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(C) When an $A.C.$ voltage $V = V_m \sin(\omega t)$ is applied to a pure inductor of inductance $L$,the induced electromotive force $(EMF)$ is given b

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lags behind the voltage by $(\pi / 2)^c$

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(C) When an $A.C.$ voltage $V = V_m \sin(\omega t)$ is applied to a pure inductor of inductance $L$,the induced electromotive force $(EMF)$ is given by $\varepsilon = -L \frac{di}{dt}$.Applying Kirchhoff's voltage law,$V - L \frac{di}{dt} = 0$,which implies $V = L \frac{di}{dt}$.Substituting $V$,we get $V_m \sin(\omega t) = L \frac{di}{dt}$,so $di = \frac{V_m}{L} \sin(\omega t) dt$.Integrating both sides,$i = \int \frac{V_m}{L} \sin(\omega t) dt = -\frac{V_m}{\omega L} \cos(\omega t) = \frac{V_m}{\omega L} \sin(\omega t - \pi / 2)$.Comparing the phase of voltage $(\omega t)$ and current $(\omega t - \pi / 2)$,it is clear that the current lags behind the voltage by a phase angle of $\pi / 2$ radians.

An $A.C.$ voltage is applied to a pure inductor. The current in the inductor

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