. In order for the capacitor to become

charged, it must be connected to a source of charge such as a battery or power supply. The

amount of charge that a capacitor can hold depends on the voltage applied to the capacitor, and

is given by Q = CV, where Q is the total charge in the capacitor of capacitance C, and V is the

voltage on the capacitor. So the capacitance C is a measure of how much charge can be stored

in the device. The accumulation of charge is not instantaneous, but it takes some time to build

up from zero. Consider charging a capacitor through a resistance R as shown in the circuit in

figure 3.1:

PHYS 102 /

Experiment 6

RC and RL Circuits

43

Figure 5.1. Series RC circuit.

The capacitor starts to be charged when the square signal is on. Kirchhoff’s voltage law to find

the accumulated charge;

0Q

IRC

(1)

where is the potential difference applied to the circuit. Recalling that /I dQ dt , Eq. (1)

can be rewritten as ;

0dQ Q

dt RC R

. (2)

This is a linear inhomogeneous differential equation. In a couple of steps, the solution can be

obtained as,

/

0 1 ctQ Q e

(3)

where RCC is the time constant of the circuit and 0 0Q V C is the saturation value of Q .

When Ct , the capacitor has been charged to a fraction ( 11e

, about 63 %) of its saturation

value. This solution implies that as time elapses, Q converges to 0Q . To see what happens after

the capacitor is saturated to 0Q and square signal goes to the low state, (that is the state where

no voltage is supplied to the circuit), simply take 0 in Eq. (2).

0c

dQ Q

dt (4)

This equation is easier to solve than (2) and the solution is:

/

0Ct

Q Q e

(5)

This solution tells us that, the capacitor discharges through the resistor and Q decays to zero.

Capacitor voltage has the same exponential character as Q (recall /CV Q C ).

Using Eq. (3) and Eq. (5), the curve of CV versus t can be plotted.

44

The time it takes for the charge of a capacitor to reduce to half of its initial value ( 0 / 2Q ) is

called half life of the circuit. Let us denote this by T . When Tt , the charge Q will be half

of 0Q . Substituting these statements into Eq. (4), we have,

/00

2cTQ

Q e

(6)

and solving this equation for T yields;

2lnCT (7)

Theory for RL circuits

Figure 5.2. Series RL circuit.

To derive an expression for the potential drop across the inductor when the square signal in Fig.

3 is on,we need the current as a function of time. For this, let us again write the Kirchhoff

equation;

0 lVIR (8)

where lV , is the potential difference induced across the inductor and its magnitude is given by,

dt

dILVl (9)

Eq. (8) can be rewritten as,

0LL

IR

dt

dI (10)

The solution to this equation can be written as

45

/1 Lt

I eR

(11)

where /L L R is known as the time constant of the circuit, which determines the rate of

increase. This solution means that I starts to increase from zero to its saturation value R/ .

When the square signal drops to 0, taking 0 in Eq. (10), the solution can be written as;

/ Lt

I eR

(12)

In both cases ( 0 and 0 ) the inductor voltage lV given by Eq. (9) can be evaluated using

Eq. (11) and Eq. (12). In the first case where 0 , Eq. (11) and Eq. (9) together give;

/ Lt

lV e

(13)

Eq. (13) indicates that, the inductor voltage jumps to at the same instant as the square signal

does, and then decays exponentially to zero. In the second case where 0 , again Eq. (12)

and Eq. (9) together give;

/ Lt

lV e

(14)

This solution indicates that lV first jumps to ( ) and then decays to 0. Eq. (13) and Eq. (14),

are plotted in Fig. 4. Half life of lV can be found using Eq. (13) or Eq. (14) as,

2lnLT (15)

Experimental procedure for RC circuits

1. Turn on the Interface and PC and Launch the Capstone software.

2. On the main Capstone window, click on Hardware icon on the right and introduce “voltage

sensor” to Analog Channel A of the interface. (Check that the voltage sensor should already

be connected).

3. Using the 100 resistor and one 470F capacitor, wire up the series RC circuit on the

breadboard.

4. Connect the leads of the voltage probe to measure the voltage across the capacitor. You are

now ready to take data.

5. On the main Capstone window, click on Signal Generator and apply its settings as square

wave with an amplitude of 1V with frequency of 1 Hz.

6. Click on record to acquire data and click stop after a few seconds.

7. Click on the Graph icon on the right. On the graph, select “measurement” on Y axis and

right click to view the selection of measurements. Select Analog Channel A, Voltage data.

8. On the Hardware icon of the interface, right click on “the signal generator output“ and select

voltage sensor.

9. Introduce a second Y axis on the graph and right click to view the selection of measurements.

Select “Signal Generator Ouptput voltage”.

