Question

A coil of 'n' turns and resistance \(R\,\Omega\) is connected in series with a resistance \(R/4\). The combination is moved for time 't' second through flux \(\Phi _1\) to \(\Phi _2\). The induced current in the circuit is

• A. \(\frac{4n(\Phi _1-\Phi _2)}{5RT}\)
• B. \(\frac{5n^2(\Phi _1-\Phi _2)}{4RT}\)
• C. \(\frac{2n(\Phi _1-\Phi _2)}{3RT}\)
• D. \(\frac{3n(\Phi _1-\Phi _2)}{4RT}\)

Hint:

EMF is n times flux change over t; resistance is R + R/4.

Answer 1

The Correct Option is A

Step 1: Charge approach:
The charge that flows is $q=\dfrac{n\Delta\Phi}{R_{total}}$, independent of the time taken.

Step 2: Average current:
Current $=\dfrac qt=\dfrac{n(\Phi_1-\Phi_2)}{t\cdot\frac{5R}4}$.

Step 3: Simplify:
$=\dfrac{4n(\Phi_1-\Phi_2)}{5Rt}$. Option (A).

Final Answer:
The total resistance is 5R/4. \[ \boxed{A} \]