(a) Prove that an ideal capacitor in ac circuit does not dissipate power.
(b) An inductor of 200m H, capacitor of `400 mu f` and a resistaor of `10 Omega` are connected in series to ac source of 50 V of variable frequency. Calculate the
(i) angular frquency at which maximum power dissiplation occurs in the circuit and the corresponding value of the effective current, and
(iii) value of Q-factor in the circuit.

Explanation

(b) Here `L = 200 mH = 200 xx 10^(-3) H " " R = 10 Omega`
`C = 400 mu F = 400 xx 10^(-6) F " " V = 50 V`
(i) From `E = I_(v)R rArr I_(v) = (E_(v))/(R) = (50)/(10) = 5A`
Angular frquency in resonance condition `omega_(r) = (1)/(sqrt(L_(C)) = (1)/(sqrt(200 xx 10^(-3) xx 400 xx 10^(-6)) Hz`
`= (1)/(sqrt(800 xx 10^(-9))) Hz = (sqrt5 xx 10^(4))/(20)`
(ii) From the relation `Q = (1)/(R) sqrt((L)/(C)) = (1)/(10) sqrt((L)/(C))`
`= (1)/(10) sqrt((200 xx 10^(-3))/(400 xx 10^(-6))) = (1)/(10) xx sqrt((1 xx 10^(3))/(2)) = (1)/(10) xx (10 sqrt10)/(sqrt2) = sqrt5`
`1.1 xx 10^(3) = 1100s^(-1)`