46

12. On the Graph window on the toolbar, click on the scale icon to automatically scale your

graph. Click on the zoom icon to take the resulting image to the graph and draw a box around

the rising portion of the curve. This will result in an expanded view of this region.

13. Measure the potential difference across the capacitor for the cases of discharging and

charging and record your readings in Table 1.

Experimental procedure for RL circuits

14. Using the 100 resistor and one 22mH inductor, wire up the series RL circuit on the

breadboard.

15. Connect the leads of the voltage probe to measure the voltage across the inductor. You are

now ready to take data.

16. Repeat steps 5 to 12, measure the potential difference across the inductor for the cases of

discharging and charging and record your readings in Table 2.

Table 1. (10 PTS) Potential Difference Across the Capacitor

Discharging Charging

𝑉𝐶 (v) 𝑡 𝑉𝐶 (V) 𝑡

𝑉𝐶(max) 0

3𝑉𝐶(max)/4 𝑉𝐶(max)/4

𝑉𝐶(max)/2 𝑉𝐶(max)/2

𝑉𝐶(max)/4 3𝑉𝐶(max)/4

0 𝑉𝐶(max)

Table 2. (10 PTS) Potential Difference Across the Inductor

Discharging Charging

𝑉𝐿 (v) 𝑡 𝑉𝐿 (V) 𝑡

𝑉𝐿(max) 0

3𝑉𝐿(max)/4 𝑉𝐿(max)/4

𝑉𝐿(max)/2 𝑉𝐿(max)/2

𝑉𝐿(max)/4 3𝑉𝐿(max)/4

0 𝑉𝐿(max)

47

Report

Questions for RC circuits 1. (10 pts) Use your recorded values in Table 1 to plot the square wave input and the capacitor

voltage on a graph paper.

2. (10 pts) Calculate RC-time constant𝐶 , using its relationship with the half-life, T that you

measured for charging and discharging.

3. (5 pts) Compare the charging and discharging time constant for the capacitor. Is the value

within your expectation?

4. (5 pts) Calculate the capacitance of the capacitor. The tolerance on capacitors is usually very

bad, and 20% is normal. Does your value agree with the stated value of 470 F within this

tolerance?

Questions for RL Circuits

1. (10 pts) Use your recorded values in Table 2 to plot the square wave input and the inductor

voltage on a graph paper.

48

2. (10 pts) Calculate RL-time constant𝐿, using its relationship with the half-life, T that you

measured for charging and discharging.

3. (5 pts) Compare the charging and discharging time constant for the inductor. Is this what you

expect?

4. (5 pts) Calculate the inductance of the inductor. Compare it to the stated value of 22 mH.

5. (10 pts) Discuss the similarities and differences between RL and RC circuits.

Conclusion (10 pts)

(Summarize what you have learned from the experiment in a few sentences and discuss the main errors

you encountered and possible measurement improvements.)

49

Completed by:



Verified by:

50

Introduction

The purpose of this experiment is to study the electrical characteristics of transformers, half

wave rectifiers and full wave rectifiers.

Equipment Needed


- 1x100 Resistor


- 5x1N 4001 diodes

- 1xtransformer

-----------------------------------------------------------------------------------------------------------------------

Important note !

-----------------------------------------------------------------------------------------------------------------------







-----------------------------------------------------------------------------------------------------------------------

Part A: Transformers

Transformers are used to convert electrical signal from one voltage to another with minimal

loss of power. Transformers can increase voltage (step-up) as well as reduce voltage (step-

down). A transformer can be used to increase or decrease AC voltages. An AC voltage is

applied to the primary coil of a transformer, which is surrounded by the secondary coil but is

not electrically connected to it.

A single-phase transformer consists of two (or more) coils of copper wire wound on an iron

framework, as shown in Fig. 5.1. We neglect the resistance of the windings and assume that all

magnetic field lines are confined to the iron core, so at any instant the magnetic flux is the

same in each turn of the primary and secondary windings which are connected to AC source.

PHYS 102 /

Experiment 7

Transformers and Rectifiers

51

Figure 5.1 Schematic of the transformer

The primary winding has 1N turns and secondary winding has 2N turns. When the magnetic

flux changes because of changing currents in the two coils, the resulting induced emf’s are,

dt

dN

11 and

dt

dN

22 (5.1)

The flux per turn is the same in both in the primary and secondary windings so the equation

5.1 shows that the induced emf per turn is the same in each. The ratio of the primary emf 1 to

the secondary emf 2 is therefore equal at any instant to the ratio of primary to secondary turns.

