Question

Three resistors of 6 Ω, 2 Ω and x are connected in series to a cell of e.m.f. \[ \frac{3}{2} \ \text{V} \], when the current registered in the circuit is \[ \frac{1}{6} \ \text{A} \]. Draw the circuit diagram and calculate the value of x.

Answer 1

\[\text{e.m.f.} = \frac{3}{2}\text{V; Current in the circuit} = \frac{1}{6}\text{A}\]

Equivalent resistance of all the resistors in series

R = 6 + 2 + x = 8 + x

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

\[\therefore \frac{1}{6} = \frac{\frac{3}{2}}{8 + x}\]

\[\Rightarrow 8 + x = 6 \times \frac{3}{2}\]

\[\Rightarrow 8 + x = 9\]

\[\therefore x = 9 - 8\]

\[\therefore x = 1\Omega\]