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

(i) Potential difference, V = 6 V

1 R and 2 R resistors are connected in series. Therefore, equivalent resistance of the circuit,

Resistance = 1 + 2 = 3 R
According to Ohm’s law, V = IR

Where, I is the current through the circuit

I= \(\frac{6}{3} \) = 2 A

This current will flow through each component of the circuit because there is no division of current in series circuits. Hence, current flowing through the 2 \(\Omega \) resistor is 2 A. Power is given by the expression,

P= (I)2R = (2)2 x 2 = 8 W


(ii) Potential difference, V = 4 V

12 R and 2 R resistors are connected in parallel. The voltage across each component of a parallel circuit remains the same. Hence, the voltage across 2 R resistor will be 4 V.

Power consumed by 2 \(\Omega \) resistor is given by

\( P= \frac{V_2}{R} = \frac{42}{2} = 8 W \)

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