Question

A coil having ' \(N\) ' turns and resistance ' \(R \Omega\) ' is connected to a galvanometer of resistance ' \(6 \text{ R } \Omega\) '. The magnetic flux linked with this coil changes from \(\phi_1\) weber to \(\phi_2\) weber in time ' \(t\) ' second. The induced current in the circuit is

• A. \(\frac{N(\phi_2 - \phi_1)}{t}\)
• B. \(\frac{N(\phi_2 - \phi_1)}{7Rt}\)
• C. \(\frac{N(\phi_2 - \phi_1)}{Rt}\)
• D. \(\frac{N(\phi_2 - \phi_1)}{6Rt}\)

Hint:

The induced current depends on the total resistance of the entire closed loop, not just the coil itself.

Answer 1

The Correct Option is B

Step 1: Induced EMF
According to Faraday's law, induced EMF $e = N \frac{\Delta \phi}{t} = N \frac{(\phi_2 - \phi_1)}{t}$.

Step 2: Total Resistance
The coil and galvanometer are in series, so total resistance $R_{total} = R + 6R = 7R$.

Step 3: Induced Current
Current $I = \frac{e}{R_{total}} = \frac{N(\phi_2 - \phi_1)}{t \cdot 7R}$.
Final Answer: (B)