Question

Compare the power used in the 2 Ω resistor in each of the following circuits (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors. ​

Answer 1

Answer:

(i) 6 V battery in series with 1 Ohm and 2 Ohm resistors

A 6 V battery in series with 1 Ohm and 2 Ohm resistors

Potential difference (V) = 6 V

1 Ohm and 2 Ohm resistors are connected in series.

The equivalent resistance of the circuit,

R = 1 + 2

R = 3 Ohm

According to Ohm’s law,

V = IR

Where,

I = Current through the circuit

I= 6/3

I = 2 A

This current will flow through each component of the circuit because there is no division of current in series circuits. Hence, the current flowing through the 2Ohm resistor is 2 A.

Power is given by the expression,

P= I²R

P = 2²× 2

P = 8 W

(ii) 4 V battery in parallel with 12 Ohm and 2 Ohm resistors

Potential difference (V) = 4 V

12 Ohm and 2 Ohm resistors are connected in parallel.

The voltage across each component of a parallel circuit remains the same. Hence, the voltage across 2 Ohm resistor will be 4 V.

Power consumed by 2 Ohm resistor is given by

P= V²/R

P = 4²/2

P = 8 W

Therefore, the power used by 2 Ohm resistor is 8 W.