Question

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. \( \frac{2n(\phi_1 - \phi_2)}{3Rt} \)
• B. \( \frac{n(\phi_1 - \phi_2)}{3Rt} \)
• C. \( \frac{n(\phi_1 - \phi_2)}{Rt} \)
• D. \( \frac{2n(\phi_1 - \phi_2)}{Rt} \)

Hint:

Always use Faraday’s law and Ohm’s law when calculating induced current due to a changing magnetic flux.

Answer 1

The Correct Option is A

Step 1: Formula for induced current.
The induced electromotive force (EMF) is given by Faraday’s law of induction: \[ \mathcal{E} = -n \frac{d\phi}{dt} \] where \( \phi \) is the magnetic flux. For a change in magnetic flux \( \Delta \phi = \phi_1 - \phi_2 \), the induced current \( I \) is: \[ I = \frac{\mathcal{E}}{R_{\text{total}}} \] where \( R_{\text{total}} = R + \frac{R}{2} = \frac{3R}{2} \).
Step 2: Substituting values.
Substituting \( \Delta \phi \) and \( R_{\text{total}} \) into the equation for current: \[ I = \frac{2n(\phi_1 - \phi_2)}{3Rt} \]
Step 3: Conclusion.
Thus, the correct answer is (A) \( \frac{2n(\phi_1 - \phi_2){3Rt} \)}.