JEE Main 2024 — 4 April, Shift 1 — Question 44

Let potential gradient be $\lambda$.

$\therefore \mathrm{i} \times 10=\lambda \times 500=\varepsilon-\mathrm{ir}_{\mathrm{s}}$ $\Rightarrow 500 \lambda=\varepsilon-50 \lambda \mathrm{r}_{\mathrm{s}}$ Also, $\mathrm{i}^{\prime} \times 1=\lambda \times 400=\varepsilon-\mathrm{i}^{\prime} \mathrm{r}_{\mathrm{S}}$

$\Rightarrow 400 \lambda=\varepsilon-400 \lambda \mathrm{r}_{\mathrm{s}}$ $\therefore 100 \lambda=350 \lambda \mathrm{r}_{\mathrm{s}} \Rightarrow \mathrm{r}_{\mathrm{s}}=\frac{10}{35} \approx 0.3 \Omega$