2

1

2

1

N

N

(5.2)

The primary winding is connected to the AC source shown as Vp, while the secondary supplies

power to a load at a voltage Vs (Both Vp and Vs are AC voltages). RMS value for Vs is

2

.)(maxsRMS

VV (5.3)

If N2 is greater than N1, then Vs is greater than Vp, and this is called the transformer a step-up

transformer. The turn ratio is defined as

2

1

N

Na (5.4)

Since 1 and 2 both oscillate with the same frequency as the AC source, equation 5.2 also

gives the ratio of the turns values of induced emf’s. If the windings have zero resistance, the

induced emf’s 1 and 2 are equal to the terminal voltages across the primary and secondary

respectively. If the transformer is ideal, then the voltages are directly proportional to the

number of turns, and the currents are inversely proportional to the number of turns.

2

1

N

N

V

V

s

p (5.5)

Primary Coil

Soft iron core

+

-

+

-

Ip

Vp

N1 Is

Vs

N2

Secondary

Coil

52

1

2

N

N

I

I

s

p (5.6)

Rectifiers

Electric power is delivered to our homes and factories in the form of Vrms = 220 V at 50 Hz AC,

but many end uses require DC. This conversion from AC to DC is accomplished by using one

or more diodes in a rectifier following to the transformers. A modern diode, as shown in Fig

5.2, is a two terminal (di-electrode) solid state device that allows current to flow in only one

direction. For instance, the voltage drop across the diode when current is flowing is about 0.7

V. If the other voltages in the circuit are sufficiently high, then this 0.7 V can be ignored without

significant loss of accuracy. In this case, we are assuming the diode to be ideal, that is, with

zero voltage drop, when conducting and infinite impedance when reverse biased.

Figure 5.2 (a) The schematic and (b) the symbol of a diode.

Half Wave Rectifiers

When a load resistor is connected to an AC source through a diode, half wave rectification

occurs. Since an AC wave alternates between positive and negative cycles, we would first

examine what happens when the ac wave, or sine wave, goes positive. The simplest rectifier

circuit is the single-phase half wave rectifier shown in Fig. 5.3. The secondary voltage is Vs =

Vm cos t. When Vs is positive, the diode is forward biased and conducting so that the load

voltage VL is the identical Vs (assuming an ideal diode). When Vs is negative, the diode is

reverse biased, no current flows, and the output voltage is zero. It can be seen that an output

wave consisting of a half cycle of a cosine wave and a half cycle of zero voltage. This waveform

is used to drive some small household motors, but many applications require a smoother output.

RMS output voltage of the half wave rectifier is

2

.maxVVRMS

(5.7)

(a)

(b)

(a) (b)

http://www.eece.ksu.edu/~starret/589/man/Efig1.gif

53

Figure 5.3

(a) single-phase half wave rectifier circuit,

(b) input waveform, (c) output waveform.

Full Wave Rectifiers

The other rectifier circuit is the single-phase full wave rectifier. The analysis will be for the

case where each half of the secondary has an instantaneous voltage Vs = Vm cos t. When Vs

is positive, the diodes A and B will conduct, and when Vs is negative, the diodes C and D will

conduct, yielding the voltage waveform shown in fig 6.4 (c). Compared with every other half

cycle is present from the half wave rectifier case, this produces a much smoother waveform but

the voltage still varies all the way from zero to Vm. When the AC input is positive, diodes A

and B are forward-biased, while diodes C and D are reverse-biased. When the AC input is

negative, the opposite is true, i.e. diodes C and D are forward-biased, while diodes A and B are

reverse-biased. RMS output voltage of the full wave rectifier is

2

.maxVVRMS (5.8)

(a)

Vp VsC

B D

A

VLoutput

+

_

Figure 5.4 (a) single phase full wave rectifier, (b)

input waveform, and (c) output waveform.

Experimental Procedure for Transformers

1. In this part, you will observe the output signal of the transformer. The input voltage is

supplied by the output voltage will be measured by voltage sensor which is connected to

signal interference and the PC.

2. You will use the Capstone software to measure the voltage across the transformers as a

function of time. Make sure your transformer’s plug is connected to electricity power outlet.

(c)

(c)

(b)

54

3. The voltage sensor should have already been connected, and you should verify that the voltage

sensor is connected to Analog Output A of the Interface.

4. Introduce the voltage sensor onto the Analog Channel A as shown in Figure 5.5.

5. You should convert frequency from 10 Hz to 2000 Hz. These operations are performed to

have the computer recognize the connections you have just done at the beginning of the

experiment.

3. After you have given voltage, open the graph frame. Assign Y axis as Analog Output A,

Voltage, and X-axis, Time.

