Combination of Resistors in Series and Parallel

An important part of electric circuits is Resistors. When a resistor

connects to a combination of series and parallel connection it forms

more complex circuit networks. Regulation of the current level of a

device is a resistor’s functionality. To know more about resistors in

series or parallel, let’s explore the article further!

Introduction

Resistors are two-terminal devices. Therefore, voltage division,

regulation of current in the device and adjusting signal level are the

functionality of a resistor. Representation of a resistor is done through

Ohm’s Law.

R =

V

I

Many types of resistors are available and some are the following:

1. Wire-wound resistor.

2. Semi-conductor resistor.

3. Flim resistor.

4. Carbon Composition resistor.

Resistor in Series

In this kind of connection, resistors are in a sequential array of

resistors to form an electronic circuit/ device. Resistors are connected

is in a single line and hence common current flows in the circuit.

The connection is in such a manner that the current flowing through

the 1st register has to then flow further through the 2nd register and

then through 3rd. Therefore, a common current is flowing in

connection with a resistor in series. At all point in the circuit, the

current amoung the resistors is same. For example,

I1 = I2 = I3 = It = 2ma

All the resistors in series that is R1, R2, R3 have current I1, I2, I3

respectively and the current of the circuit is It.

As resistors are connected in series the sum of the individual resistor

is equal to the total resistance of the circuit. Let R1, R2, R3 be the

resistors connected in series and Rt be the total resistance of the

circuit. so the total resistance of the circuit that is 12Ω, is the sum of

all individual resistors R1, R2, R3 having 6KΩ, 4KΩ, 2KΩ

respectively.

This circuit of the resistors in series can also be represented by

Therefore, the total resistance can be calculated as

R1 + R2 + R3 = Rt

furthermore, the total resistance of the above resistors in series is

given by

Rt = 6KΩ + 4KΩ + 2KΩ = 12KΩ

The Equation of Resistors in Series

Since the connection of resistor is in a series fashion that is in the

sequential array or continuously one after other. The total resistance is

equal to the resistance value of each resistor in the device/ circuit.

R1+R2+R3+R4+………………….Rn=Rt

where R is the resistance of the resistor and Rn represents the resistor

number or the total resistance value.

Resistor in Parallel

In this kind of connection, the terminals of resistors are connected to

the same terminal of the other resistor to form an electronic circuit/

device. Resistors are connected is in parallel fashion and hence

common voltage drop in the circuit.

Unlike, series connection, in parallel connection, current can have

multiple paths to flow through the circuit, hence parallel connection is

also current dividers. Common voltage drop is across the parallelly

connected circuits/networks. At the terminals of the circuit, the

voltage drop is always the same. For example

VR1=VR2=VR3=VRT=14V

The voltage across R1 is equal to the voltage across R2 and similarly,

equal to R3 and hence the total voltage drop is equal to the voltage

across the circuit. Reciprocal of individual resistance of each resistor

and the sum of all the reciprocated resistance of resistor will us the

total resistance of the circuit.

1

(

R

t

)

=

1

(

R

1

)

+

1

(

R

2

)

+

1

(

R

3

)

+…………

1

(

R

n

)

Questions For You

Q1: When three identical resistances are connected to form a triangle

the resultant resistance between any two corners is 30Ω .The value of

each resistance is:

1. 90Ω54Ω

2. 15Ω

3. 45Ω

Answer. 45Ω. 1/RAB=1/2R+1/R=2R3=30

RAB=3R/2=3*30/2

⇒R=45Ω

Q2. Identify the changes in a circuit on adding a light bulb in parallel

to the actual resistance of the circuit. It will:

● decrease the total resistance

● increase the total resistance

● make the voltage lost in each light bulb different

● make the current through each light bulb the same

● not change the total current through the circuit

Answer. decrease the total resistance. For a parallel combination of

two resistances,

1/Req=1/R1+1/R2

⟹Req< min {R1, the R2}

A light bulb has its own resistance and hence the total resistance of the

circuit decreases when it is connected in parallel to the actual

resistance of the circuit.

Q3.The least resistance that one can have from six resistors of each 0.1 ohm

resistance is:

1. 0.167 Ω

2. 0.00167 Ω

3. 1.67 Ω

Answer. 1.67 Ω. Least resistance is possible when all are in parallel.

