A series $LR$ circuit is connected to a voltage source with $V\left(t\right)=V_0\sin \left(\omega t\right)$ . After a very large time, current $I\left(t\right)$ behaves as $\left(t_0\gg \frac{L}{R}\right)$:

When sinusoidal voltage is applied across $LR$ circuit, current is also sinusoidal but it lags by some phase.

Current will be in the form of
$I=I_{0}sin\left(\omega t-\varphi \right)$
Graph will be sinusoidal.

Here $I_0$ is the maximum current and $\varphi$ is phase difference between $V \& I$