Question

A coil having \(n\) turns and resistance \(R\Omega\) is connected with a galvanometer of resistance \(4R\Omega\). This combination is moved in time \(t\) second from a magnetic field \(w_1\) weber to \(w_2\) weber. The induced current in the circuit is

• A. \(\frac{-(w_2 - w_1)}{5Rt}\)
• B. \(\frac{-n(w_2 - w_1)}{5Rt}\)
• C. \(\frac{-(w_2 - w_1)}{Rnt}\)
• D. \(\frac{-n(w_2 - w_1)}{Rt}\)

Hint:

Remember to include total resistance (coil + galvanometer) in the circuit.

Answer 1

The Correct Option is B

Step 1: Underlying Concept: 
Induced emf: \(E = -n\frac{d\phi}{dt}\), current: \(I = \frac{E}{R_{\text{total}}}\). 
Step 2: Explanation: 
Change in flux: \(E = -n\frac{w_2 - w_1}{t}\). Total resistance: \(R_{\text{total}} = R + 4R = 5R\). Current: \[ I = \frac{E}{5R} = \frac{-n(w_2 - w_1)}{5Rt} \] Step 3: Conclusion: 
\[ \boxed{\frac{-n(w_2 - w_1)}{5Rt}} \]