⇒Req=R/6=0.16=0.0167 Ω

Ohm’s Law

Whenever the fan in your room is on and when you feel cold you

reduce the fan’s speed. For doing so you use the speed control knob

on the switchboard. But how does the knob work? What’s its

mechanism? The knob works on the principles of ‘Ohm’s Law’. But

what does Ohm’s law of current electricity state? Let us study Ohm’s

law of current electricity.

Ohm’s Law of Current Electricity

Ohm’s Law of Current Electricity is named after the scientist ”Ohm”.

Most basic components of current electricity are voltage, current, and

resistance. Ohm’s law shows a simple relation between these three

quantities.

Ohm’s law of current electricity states that the current flowing in a

conductor is directly proportional to the potential difference across its

ends provided the physical conditions and temperature of the

conductor remains constant.

Voltage= Current× Resistance

V= I×R

where V= voltage, I= current and R= resistance. The SI unit of

resistance is ohms and is denoted by Ω. In order to establish the

current-voltage relationship, the ratio V / I remains constant for a

given resistance, therefore a graph between the potential difference(V)

and the current (I) must be a straight line.

This law helps us in determining either voltage, current or impedance

or resistance of a linear electric circuit when the other two quantities

are known to us. It also makes power calculation simpler.

Limitations of Ohm’s Law of Current Electricity

● The law is not applicable to unilateral networks. Unilateral

networks allow the current to flow in one direction. Such types

of network consist of elements like a diode, transistor, etc.

● Ohm’s law is also not applicable to non – linear elements.

Non-linear elements are those which do not have current

exactly proportional to the applied voltage that means the

resistance value of those elements changes for different values

of voltage and current. Examples of non – linear elements are

the thyristor.

● The relation between V and I depends on the sign of V. In other

words, if I is the current for a certain V, then reversing the

direction of V keeping its magnitude fixed, does not produce a

current of the same magnitude as I in the opposite direction.

This happens for example in the case of a diode.

How do we find the unknown Values of Resistance?

It is the constant ratio that gives the unknown values of resistance. For

a wire of uniform cross-section, the resistance depends on the length l

and the area of cross-section A. It also depends on the temperature of

the conductor. At a given temperature the resistance,

R =

ρl

A

where ρ is the specific resistance or resistivity and is characteristic of

the material of wire. Using the last equation,

V = I × R =

Iρl

A

I/A is called the current density and is denoted by j. The SI unit of

current density is A/m². So,

E I = j ρ I

This can be written as E = j ρ or j = σ E, where σ is 1/ρ is

conductivity.

Solved Questions for You

Q1. The unit for electric conductivity is

A. per ohm per cm

B. ohm × cm

C. ohm per second

D. who

Solution: A. We know that R =

Iρl

A

. R has dimensions of an ohm, L has dimensions of length A has

dimensions of (length)². Therefore, ρ has dimensions of ohm-cm.

Q2. What will happen to the current passing through a resistance, if

the potential difference across it is doubled and the resistance is

halved?

A. Remains unchanged

B. Becomes double

C. Becomes half

D. It becomes four times.

Solution: A. Using ohm’s law

I =

V

R

I’ =

2V

R/2

so, I’ = 4I

Hence the current becomes four times.

Electrical Energy and Power

Surely you have faced a situation where some important appliance

stops working because the cells run out. What does that mean? That

means the cell is no more able to give current or we can say that it has

no more energy stored. This means that the energy that is the

chemical energy is consumed in the electric circuits. So in order to

find out the amount of energy consumed, we study the electric energy

or electric power.

Electric Energy

To under the concept of electric energy, let us consider a conductor

carrying the current I and potential difference V between the two

endpoints A and B. Let us denoted the electric potential of A and B as

V(A) and V(B). As we know that current is flowing from A to B so

V(A) >V(B) and the potential difference across AB is V = V(A) –

V(B) > 0

NOW, in a time interval Δt, an amount of charge ΔQ is equal to IΔt

moves from point A to B of the circuit and the work was done by the

electric field is equal to the product of V and ΔQ.

Here if the charges in the conductor move without collisions, their

kinetic energy would also change. Conservation of total energy is ΔK

= I V Δt > 0. The amount of energy dissipated as heat in a conductor

in a time interval Δt is,

ΔW = V ΔQ = VI Δt

Electric Power

The rate at which the electric energy enters the portion of the circuit is

called the electrical power input. The rate at which work is done in

bringing the charged particles from one point to another is known as

electric power. It is denoted by P.

The SI unit of power is watt (W). One watt is the power consumed by

the device catting 1A of current when operated at a potential

difference of 1 V.

