Q135 / 150 · MHT CET 2025 (25 Apr Shift 2) · Physics

A coil of ' $n$ ' turns and resistance $R \Omega$ is connected in series with a resistance $\frac{R}{2}$. The combination is moved for time 't' second through magnetic flux $\Phi_1$ to $\Phi_2$. The induced current in the circuit is

  • A
    $\frac{\mathrm{n}\left(\Phi_1-\Phi_2\right)}{3 \mathrm{Rt}}$
  • Correct answer
    B
    $\frac{2 \mathrm{n}\left(\Phi_1-\Phi_2\right)}{3 \mathrm{Rt}}$
  • C
    $\frac{2 \mathrm{n}\left(\Phi_1-\Phi_2\right)}{\mathrm{Rt}}$
  • D
    $\frac{\mathrm{n}\left(\Phi_1-\Phi_2\right)}{\mathrm{Rt}}$

Solution

Induced current in the circuit

The total resistance is the sum of the coil resistance $R$ and the series resistance $\frac{R}{2}$, giving $R_{\text{total}} = \frac{3R}{2}$.

The magnitude of the induced EMF from Faraday's law is $\varepsilon = n \frac{(\Phi_1 - \Phi_2)}{t}$, where the flux changes from $\Phi_1$ to $\Phi_2$ in time $t$.

Applying Ohm's law, the induced current is $I = \frac{\varepsilon}{R_{\text{total}}} = \frac{n (\Phi_1 - \Phi_2)}{t} \times \frac{2}{3R} = \frac{2n (\Phi_1 - \Phi_2)}{3Rt}$.

This matches option B.

Hence, the correct answer is option: 'B'.

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