A potentiometer wire, $10\,m$ long, has a resistance of $40\,\Omega $. It is connected in series with a resistance box and a $2\,V$ storage cell. If the potential gradient along the wire is $0.1\,m\,V/cm$, the resistance unplugged in the box is .............. $\Omega$
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Potential gradient along wire $=\frac{\text { potential difference along wire }}{\text { length of wire }}$
or, $0.1 \times 10^{-3}=\frac{1 \times 40}{1000} \,\mathrm{V} / \mathrm{cm}$
or, Current in wire, $I$ $=\frac{1}{400} \,\mathrm{A}$
or, $\frac{2}{40+R}=\frac{1}{400}$ or $R=800-40=760\,\Omega$
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