An AC voltage V = 20sin 200 πt is applied to a series LCR circuit which drives a current

Question

An AC voltage \(V=20sin\,200\pi t\) is applied to a series LCR circuit which drives a current \(I = 10sin \left(200\pi t + \frac {\pi}{3}\right).\) The average power dissipated is

(1) 21.6 W 

(2) 200 W 

(3) 173.2 W 

(4) 50 W

Answer 1

Correct option is (4) 50 W

\(<P>=V_{rms}I_{rms}cos \phi\)

\(=\frac {10}{\sqrt {2}}\times \frac {20}{\sqrt{2}}cos \,60^\circ\)

\(=\frac {20\times 10}{2\times 2}= 50w\)