Answer
True
Work Step by Step
Given an alternating current in an $RL$ circuit
The solution for this $RL$ circuit can be expressed as:
$i(t)=c_1e^{-\frac{Rt}{L}}-\frac{V_0(Lw\cos (tw)-R\sin (tw))}{L^2w^2+R^2}\\
=c_1e^{-\frac{Rt}{L}}-\frac{V_0}{\sqrt L^2w^2+R^2}\cos(wt+tan^{-1}(\frac{R}{Lw}))$
We can see the transient part $c_1e^{-\frac{Rt}{L}}$ of the current decays to zero with time, while the steady-state part of the current oscillates with the same frequency $w$ as the applied EMF.
