Q 12-03-186JEE MainJEE Main 2022 (28 Jul, Shift 1)Medium
A potentiometer wire $AB$ of resistance $20\ \Omega$ and length $300$ cm is connected in series with a resistance box (R.B.) and a standard cell of emf $4$ V. For a resistance $R$ of resistance box introduced into the circuit, the null point for a cell of $20$ mV is found to be $60$ cm. The value of $R$ is ______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 780
Potential gradient $= \dfrac{20\ \text{mV}}{60\ \text{cm}}$, so the full $300$ cm wire carries $100$ mV $= 0.1$ V.
Current in the wire: $I = \dfrac{0.1}{20} = 5\times10^{-3}$ A.
$$4 = 5\times10^{-3}(20 + R) \Rightarrow 20 + R = 800 \Rightarrow R = 780\ \Omega$$
Solution by Sreeraj P, M.Sc Physics