Q: If the voltage in an ac circuit is represented by the equation.

$\large V = 220 \sqrt{2}sin(314t -\phi) $ volt . calculate (a) peak and rms value of the voltage (b) average voltage (c) frequency of ac.

Sol: (a) As in case of ac,

$\large V = V_0 sin(\omega t -\phi) $

The peak value is V_{0} = 220 √2 = 311 V

V_{rms} = V_{0}/√2; V_{rms} = 220 V ;

(b) In case of ac

V_{avg} = 2V_{0}/π = 198.17V

(c) As ω = 2πf , 2πf = 314

i.e., f = 314/2π = 50 Hz.