P = VI

Applying ohms law we can write

P = I² R = V²/R

The above equation is the power loss in a conductor of resistance R

which carries the current I. The application of electrical power is that

it is transmitted from the power stations which later on reaches our

homes and the industrial factories via transmission cables.

Now we know that the transmission of power is very costly. So how

do we minimize the power loss in transmission cables? Let us consider

a device R to which a power is to be delivered via the cables having

resistance Rc. So if V is the voltage across R and current I then,

P = V I

The wires which are connected to the device from the power station

has finite resistance Rc. So, Pc = I² Rc

∴ P² Rc / V²

Hence the power wasted in connecting the wires is inversely

proportional to V². So the resistance Rc of the transmission cable is

considerable.

Solved Questions

Q1. The circuit given below is for the operation of an industrial fan.

The resistance of the fan is 30 ohm. The regulator provided with the

fan is a fixed resistor and a variable resistor in parallel. Under what

value of the variable resistance given, power transferred to the fans

will be maximum? The power source of the fan is a dc source with an

internal resistance of 60 oh.

A. 3 0HM

B. 0

C. ∞

D. 6 ohm

Solution: The correct option is “B”. The power which transfers to the

fan is P = V²/R where R is the total resistance of the circuit. As power

is inversely proportional to total resistance. So for maximum power,

the total resistance should be minimum. Total resistance here is R =

6r/6 +r + 3. r is the variable resistance. R is minimum when r = 0

Q2. An electric heater has a resistance of 150 ohms and can bear a

maximum current of 1 ampere. If we use the heater on 220-volt mains, the

least resistance required in the circuit will be

A. 70 ohms

B. 5 ohms

C. 2.5 ohms

D. 1.4 ohms

Solution: The correct option is “A”. Given that the heater can bear a

maximum current of 1 ampere we need to add a resistance to the

circuit in series with the heater so that current is less or equal to 1

ampere. Let that resistance be R, then (150+ R) × 1 = 220. R = 70

ohm.

Resistivity of Various Materials

You must have had electric shocks! Haven’t you? Did you get the

shock on a plastic wire? It is not possible. You can’t get shocks from

plastic wires. But, why is it so? It is because of a phenomenon that we

will read about in this chapter. We will study about resistivity of

various materials.

What is Resistance?

We know that electric current that flows in a circuit is as similar to the

water flowing through a river. In a river rock, branches and other

particles resist the flow of water. in a very similar fashion, a circuit

has elements to resist the flow of electrons.

Resistance is nothing but this property of resisting the flow of

electrons or the current. The unit of resistance is ohm. One ohm is

equal to volt per ampere. From Ohm’s law, we have seen that R = V /

I, Where V is the voltage and I is the current.

Resistors are used to resist or control the flow of electrons by the

conductive material. They do not provide any power to the circuit.

They may reduce the voltage and current passing through the circuit.

Hence, resistors are passive devices. Most of the resistors are made up

of carbon, metal or metal oxide film.

Resistivity

Resistivity is the resistance per unit length and cross-sectional area. It

is the property of the material that opposes the flow of charge or the

flow of electric current. The unit of resistivity is ohm meter.

We know that R = ρ L / A. Thus we can derive the expression for

resistivity from this formula. ρ = R A / L, where R is the resistance in

ohms, A is the area of cross-section in square meters and L is the

length in meters. When the values of L, the length, and A, the area is

equal to one, we can say that the resistivity is equal to the resistance.

So, resistivity is the specific resistance of a material. When we have a

thick wire, the resistance decreases. The resistance increases when the

wire is thin as the area of cross-section is less. When the length of the

wire increases, the resistance also increases. When the length of the

wire decreases, the resistance decreases as the length is less.

The Resistivity of Various Materials

A material with high resistivity means it has got high resistance and

will resist the flow of electrons. A material with low resistivity means

it has low resistance and thus the electrons flow smoothly through the

material.

For example, Copper and Aluminium have low resistivity. Good

conductors have less resistivity. Insulators have a high resistivity. The

resistivity of semiconductors lies between conductors and insulators.

Gold is a good conductor of electricity and so it has low resistivity.

The glass is a good insulator which does not allow the flow of

electrons. Hence, it has a high resistivity. Silicon is a semiconductor

and so it allows partial movements of electrons. The Resistivity of

Silicon comes between glass and gold. The resistivity for perfect

conductors is zero and the resistivity for perfect insulators is infinite.

Solved Examples for You

Question 1: The resistivity of alloys is ______ than its constituent

elements.

