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.

#### Solution

(i) Potential difference, *V* = 6 V

1 Ω and 2 Ω resistors are connected in series. Therefore, equivalent resistance of the circuit, *R* = 1 + 2 = 3 Ω

According to Ohm’s law,*V* = *IR*

Where,*I* is the current through the circuit*I*= 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 Ω resistor is 2 A. Power is given by the expression,*P*= (*I*)^{2}*R* = (2)^{2} x 2 = 8 W

(ii) Potential difference, *V* = 4 V

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

Power consumed by 2 Ω resistor is given by*P*= *V ^{2}*/

*R*= 4

^{2}/2 = 8 W

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