State Kirchhoff's law for an electrical network. Using these laws deduce the condition for balance in a Wheatstone bridge.

Kirchhoff's two rules are as under: (a) Junction rule: At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction. (b) Loop rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero. The circuit diagram for Wheatstone bridge is as under: This bridge has four resistors R 1 , R 2 , R 3 and R 4 . Across one pair of diagonally opposite points, that is points A and C , a source is connected. This is called the battery arm. Between the other two vertices, B and D , a galvanometer G is connected. This is called the galvanometer arm. There will be currents flowing across all the resistors as well as a current I g through G . In the case of a balanced bridge, the resistors are such that I g = 0 . In this case, Kirchhoff's junction rule is applied to junctions D and B . Now, we apply Kirchhoff's loop rule to closed loops A D B A and C B D C . The loop A D B A gives, - I 1 R 1 + 0 + I 2 R 2 = 0 ( ∵ I g = 0 ) ∴ I 1 R 1 = I 2 R 2 or I 1 I 2 = R 2 R 1 ...(a) And the loop C B D C gives, I 4 R 4 + 0 - I 3 R 3 = 0 ( ∵ I g = 0 ) ∴ I 3 R 3 = I 4 R 4 or I 3 I 4 = R 4 R 3 ....(b) Now, let the current entering A be I then it divides into I 1 and I 2 such that, I 2 = I - I 1 . The current I 2 further divides into I g and I 4 such that I 4 = I 2 - I g . In the case of a balanced bridge, I g = 0 therefore, I 4 = I 2 . Similarly, we get I 3 = I 1 . Substituting I 3 = I 1 and I 4 = I 2 in the equation (b) we get, I 1 I 2 = R 4 R 3 ...(c) From the equations (a) and (c), we get, I 1 I 2 = R 2 R 1 = R 4 R 3 Hence, we obtain the condition, R 2 R 1 = R 4 R 3 which is the equation relating the four resistors called the balance condition for the galvanometer to give zero or null deflection.

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IMPORTANT

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A silver wire has a resistance of $2.1 Ω$ at $27.5 ℃$ and a resistance of $2.7 Ω$ at $100 ℃$ . The temperature coefficient of resistivity of silver is $x \times 10^{- 3} ℃^{- 1}$ . Determine $x$ to the nearest integer.

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Important Questions on Current Electricity

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12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 8

If the length of a wire conductor is doubled by stretching it while keeping the potential difference constant, by what factor will the drift speed of the electrons change?

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IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 9

Two

120 V

light bulbs, one of

25 W

and another of

200 W

are connected in series. One bulb burnt out instantaneously. Which one was burnt and why?

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 10

A cylindrical metallic wire is stretched to increase its length by

5 %

. Calculate the percentage change (in

%

) in resistance.

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12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 11

Two wires

A

and

B

of same length and same material, have their cross-sectional areas in the ratio

1 : 4

. What would be the ratio of heat produced in these wires when the voltage across each is constant?

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12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 12

Two bulbs whose resistances are in the ratio of

1 : 2

are connected in parallel to a source of constant voltage. What will be the ratio of power dissipation in these?

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Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 13

A potentiometer wire is

5 m

long and a potential difference of

6 V

is maintained between its ends. Find the emf (in

V

) of a cell which balances against a length of

180 cm

of the potentiometer wire.

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12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 14

A battery of emf

2.5 V

and internal resistance

r

is connected in series with a resistor of

45

ohm through an ammeter of resistance

1

ohm. The ammeter reads a current of

50 mA

. Draw the circuit diagram and calculate the value of

r

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12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 15

Amount of charge passing through the cross-section of a wire is

q (t) = a t^{2} + b t + c

. Write the dimensional formula for

a

b

and

c

. If the values of

a

b

and

c

in SI unit are

6

4

2

respectively, find the value of current at

t = 6

seconds.

A silver wire has a resistance of 2.1 Ω at 27.5 ℃ and a resistance of 2.7 Ω at 100 ℃. The temperature coefficient of resistivity of silver is x×10-3 ℃-1. Determine x to the nearest integer.

Important Questions on Current Electricity

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A silver wire has a resistance of $2.1 Ω$ at $27.5 ℃$ and a resistance of $2.7 Ω$ at $100 ℃$ . The temperature coefficient of resistivity of silver is $x \times 10^{- 3} ℃^{- 1}$ . Determine $x$ to the nearest integer.