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.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Earn 100

Three resistors of $4$ ohms, $6$ ohms and $12$ ohms are connected in parallel. The combination of the above resistors is connected in series to a resistance of $2$ ohms and then to a battery of $6$ volts. Draw a circuit diagram and calculate the potential difference and the power used by the $2$ ohm resistor.

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 5

Two lamps, one rated

100 W

220 V

and the other

60 W

220 V

are connected in parallel to a

220

volt supply. What current (in

A

) is drawn from the supply line?

HARD

12th Andhra Pradesh Board

IMPORTANT

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

The average drift speed of conduction electrons in a copper wire of cross-sectional area $3.0 \times 10^{- 7} m^{2}$ carrying a current of $5 A$ is $x \times 10^{- 4} m s^{- 1}$ . Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0 \times 10^{3} kg m^{- 3}$ and its atomic mass is $63.5 u$ . Write the value of $x$ to the nearest integer.

(Take $1 e = 1.6 \times 10^{- 19} C$ and $N_{A} = 6 \times 10^{23} {mol}^{- 1}$ )

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 7

Compare the average drift speed of conduction electrons in a copper wire of cross-sectional area

3.0 \times 10^{- 7} m^{2}

carrying a current of

5 A

with the thermal speed of copper atoms at ordinary temperatures. Assume that each copper atom contributes roughly one conduction electron. The density of copper is

9.0 \times 10^{3} kg m^{- 3}

and its atomic mass is

63.5 u

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 7

Compare the average drift speed of conduction electrons in a copper wire of cross-sectional area

3.0 \times 10^{- 7} m^{2}

carrying a current of

5 A

with the speed of propagation of electric field along the conductor which causes the drift motion. Assume that each copper atom contributes roughly one conduction electron. The density of copper is

9.0 \times 10^{3} kg m^{- 3}

and its atomic mass is

63.5 u

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 1

10 Ω

thick wire is stretched so that its length becomes three times. Assuming that there is no change in its density on stretching, calculate the resistance (in

Ω

) of the stretched wire.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 2

A wire of resistance

4 R

is bent in the form of a circle. What is the effective resistance between the ends of the diameter?

EASY

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 3

Find the resistivity ( in _____

\times 10^{- 6} Ωm

) of a conductor which carries a current of density

2.5 \times 10^{6} A m^{- 2}

when an electric field of

15 V m^{- 1}

is applied across it.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 6 - Current Electricity>MODEL QUESTIONS (IPE PATTERN)>Q 4

What is the colour code for a resistor of resistance

350 mΩ

with

5 %

tolerance?

Three resistors of 4 ohms, 6 ohms and 12 ohms are connected in parallel. The combination of the above resistors is connected in series to a resistance of 2 ohms and then to a battery of 6 volts. Draw a circuit diagram and calculate the potential difference and the power used by the 2 ohm resistor.

Important Questions on Current Electricity

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