A. Higher

B. Lower

C. Same

D. None

Answer: Option A – Higher. Metal alloy has a greater resistivity than

the corresponding metals because of lattice distortion from the

alloying elements. A metal with no alloying elements would transport

electron by drift oscillation over the lattice.

The difference in atomic radii of alloying elements and in

electronegativity from base metal, the presence of alloying element

changes the local electronic structure of the base metal. Such change

modulates the typical drift oscillation mechanism in electron

conduction by scattering and leads to higher resistance.

Question 2: Name three materials or substances that have good

resistance.

Answer: Insulators have good resistance. Examples include glass,

ceramics, wood etc.

Temperature Dependence of Resistivity

Resistivity is the nature of a material that allows or resists the flow of

electric current through a given element or material. What is

surprising about resistivity is the temperature dependence of electrical

resistance! It is hard to comprehend how the temperature of an

element can affect the degree of conductance of such material but

believe it or not, this is the world of science and it happens almost

every day, all around us!

The Concept of Electrical Resistance

Resistivity is the phenomenon of specific electrical resistance of a

material or volume resistivity of a material. It can also be defined as

the intrinsic property of a material that displays how the material

resists the flow of current in the material. The concept can also be

defined as the resistance that is displayed by a conductor which has

unit length and unit area of the given cross section.

So resistivity is not dependent upon the length and area of a

cross-section of a given material. However, the resistance of a

material depends upon the length and area of the cross-section of the

material in question. The resistivity manifests as:

ρ = RA/L,

where R is the resistance in ohms, A is the area of cross-section in

square meters and L is the length in meters. The unit of resistivity is

universally accepted as ohm-meter.

The Concept of Temperature Resistivity

The resistivity of materials is dependent upon the temperature of the

material.

ρt = ρ0 [1 + α (T – T0)]

is the equation that defines the connection between the temperature

and the resistivity of a given material. In this equation ρ0 is the

resistivity at an equilibrium temperature, ρt is the resistivity at t0 C, T0

is referred to as the reference temperature and α is the temperature

coefficient of resistivity.

Understanding the Equation

It is known that an electric current is the movement of free electrons

from one atom to the other when there is a potential difference

between the two. In the case of conductors, no gap is present between

the conduction band and valence band of the electrons. In most cases,

these bands overlap each other.

The valence electrons in a given atom are loosely bound to the nucleus

in a conducting material. Quite often, metals or conductors have a low

ionization energy and therefore, they tend to lose electrons very

fluidly. When an electric current is applied, the electrons are free to

move within the structure on their own. This happens in the case of

the normal temperature of a material.

However, when the temperature increases gradually, the vibrations in

the metal ions in the lattice structure also undergo an increase. In this

case, the atoms begin to vibrate with a higher amplitude. Such

vibrations, in turn, cause frequent collisions between the free electrons

and the remaining electrons.

Each such collision drains out some degree of energy of the free

moving electrons and renders them in a condition in which they are

not able to move. Thus, it causes a restriction in the movement of the

delocalized electrons.

In the case of metals or conductors, it is rightly said that they hold a

positive temperature coefficient. The value α is positive. For most of

the metals, the resistivity increases in a linear pattern with an increase

in the temperature in a range of 500K.

What happens in Insulators?

In the case of insulators, the forbidden energy gap between the

conduction band and the valence band is very high. The valence band

is filled with the electrons of the atoms. Diamond is a unique example

of an insulator. Here, all the valence electrons are involved in the

covalent bond formation and as a result, conduction does not take

place. The electrons are too tightly bound to the nucleus of the atom.

Solved Examples for You

Question: State the properties and features of temperature resistivity in

conductors and insulators.

Solution: The resistivity of a material is defined as the resistance

offered by a conductor having a given unit length and unit area of

cross-section. The unit of resistivity is ohm meter. The formula for

deriving resistivity is ρ = RA/L. Here, R is the resistance in ohms, A is

the area of cross-section in square meters and L is the length in

meters.

● In the case of metals or conductors, when the temperature

increases, the resistivity of the metal increases as a result. Thus,

the flow of current in the metal decreases. This phenomenon

reflects a positive temperature coefficient. The value α is

positive in this case.

● In the case of insulators, the conductivity of the material

generally increases, when the temperature is made to increase.

When the conductivity of the material undergoes an increase, it

is easy to decipher that the resistivity of the material decreases

and the current flow of the material increases.

