In the circuit shown in Fig. 7.41, calculate
(a) the capacitance of the capacitor if the power factor of the circuit is unity, and
(b) the Q-factor of the circuit. Given that the angular frequency of the a.c. source is 100`s^(-1)` .
(C) Also calculate the average power dissipated in the circuit.

Explanation

Here, R `=10 Omega, L = 200 mH = 0.2 H, V_(rms) = 50 V`, power factor `cos phi =1 ` and `omega = 100 s^(-1)`
(a) For power factor to be one, `X_(L) = X_( C) rArr L omega = 1/(C omega)`
`rArr` Capacitance `C = 1/(L omega^(2)) = 1/(0.2 xx (100)^(2)) = 5 xx 10^(-4)F` or `500 muF`

(b) The Q-factor `=X_(L)/R = (L omega)/R = (0.2 xx 100)/10 =2`
( c) Average power dissipation `P_(av) = V_(rms)^(2)/R = (50)^(2)/10 = 250 W`