Atomic Energy Education Society, Mumbai

CLASS XII PHYSICS Chapter-3

CURRENT ELECTRICITY Module - 4

By Girish Kumar

PGT (Physics) AECS Narora

1) Kirchhoff’s junction rule

2) Kirchhoff’s loop rule

3) Wheatstone bridge

4) Metrebridge

5) Determination of resistivity by metrebridge

6) Potentiometer

7) Sensitivity of potentiometer

8) Difference between voltmeter and potentiometer

9) Application of potentiometer

Current Electricity

Topics covered in Module - 4

KIRCHHOFF’S LAWS:

I Law or Current Law or Junction Rule:

The algebraic sum of electric currents at a junction in any electrical

network is always zero.

Sign Conventions:

1. The incoming currents towards the junction are taken positive.

2. The outgoing currents away from the junction are taken negative.

Note: The charges cannot accumulate at a junction.The number of

charges that arrive at a junction in a given time must leave in the same

time in accordance with conservation of charges.

I1 - I2 - I3 + I4 - I5 = 0

II Law or Voltage Law or Loop Rule:

The algebraic sum of all the potential drops and emf’s along any closed

path in an electrical network is always zero.

Loop ABCA:

- E1 + I1.R1 + (I1 + I2).R2 = 0

Loop ACDA:

- (I1 + I2).R2 - I2.R3 + E2 = 0

Sign Conventions:

1. The emf is taken negative when we traverse from positive to negative

terminal of the cell through the electrolyte.

2. The emf is taken positive when we traverse from negative to positive

terminal of the cell through the electrolyte.

The potential falls along the direction of current in a current path

and it rises along the direction opposite to the current path.

3. The potential fall is taken negative.

4. The potential rise is taken positive.

Note: The path can be traversed

in clockwise or anticlockwise

direction of the loop.

Wheatstone Bridge: Currents through the arms are assumed by

applying Kirchhoff’s Junction Rule.

Applying Kirchhoff’s Loop Rule for:

Loop ABDA:

-I1.P - Ig.G + (I - I1).R = 0

Loop BCDB:

- (I1 - Ig).Q + (I - I1 + Ig).S + Ig.G = 0

When Ig = 0, the bridge is said to balanced.

By manipulating the above equations, we get P

Q

R

S

Metre Bridge:

When the galvanometer

current is made zero by

adjusting the jockey

position on the metre-

bridge wire for the given

values of known and

unknown resistances,

Metre Bridge is based

on the principle of

Wheatstone Bridge.

(Since,

Resistance α

length)

Therefore, X = R (100 – l) ⁄ l

R R R RAJ

X X X

AJ l

RJB 100 - l JB

Determination of resistivity If r is radius of the wire and l’ it's length, then resistivity of it's

material will be

ρ = X πr2/l'

Important points :

1) If the connections of galvanometer and cell are replaced the null point will be at the same positions.

2) When the resistance taken out from the resistance box have equal value to X the null point is obtained at mid-point of wire AC.

3) The wire AC is made up of an alloy nichrome or constantan so as to provide a sufficient resistance in it's small length.

4) In order to avoid the error in the reading dur to neglected resistance of copper strip the balance point should be preferably obtained at point of wire AC.

Potentiometer:

Principle:

V = I R

= I ρl/A

If the constant current flows

through the potentiometer wire

of uniform cross sectional area

(A) and uniform composition

of material (ρ), then

V = Kl or V α l

V /l is a constant.

The potential difference across any length of a

wire of uniform cross-section and uniform

composition is proportional to its length when a

constant current flows through it.

Sensitivity of a potentiometer: A potentiometer is sensitive if

1) It is capable of measuring very small potential differences 2) It shows a significant change in balancing length for a small change in potential

difference being measured. Sensitivity of a potentiometer is measure of the reciprocal of the potential gradient k along the length of it's wire Sensitivity = 1/k Sensitivity of a potentiometer can be increased by decreasing the potential gradient k along the length of wire, which can be achieved by

i) Increasing the resistance of series resistor like that of rheostat

ii) Decreasing the applied voltage of the battery connected across the potentiometer wire, provided that potential difference across the wire remains more than emf of cell to be measured

iii) For a given potential difference, the sensitivity can be increased by increasing the length of the potentiometer wire.

iv) For a potentiometer wire of fixed length, the potential gradient can be decreased by reducing the current in the circuit with the help of rheostat.

Difference between voltmeter and potentiometer

Voltmeter Potentiometer

Its resistance is high but finite. Its resistance is infinite.

It draws some current from source of emf. It does not draw any current from the source of unknown emf.

The potential difference measured by it is lesser than the actual potential difference.

The potential difference measured by it is equal to actual potential difference.

Its sensitivity is low. Its sensitivity is high.

It is based on deflection method. It is based on non-deflection method.

1. Comparison of emf’s using

Potentiometer:

The balance point is obtained

for the cell when the potential at

a point on the potentiometer

wire is equal and opposite to

the emf of the cell.

E1 = VAJ1 = I ρl1 /A

E2 = VAJ2 = I ρl2 /A

Note:

The balance point will not be obtained on the potentiometer wire if the fall

of potential along the potentiometer wire is less than the emf of the cell to

be measured.

The working of the potentiometer is based on null deflection method. So

the resistance of the wire becomes infinite. Thus potentiometer can be

regarded as an ideal voltmeter.

E1 / E2 = l1 /l2

Applications of Potentiometer

2) Internal resistance of a primary cell by potentiometer

When key K2 kept open emf of cell will be, E = KL1

with the help of resistance R and close key K2 The potential difference of cell will be V = KL2 -----2

From eq 1 & 2, E/V= L1/L2 ----- 3

Since E = I(R+r) V = IR Now, eq 3 becomes

r = R[(L1-L2)/L2]

----- 1

3) Let E1 and E2 are connected in series (E1 > E2)

when cells assist each other, let balancing length is L1,

(E1+E2 = KL1)

when cells oppose each other, let balancing length is L2,

(E1-E2 – KL2)

4) Comparison of resistance by potentiometer

Let the balancing length for resistance R1

(YX connected ) is L1, Let the balancing length for resistance R1+R2 (when YZ connected ) be L2,

IR1= KL1

and i(R1 + R2) = KL2

R2/R1= (L2-L1)/L1

E1+E2/E1-E2 = L1/L2

E1/E2 = L1+L2/L1-L2 Or