Electromagnetic Induction

JEE Main level, single correct, medium

66 of 153

Question 66 of 153

A coil having nn turns and resistance 4RΩ4 \mathrm{R} \Omega. This combination is moved in time tt seconds from a magnetic field W1W_1 weber to W2W_2 weber. The induced current in the circuit is

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Answer: (B) −(W2−W1)5Rt-\frac{\left(\mathrm{W}_2-\mathrm{W}_1\right)}{5 \mathrm{Rt}}

I=−IR′dϕdt\mathrm{I}=-\frac{\mathrm{I}}{\mathrm{R}^{\prime}} \frac{\mathrm{d} \phi}{\mathrm{dt}}
or, I =−1R′n[W2−W1t2−t1]=-\frac{1}{R^{\prime}} \mathrm{n}\left[\frac{\mathrm{W}_2-\mathrm{W}_1}{\mathrm{t}_2-\mathrm{t}_1}\right]
( W1W_1 and W2W_2 are not the magnetic field, but the values of flux associated with one turn of coil) I=−1(R+4R)n(W2−W1)tI=\frac{-1}{(R+4 R)} \frac{n\left(W_2-W_1\right)}{t}
or, I=−n(W2−W1)5Rt\mathrm{I}=-\frac{\mathrm{n}\left(\mathrm{W}_2-\mathrm{W}_1\right)}{5 \mathrm{Rt}}

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