Question

Calculate 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.
(ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Answer 1

(i) As the 6 V battery is connected in series, the potential difference will be different across the two given resistors. So we need the current to calculate the power.
Therefore, the net resistance, R of the circuit = (1 + 2) Ώ = 3 Ώ
Current, I = $\frac{\mathrm{V}}{\mathrm{R}}$ = $\frac{6}{3}$ = 2 A
Power consumed by the 2-ohm resistor,
P = I² R
= 2² x 2
= 8 W

(ii) As the battery is connected in parallel to the 12 Ώ and 2 Ώ resistors, the potential difference across them will be the same.
Therefore, the power,
$$\begin{gathered} P=\frac{V^2}{R} \\ P=\frac{4^2}{2}=\frac{16}{2} \\ =8W \end{gathered}$$