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(B) According to Faraday's law of electromagnetic induction,the induced electromotive force $(e)$ in a coil of $n$ turns is given by $e = -n \frac{d\P

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$\frac{2n(\Phi_1-\Phi_2)}{3Rt}$

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(B) According to Faraday's law of electromagnetic induction,the induced electromotive force $(e)$ in a coil of $n$ turns is given by $e = -n \frac{d\Phi}{dt}$.For a finite change in flux $\Delta\Phi = \Phi_2 - \Phi_1$ over time $t$,the average induced emf is $|e| = n \frac{|\Phi_2 - \Phi_1|}{t} = n \frac{|\Phi_1 - \Phi_2|}{t}$.The total resistance of the circuit is $R_{total} = R + \frac{R}{2} = \frac{3R}{2}$.Using Ohm's law,the induced current $I$ is given by $I = \frac{|e|}{R_{total}}$.Substituting the values,$I = \frac{n|\Phi_1 - \Phi_2| / t}{3R / 2} = \frac{2n|\Phi_1 - \Phi_2|}{3Rt}$.Thus,the correct option is $B$.

$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\Phi_1$ to $\Phi_2$. The induced current in the circuit is:

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