4. In order to start recording, click “Record” at the left bottom of this frame. During recording

you can observe the AC output in voltage by activating the graph frame.

5. When you are done with recording activate the Graph frame. The data just recorded will be

displayed as a voltage-time graph on this frame. The x- and y-coordinates will be displayed

next to the horizontal and vertical axes respectively. For a more precise selection (this is what

you need actually for this experiment), you can magnify the graph both in horizontal and

vertical directions by clicking the icon of relevant direction.

6. Record five consecutive maximum and minimum values in the voltage time graph display in

Table 1.

Experimental Procedure for Half Wave Rectifiers

1. Now, you need to wire up the circuit as shown in figure 5.6. Connect a diode and a resistor

in the circuit board. Make sure you connect the circuit with transformer. Vs + and Vs - are AC

inputs and show the voltage across the secondary coil of the transformer.

Figure 5.6. Half wave rectifier circuit.

2. Plug the voltage sensors into VL- and VL+ which are the outputs of the half wave rectifier.











Table 2.

55

Experimental Procedure for Full Wave Rectifiers

1. Using 4 diodes, wire up the circuit shown in figure 5.7.

Figure 5.7 Full wave rectifier circuit.

2. Vs+ and Vs- are AC inputs from transformer, VL- and VL+ are output of the full wave

rectifier. Plug the voltage sensors in both VL- and VL+ to measure the output voltages.











Table 3.

Table 1. (10 pts) Transformer output voltage

Wave# Vmax Time for Vmax Vmin Time for Vmin

1

2

3

4

5

56

Table 2. (10 pts) Half Wave Rectifier output voltage


1

2

3

4

5

Table 3. (10 pts) Full Wave Rectifier output voltage


1

2

3

4

5

Report

1. (15 pts) Sketch the observed AC output signal for Transformer, half wave rectifier and

full wave rectifier on the graph paper. Indicate the measured voltage and time values.

2. (5 pts) Calculate root-mean square (RMS) output voltage of the transformer.

3. (10 pts) Calculate the turn ratio of the transformer.

4. (10 pts) Why the transformers only work with AC (alternating current)? Explain.

5. (5 pts) Calculate RMS output voltage of the half wave rectifier.

57

6. (5 pts) Calculate RMS output voltage of the full wave rectifier.

7. (10 pts) In your Labbook, draw the full wave rectifier circuit to obtain negative output

voltage.

Conclusion (10 pts)

(Summarize what you have learned from the experiment in a few sentences and discuss the main errors

you encountered and possible measurement improvements.)

58

Completed by:



Verified by:

59

Appendices

APPENDIX A. SOME IMPORTANT POINTS ON DRAWING A GRAPH

Names and units of axes:

The names and units of the axes must be written on

the axes clearly.

Scaling the axes:

It is very important to scale the axes of a graph

according to data obtained in the experiment. This

is because the slope of the graph will be more

precise, when the data is spread on a larger area of

the millimetric paper. After placing the axis so that

the whole paper is being used, the coordinates of

the starting point is named (Vsmall, msmall). The mass

axis is scaled equally between msmall and mbig

values. Similarly, the volume axis is scaled equally

between Vsmall and Vbig values. The scales of the

axes should not be expected to be the same.

Marking data obtained in the experiment: The data

obtained in the experiment must be marked on the

graph clearly. Never write and mark the values of

the data on the axes. Don’t write the values around

the data points which you marked on the graph.

Don’t draw line between the data points on the

graph.

Vsm

all

Vbi

msmall

mbig

I (Amper)

U (

Volt

)

wrong

60

Fitting:

After marking the data obtained during the

experiment on the graph, you must fit the data to

an appropriate function. For example, since the

relation between the potential difference and the

current is known to be linear, a line is drawn using

the data points. In constructing a graph, the least

square method is used in order to minimize the

error. The method of least squares says that the line

drawn between data points should be such that the

sum of the squares of perpendicular distances from

the data points to the line is minimum.

The slope of the line is calculated using the

coordinates of any two points on the line. It should

be noted that data points should not be used in

determining the slope because, otherwise, one

would be skipping error reduction. Another

important point that should be kept in mind is that

the coordinates of the points are determined by

reading the corresponding values in the axes.

If you have huge or very small numbers, you can

multiply the axes with the powers of 10.

I (Amper)

U (

Volt

) Fit

line

61

APPENDIX B. THE INTERNATIONAL SYSTEM OF UNITS*

*University Physics, Young and Freedman, 14th ed.Addison-Wesley.

62

APPENDIX C. UNIT CONVERSION FACTORS*


63

APPENDIX D. FUNDAMENTAL PHYSICAL CONSTANTS and

PREFIXES for POWERS of 10 *


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