A coil having 'n' turns and resistance 'R' Ω is connected with a galvanometer of resistance '4R' Ω. What is the induced current in the circuit when this combination (coil+galvanometer) is moved in time t from a magnetic flux $\phi_1$ to $\phi_2$?

$\frac{-n(\phi_2-\phi_1)}{5Rt}$

The correct answer is Option (3) → $\frac{-n(\phi_2-\phi_1)}{5Rt}$

The magnitude of the induced electromotive force (ε) in a given coil -

$ε=-n\frac{Δ\phi}{Δt}=-\frac{n(\phi_2-\phi_1)}{t}$

where,

$\phi_1$ and $\phi_2$ are initial and final magnetic flux.

t = Duration of charge

$∴I=\frac{ε}{R_{total}}$ [By ohm's law]

$=\frac{\frac{n(\phi_2-\phi_1)}{t}}{5R}=-\frac{n(\phi_2-\phi_1)}{5Rt}$