An alternating emf 200 virtual volts at $50Hz$ is connected to a circuit of resistance $1\Omega$ and inductance $0.01 H$. What is the phase difference between the current and the emf in the circuit? Also, find the virtual current in the circuit.

In case of an $L-R$ AC circuit, the voltage leads the current in phase by an angle, $\varphi ={\tan }^{-1}\left(\frac{X_L}{R}\right)$.

Here, 

$$\begin{gathered} X_L=\omega L=\left(2\pi fL\right) \\ =\left(2\pi \right)\left(50\right)(0.01)=\pi \Omega . \end{gathered}$$

and, $R=1\Omega$.

Therefore, $\varphi ={\tan }^{-1}\left(\pi \right)\approx 72.3° .$

Further, $i_{rms}=\frac{V_{rms}}{\left|\mathit{Z}\right|}=\frac{V_{rms}}{\sqrt{R^2+{X_L}^2}}$,

Substituting the values, we have

$i_{rms}=\frac{200}{\sqrt{{\left(1\right)}^2+{\left(\pi \right)}^2}}=60.67 A .$