• # question_answer A coil of 0.01 H inductance and $1\Omega$ resistance is connected to 200 V 50 Hz AC supply. Find the impedance of the circuit and time lag between maximum alternating voltage and current.

Given,   inductance,        L = 0.01 H Resistance,         $R=1\Omega$ Voltage,             ${{V}_{rms}}=200\,V$ and       Frequency,         f = 50 Hz Impedance of the circuit,             $Z=\sqrt{{{R}^{2}}+X_{L}^{2}}=\sqrt{{{R}^{2}}+{{(2\pi fL)}^{2}}}$             $=\sqrt{{{1}^{2}}+{{(2\times 3.14\times 50\times 0.01)}^{2}}}$ or         $Z=\sqrt{10.86}=3.3\,\Omega$ As,        $\tan \phi =\frac{\omega L}{R}=\frac{2\pi fL}{R}$             $=\frac{2\times 3.14\times 50\times 0.01}{1}=3.14$ $\Rightarrow$   $\phi ={{\tan }^{-1}}(3.14)=72.33{}^\circ$ $\therefore$ Phase difference, $\phi =\frac{72.33\times \pi }{180}\text{rad}$ Time lag between alternating voltage and current, $\Delta \,t=\frac{\phi }{\omega }=\frac{72.33\pi }{180\times 2\pi \times 50}$        $[\because \,\omega =2\pi f]$             $\approx \frac{1}{250}s$