Question

A sinusoidal voltage of peak value 300 V and an angular frequency $ \omega =400\,\text{rad/s} $ is applied to series L-C-R circuit, in which $ R=3\Omega ,\,L=20\,mH $ and $ C=652\mu F. $ The peak current in the circuit is

• A. $ 30\sqrt{2}A $
• B. $ 60\,A $
• C. $ 100\,A $
• D. $ 60\sqrt{2}\,A $

Answer 1

Answer: (B)

The impedance of the circuit is
$ Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{C}_{C}})}^{2}}} $
$ {{X}_{L}}=\omega L=400\times 20\times {{10}^{-2}}=8H $
$ {{X}_{C}}=\frac{1}{\omega C}=\frac{1}{400\times 625\times {{10}^{-6}}}=4F $
$ X=\sqrt{{{(3)}^{2}}+{{(8-4)}^{2}}}=5 $
The peak current in the circuit
$ i=\frac{E}{Z}=\frac{300}{5}=60A $