Question

Two resistors of 12 Ω and 6 Ω are connected in parallel and draw a current of 0.6 A from a cell.

1. Draw the circuit diagram of the above arrangement.
2. Calculate the magnitude of the current in each resistor.

Answer 1

(i)

(ii) Equivalent resistance of 12 Ω and 6 Ω in parallel

\[ \frac{1}{\mathrm{R}_{p}} = \frac{1}{12} + \frac{1}{6} \]

\[ = \frac{1 + 2}{12} \]

\[ = \frac{3}{12} \]

\[ = \frac{1}{4} \]

\[ \therefore \mathrm{R}_{p} = 4 \ \Omega \]

Potential difference across the combination

\[ \mathrm{V} = \mathrm{I} \times \mathrm{R}_{p} \]

\[ = 0.6 \times 4 \]

\[ = 2.4 \ \text{V} \]

Current in 12 Ω resistor

\[ \mathrm{I}_{1} = \frac{\mathrm{V}}{\mathrm{R}_{1}} \]

\[ = \frac{2.4}{12} \]

\[ = 0.2 \ \text{A} \]

Current in 6 Ω resistor

\[ \mathrm{I}_{2} = \frac{\mathrm{V}}{\mathrm{R}_{2}} \]

\[ = \frac{2.4}{6} \]

\[ = 0.4 \ \text{A} \]