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Physics Question on Electromagnetic induction

A coil having n turns and resistance R is connected with a galvanometer of resistance 4R. This combination is moved in time t seconds from a magnetic field W1W_1 weber to W2W_2 weber. The induced current in the circuit is

A

−W2+W15Rnt-\frac{W_2+W_1}{5Rnt}

B

−n(W2+W1)5Rt-\frac{n(W_2+W_1)}{5Rt}

C

−(W2+W1)5Rnt-\frac{(W_2+W_1)}{5Rnt}

D

−n(W2+W1)Rt-\frac{n(W_2+W_1)}{Rt}

Answer

−n(W2+W1)5Rt-\frac{n(W_2+W_1)}{5Rt}

Explanation

Solution

E = ndϕdt ∴ I=εReq=ndϕReqdtn \frac{d \phi}{dt} \, \therefore \, I = \frac{\varepsilon}{R_{eq}} = \frac{nd \phi}{R_{eq} dt} i.e.i.e. I = −IReqn(W2+W1)t2−t1=−1(R+4R)n(W2+W1)t- \frac{I}{R_{eq}} \frac{n(W_2 + W_1)}{t_2 - t_1} = - \frac{1}{(R + 4R)} \frac{n(W_2 + W_1)}{t} i.e.i.e. I = −n(W2+W1)5Rt-n \frac{(W_2 + W_1)}{5 Rt}