Drift of Electrons and the Origin of Resistivity

What is resistance? The property of the material to oppose the electric

current is known as resistivity. It is inversely proportional to the drift

of electrons. To more about drift of electrons and resistivity, let’s

explore the article further to know what is resistance, the drift of

electrons and the origin of resistivity!

Introduction

The net velocity of the circuit is zero when electrons move randomly

in the circuit and electric field is not applied to the circuit. Drift force

is the force driving the electrons through a conductor and the force

opposing the drift force is resistivity.

What is Resistance or Resistivity?

The tendency of a material/device towards resistance is the resistivity

of the device/circuit. The SI unit of resistivity is ohm-meter. The unit

length across the cross-sectional area of the device is also resistivity.

Therefore, the nature and temperature of the material also define

resistivity (σ).

σ= [Math Processing Error]

The graph of resistivity as follows. The graphs depict current (I) to

voltage (V) ratio, whereas, dotted line A, B, C shows the idealized

graph. After a certain amount of current, the device starts resisting to

the current flowing in the system and the resistivity becomes constant.

Drift of Electrons

The free electrons in a conductor have random velocities and move in

random directions. When current is applied across the conductor the

randomly moving electrons are subjected to electrical forces along the

direction of the electric field.

Due to this electric field, free electrons still have their random moving

nature, but they will move through the conductor with a certain along

with force. The net velocity in a conductor due to the moving of

electrons is referred to as the drift of electrons.

Drift Velocity = \( \frac {Current} {(no.of free Electrons )*(Area of

conductor)*(Charge of Eletrons)} \)

Vd=I/(A*n*e)

For example, let’s say you are crossing a river and moving from one

bank to another bank along with the river flow, then you are the

electron which is randomly moving and river water acts as the drift

force. Then the force applied to the randomly moving electron will

result in the change of course of the path of an electron.

Examples for You on What is Resistance!

Question 1: When a potential difference V is applied across a

conductor at a temperature T, the drift velocity of electrons is

proportional to

a. √V

b. V

c. √T

d. T

Solution: V. We know that Drift velocity vd ∝ E ∝ (Vl) (∵E=Vl), so

for a particular conductor of a particular length, the drift velocity will

directly depend upon the voltage. Hence vd∝V.

Question 2: A steady current flows in a metallic conductor of

non-uniform cross-section. Which of the following quantities is

constant along the conductor?

a. Drift speed

b. Current

c. Currently density

d. None of these

Solution: Current. When a steady current flows through a metallic

conductor of non-uniform cross-section, then drift velocity

Vd=I/(Ane) or Vd∞(1/A). E∞(1/A). Both Vd and E change with A,

only current I remain constant.

Question 3: Relation between drift velocity (vd) of electron and

thermal velocity (vt) of an electron at room temp is expressed as

a. vd=vt

b. vd>vt

c. as vd<vt

d. vd=vt=0

Solution: vd<vt. Electrons with the Fermi energy carry considerable

kinetic energy. Their mean thermal velocity at temperature T should

be vt= √3kTm, which generally turns out to be quite large. The

average velocity with which electrons must pass along a conductor to

carry a current is called drift velocity is given by vd=I/(Ane) which is

much less than the thermal velocity. Hence vd<vt.

Atmospheric Electricity and Kirchhoff’s Law

Some relationship between current and voltage does exist in an

electrical circuit network. Kirchhoff’s Law helps us in solving these

relations and also help us understand those. This set of rules helps us

in solving many complex circuits, for this reason, explore the article to

know more about the Law!

Atmospheric Electricity

The global atmospheric electrical circuit is the relation between the

Earth’s surface, ionosphere, and the atmosphere. Atmospheric

electricity is the regular result of the peak results in earth’s

electromagnetic network. The induction of EArth’s surface and other

electromagnetic devices is because of the free electricity present in the

air and the clouds.

The thunderstorm acts like the batteries of the atmosphere providing

the atmosphere with the charge it needs. The atmospheric electricity

charges the ionosphere up to 400,000 volts with respect to earth’s

surface. Lighting is caused due to electric discharge is proved by some

physicists experimenters.

Video on Current Electricity

Kirchhoff’s Law

In 1845, Gustav Kirchoff, a German physicist, developed a set of rules

and theorems. To deal with the conservation of energy and potential

difference within the circuit. Kirchhoff’s Law helps us in solving

complex relation between current and potential difference commonly

known as voltage. The 2 rules developed are Kirchhoff’s Current Law

and Kirchhoff’s Voltage Law. Electrical Engineering widely uses this

Law.

