Question

A circuit contains a resistance $R$ and an inductance $L$ in series. An alternating voltage $V=V_0\sin \omega t$ is applied across it. The currents in $R$ and $L$ respectively will be ($I_0$ is the peak current)

• A. $I_R=I_0\cos \omega t,I_L=I_0\cos \omega t$
• B. $I_R=I_0\sin \omega t,I_L=I_0\cos \omega t$
• C. $I_R=I_0\sin \omega t,I_L=-I_0\cos \omega t$
• D. $I_R=I_L=I_0\sin \omega t$

Answer 1

The correct option is D $I_R=I_L=I_0\sin \omega t$

Phasor diagram for resistor and inductor, shown below:


For resistance $R$, voltage and current has the same phase.

$\therefore I_R=\left(\frac{V_0}{R}\right)\sin \omega t=I_0\sin \omega t$

For inductor $L$, voltage leads to current by $\frac{\pi }{2}$ but both the currents $I_R$ and $I_L$ has same phase.

$\therefore I_L=\frac{V_0}{X_L}\sin \left(\omega t\right)=I_0\sin \omega t$

$\Rightarrow I_L=I_R=I_0\sin \omega t$

Hence, option $\left(D\right)$ is correct.