Question

Carefully study the circuit diagram and calculate the value of resistor x.

Answer 1

e.m.f. = 6 V; Current in the circuit = 0.4 A

Equivalent resistance of 12 Ω, 6 Ω and 3 Ω in parallel

\[\frac{1}{R_p} = \frac{1}{12} + \frac{1}{6} + \frac{1}{3}\]

\[\frac{1}{R_p} = \frac{1 + 2 + 4}{12} \]

\[\frac{1}{R_p} = \frac{7}{12}\]

\[R_p = \frac{12}{7}\]

\[\therefore R_p = 1.71\Omega\]

Equivalent resistance of all the resistors in series

R = 2 + 1.71 + x = 3.71 + x

\[\text{By Ohm's law, }\mathrm{I} = \frac{\mathrm{V}}{\mathrm{R}}\]

\[\therefore 0.4 = \frac{6}{3.71 + x}\]

\[\Rightarrow 0.4 \times (3.71 + x) = 6\]

\[\Rightarrow 0.4 \times 3.71 + 0.4x = 6\]

\[\Rightarrow1.484 + 0.4x = 6\]

\[\Rightarrow 0.4x = 6 - 1.484\]

\[\Rightarrow 0.4x = 4.516\]

\[\therefore x = \frac{4.516}{0.4}\]

\[\therefore x = 11.29\Omega\]

\[\therefore x \approx 11\Omega\]