1. Kirchhoff’s Current Law

Kirchhoff’s Current rule, in other words, is Kirchhoff’s first Law,

Kirchhoff’s point rule or Kirchhoff’s junction rule. The principle of

conservation of electric charges states that: At any node ( junction ) in

an electrical circuit, the sum of all currents flowing into that node is

equal to the sum of currents flowing out of that node or equivalently.

If I1, I2, and I3 are current entering junction and I4 and I5 are current

leaving junction. Then the sun of all Current entering and leaving

junction is always zero, in the case of Kirchhoff’s Current Law.

I1+I2+I3-I4-I5=0

Adding all the Current entering junctions and subtracting all the

Current leaving junctions the Current Law is derived, as the result of

this equation, the result will always be Zero. Therefore, we conclude

Kirchhoff’s current Law or Kirchhoff’s First Law.

2. Kirchhoff’s Voltage Law

Kirchhoff’s Voltage Law, in other words, is Kirchhoff’s Second Law,

Kirchhoff’s loop (or mesh). The principle of conservation of energy

states that the directed sum of the electrical potential difference

(Voltage) around any closed network is zero. In other words, the sum

of all EMFs is equivalent to the sum the potential drops in the closed

electrical network.

The algebraic sum of the emf available in the closed loop electric

network is equivalent to the product of all the resistance of the

conductors and the current in the closed loop. In conclusion, the

circuit should have the sum of Voltage drop to zero.

Solved Examples for You

Question 1: The layer of the earth’s atmosphere which contains a high

concentration of ions and free electrons and is able to reflect radio

wave is known as

A. Ionosphere

B. Stratosphere

C. Mesosphere

D. Exosphere

Solution: Option A. Ionosphere, The layer of the earth’s atmosphere

which contains a high concentration of ions and free electrons and is

able to reflect radio wave is known as the ionosphere.

Question 2: In the following circuit, the battery E1 has an emf of 12V

and zero internal resistance while the battery E has emf of 2V If the

galvanometer G reads zero, then the value of the resistance X in ohm

is

a. 10

b. 100

c. 500

d. 200

Solution: Option B. I1=12/(500+x), I2=2/x. As the galvanometer has

zero deflection we have 12/(500+x)=2/x or x=100 ohms.

3. The normal movement of electric charges among the Earth’s

surface, the various layers of the atmosphere, and especially the

ionosphere, taken together, are known as :

A. a current conducting circuit

B. the global atmospheric electrical circuit

C. charge cloud

D. none of the above

Solution: Option C. The global atmospheric electrical circuit.

Wheatstone Bridge, Meter Bridge and Potentiometer

Every other day, science presents us with one or more ways to feel

amazed. There are a host of experiments that show both how we can

use things and make newer things out of them. Experiments related to

Wheatstone Bridge and the potentiometer are among few such things

in science that invoke a curious sense of amazement. Let us study

more about the concept of Wheatstone bridge and meter bridge, along

with potentiometer.

The Concept of Wheatstone Bridge

Defined simply, a Wheatstone Bridge is an electric circuit that is used

to measure the electrical resistance of a circuit. The circuit is set out

by balancing two legs of a bridge circuit. Out of the two, one of the

legs is an unknown component which was invented by Samuel Hunter

Christie in the year 1833 and later, it improved and popularized by Sir

Charles Wheatstone in the year 1843.

Nowadays, technological progress has allowed us to make various

measurements through sophisticated tools and machines. However,

even today, the wheat bridge remains an authentic way to measure

electric resistance, down to the closest milliohms as well.

The Principle behind the Wheatstone Bridge

The usual arrangement of the Wheat stone bridge circuit has four

arms. The bridge circuit where the arms are situated consist of

electrical resistance. Out of these resistances, P and Q are the fixed

electrical resistances and these two arms are the ratio arms. Next, A

Galvanometer connects between the terminals B and D through a

switch K2. The source of voltage of this arrangement is connected to

the terminals A and C through a switch, K1.

A variable resistor S is connected between point C and D. The

potential at point D is altered by adjusting the value of a variable

resistor. If a variation in the electrical resistance value of arm CD is

brought, the value of current I2 will also vary as the voltage across

both A and C is fixed.

If we continue to adjust the variable resistance, a situation may come

when the voltage drops across the resistor S that is I2. Here, S

becomes exactly equal to the voltage drop across resistor Q that is I1.

