Compare the power used in the 2`Omega` resistor in each of the following circuits:
a 4 V battery in parallel with `12 Omega and 2Omega` resistors

Explanation

As `12 Omega` resistor and `2Omega` resistor are connected in parallel and 4 V battery is connected in parallel with this parallel combination of resistors,
The p.d. across `2Omega` resistor will also be 4 V.
`:.` Power used in `2Omega` resistor.
`P_2 = V^2/R = 4^2/2 =16/2 =8 W`
In order to compare the power used in `2 Omega` resistor in two different circuits, find the ratio of `P_1 and P_2`.
So, `P_1/P_2 =8/8 =1 :. P_1 = P_2`
Hence `2Omega` resistor uses equal power, i.e., 8 W in both the circuits.