Q 12-03-174JEE MainJEE Main 2022 (26 Jul, Shift 2)Medium
A potentiometer wire of length $300\ \text{cm}$ is connected in series with a resistance $780\ \Omega$ and a standard cell of emf $4\ \text{V}$. A constant current flows through the potentiometer wire. The length of the null point for a cell of emf $20\ \text{mV}$ is found to be $60\ \text{cm}$. The resistance of the potentiometer wire is ______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 20
With wire resistance $r$, the potential gradient is $\dfrac{4r}{(780 + r)\times300}\ \text{V cm}^{-1}$:
$$0.02 = 60\times\frac{4r}{300(780 + r)}\ \Rightarrow\ 6(780 + r) = 240r\ \Rightarrow\ r = \frac{4680}{234} = 20\ \Omega$$
Solution by Sreeraj P, M.Sc Physics