Q. So, the potential at point B becomes equal to the potential at point

D hence the potential difference between these two points is zero

hence current through galvanometer is nil. The deflection in the

galvanometer is nil when the switch K2 is closed.

Applying Kirchoff’Law, in this condition,

P/Q = R/S

How is the Meter Bridge experiment carried out using the Wheatstone Principle?

The meter bridge experiment uses the wheat bridge experiment to

demonstrate the resistance of an unknown conductor or to make a

comparison between two unknown resistors. Through the above-stated

equation, one can easily decipher the specific resistance of a given

material

Conclusions of the wheat stone bridge principle are:

According to the Wheatstone-bridge principle, the resistance of length

AB/resistance of length BC = R / X

Let l be the length of wire between A and B and then (100 – l) is the

length of wire between B and C. Here, P = ρl / A. Since the wire has a

uniform cross-section and ρ is constant. Its resistance is proportional

to the length. That is P ∝ l, and Q ∝ (100–l). So,

L / (100–l) = R / X

This is how to draw the values of X for different values of R and the

mean value gives the value of unknown resistance X.

The Concept of Potentiometer

A potentiometer is an electric device which is used to regulate EMF

and internal resistance of a given cell. This helps in providing a

variable resistance and therefore, a variable potential difference

arising between two points in an electric circuit. It is basically a

three-terminal resistor device with an adjustable arm that increases or

reduces the resistance in the loop.

Potentiometer (Source: Wikipedia)

Solved Examples for You

Question: Describe how a potentiometer works in an arrangement.

Answer: A potentiometer consists of a uniform wire AB of manganin

or constantan that has a length of usually 10 m. it is kept stretched

between copper stripes that are fixed on a wooden board by the side of

a metre scale. The wire is then divided into ten segments each of 1 m

length.

These segments join in series through metal strips between points A

and B. A steady current is maintained in the wire AB by a constant

source of EMF Eo, called driver cell, that connects between A and B

through a rheostat. A jockey slides over the potentiometer wire which

makes contact with the wire and cell.

Potentiometer (Source: Wikimedia)

Thus we can say that the potential difference across any portion of the

potential of the potentiometer wire is directly proportional to the

length of that portion provided the current is uniform.

Cells, EMF and Internal Resistance

Cells, EMF, Internal Resistance are the components which complete

the circuit and help the flow of electricity within the circuit. Cells, emf

and internal resistance are inter-related to one another. Batteries i.e.

Cells are posses internal resistance and potential difference i.e.

voltage. Know more about Cells, emf and internal resistance in this

article, explore more below!

Cells

An “electric power supply” is also an Electric cell. Cells generate

electricity and also derives chemical reactions. One or more

electrochemical cells are batteries. Every cell has two terminals

namely:

● Anode: Anode is the terminal from where the current flows in

from out i.e. it provides an incoming channel for the current to

enter the circuit or the device.

● Cathode: Cathode is the terminal from where the current flows

out i.e. it provides an outgoing current flow from the circuit or

the device.

There are different types of cells available and some of them are as

follows:

● Electric Cells

● Fuel Cells

● Secondary Cells

● Galvanic Cells

● Photovoilatatie Cells

● Solar Cells

● Storage Cells

● Primary Cells

[Source: Studytronics]

EMF

EMF is Electromotive Force, which is measured in coulombs of

charge. It is pressure developed or an electric intensity from a

electrical energy or a source. It is a device which converts any form of

energy into electrical energy which is then measured with coulombs of

charge. EMF i.e ElectroMotive Force id denoted by, .

emf = I (R + r)

Where I is the current in amperes; R is the resistance of load in the

circuit in ohms; r is the internal resistance in ohms.

emf = E/ Q

Where E is the energy in joules; Q is the charge in coulombs.

[Source: Energy Education]

Internal Resistance

When there is current present in the device or the electrical circuit and

there’s a voltage drop in source voltage or source battery is internal

resistance. It is caused due to electrolytic material in batteries or other

voltage sources.

Internal Resistance (r) = (E – V)/I

Where E is the emf of the device; V is the potential difference

between the device; I is the current in the device. Internal Resistance

is the result of the resistance in the battery or the accumulation in the

battery. the equation used to derive this is as follows:

V = (E – Ir)

[Source: Wikipedia]

Solved Examples for You

Question 1: The terminal voltage of a cell in an open circuit condition

is

A. Less than its emf

B. More than its emf

C. Equal to its emf

D. Depends on its internal resistance

Solution: Option C. Equal to its emf. The terminal voltage of a cell in

open circuit condition will be equal to the emf of the cell as the circuit

is open there won’t be any drop across the internal resistance.

