Magnetic Flux & Faraday's Law question from JEE Main 2022 (28 Jun, Shift 2)

Answer: (d)

1. $e \propto N$ (same coil area, same $dB/dt$).
2. Wire length $\propto N$, so $R = \dfrac{\rho L}{\pi r^2} \propto \dfrac{N}{r^2}$.
3. $P = \dfrac{e^2}{R} \propto \dfrac{N^2 r^2}{N} = N r^2$.
4. $N \to N/2$, $r \to 2r$: $P' = \dfrac{1}{2}\times 4\,P = 2P$. So the answer is (d) Doubled.