Question

A coil of 'n' turns and resistance $R \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time 't' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is ______.

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

Hint:

Always double-check if the question provides just the coil's resistance or an additional external resistance. A classic trap is calculating the current using only the coil's internal resistance $R$, ignoring the external series component.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
According to Faraday's Law of Induction, the induced e.m.f. ($e$) is equal to the rate of change of magnetic flux linked with the coil. For $n$ turns, $e = -n \frac{d\phi}{dt}$.

Step 2: Formula Application:
The total resistance of the circuit is $R_{total} = R + R/2 = \frac{3R}{2}$. The magnitude of the average induced e.m.f. is $e = \frac{n(\phi_1 - \phi_2)}{t}$.

Step 3: Explanation:
Induced current $I = \frac{e}{R_{total}} = \frac{n(\phi_1 - \phi_2)/t}{3R/2}$. Rearranging the terms, we get $I = \frac{2n(\phi_1 - \phi_2)}{3Rt}$.

Step 4: Final Answer:
The induced current is $\frac{2n(\phi_1 - \phi_2)}{3Rt}$.