A series LCR circuit having `L = 10 mH`, `C = (400//pi^(2)) mu F` and R = 55 ohm is connected to 220 v variable frequency a.c. supply.
(i) Find frequency of source, for which average power absorbed by the circuit is maximum
(ii) Calculate the amplitude of current.

Explanation

Here, `L = 10 mH = 10 xx 10^(-3) H = 10^(-2) H`
`C = (400//pi^(2)) mu F = (4 xx 10^(-4))/(pi^(2))`
`R = 55 ohm`
`E_(v) = 220 V`
(i) Average power absorbed by the circuit is maximum at resonance. The resonant frequency is
`v_(0) = (1)/(2 pi sqrt(LC)) = (1)/(2 pi sqrt(10^(-2) xx (400)/(pi^(2)) xx 10^(-6))`
`v_(0) = (1)/(2 xx 2 xx 10^(-3)) = (1000)/(4) = 25 Hz`
(ii) Current is maximum at resonance
`I_(0) = sqrt2 I_(0) = sqrt2 (E_(v))/(R ) = sqrt2 xx (220)/(55) = 4 sqrt2 A`