Question 2: What is the p.d. across the terminals (VT) of a cell with

emf E for the open circuit?

A. VT<E

B. VT>E

C. VT=0

D. VT=E

Solution: Option D. VT=E, When the circuit is closed, the resulting

current not only flows through the external circuit but through the

source (battery, generator, transformer, etc.) itself. All sources have an

internal resistance, which causes an internal voltage drop, slightly

reducing the voltage across the terminals.

The larger the current, the larger the internal voltage drop, and the

lower the terminal voltage. When the circuit is open, no current flows.

So there is no internal voltage drop, and the full voltage appears across

the source’s terminals. This is why the potential difference across the

terminals of a cell when connected to a circuit is slightly lesser than

the emf of the cell.

Question 3: The common dry cell produces a voltage of:

A. 1.5V.

B. 30V.

C. 60V.

D. 3V

Solution: Option A. 1.5V, A common dry cell is a type of

electricity-producing chemical cell, commonly used today for many

home and portable devices, often in form of batteries. By standards, a

common dry cell has a constant voltage of 1.5

Cells in Series and Parallel

As we know the most frequently used method to connect electrical

components is Series Connection and Parallel Connection. Since the

cell is an important part of an electric circuit. To know more about

Cells, Series Connection and parallel Connection explore the article!

Cells

Cells generate electricity and also derives chemical reactions. One or

more electrochemical cells are batteries. Every cell has two terminals

namely:

1. Anode: Anode is the terminal from where the current flows in

from out i.e. it provides an incoming channel for the current to

enter the circuit or the device.

2. Cathode: Cathode is the terminal from where the current flows

out i.e. it provides an outgoing current flow from the circuit or

the device.

Learn more about Electric Charge here in detail

There are two simplest ways for cell connectivity are as follows:

1. Series Connection: Series connection is the connectivity of the

components in a sequential array of components.

2. Parallel Connection: Parallel connection is the connectivity of

the components alongside to other components.

Cells in Series Connection

In series, cells are joined end to end so that the same current flows

through each cell. In case if the cells are connected in series the emf

of the battery is connected to the sum of the emf of the individual

cells. Suppose we have multiple cells and they are arranged in such a

way that the positive terminal of one cell is connected to the negative

terminal of the another and then again the negative terminal is

connected to the positive terminal and so on, then we can that the cell

is connected in series.

Equivalent EMF/Resistance of Cells in Series

If E is the overall emf of the battery combined with n number cells

and E1, E2, E3 , En are the emfs of individual cells.

Then E1 + E2 + E3 + …….En

Similarly, if r1, r2, r3, rn are the internal resistances of individual cells,

then the internal resistance of the battery will be equal to the sum of

the internal resistance of the individual cells i.e.

r = r1 + r2+ r3 + rn

Cells in Parallel Connection

Cells are in parallel combination if the current is divided among

various cells. In a parallel combination, all the positive terminal are

connected together and all the negative terminal are connected

together.

Equivalent EMF/Resistance of Cells in Parallel

If emf of each cell is identical, then the emf of the battery combined

with n numbers of cells connected in parallel is equal to the emf of

each cell. The resultant internal resistance of the combination is,

r =

(

1

r

1

+

1

r

2

+

1

r

3

+……..

1

r

n

)-1

Equivalent EMF/Resistance of Cells in Series and Parallel

Assume the emf of each cell is E and internal resistance of each cell is

r. As n numbers of cells are connected in each series, the emf of each

series, as well as the battery, will be nE. The equivalent resistance of

the series is nr. As, m the number of series connected in parallel

equivalent internal resistance of that series and parallel battery is nr/m.

Solved Questions For You

Q. The internal resistance of a cell of emf 1.5 V, if it can deliver a

maximum current of 3 A is,

A. 0.5 Ω

B. 4.5 Ω

C. 2 Ω

D. 1 Ω

Solution: A. For maximum amount, load resistance = 0

⇒ E = Ir

r =

E

I

=

1.5

3

= 0.5 Ω

Q.2 For a given cell, its terminal voltage depends on

A. External resistance, Internal Resistance

B. External resistance

C. Internal Resistance

D. None of these

Solution: A. Inside the cell, the energy is put into the circuit by the

cell, but some of this energy is out by the internal resistor. So the

potential difference available to the rest of the circuit is the emf minus

the potential difference lost inside the cell.