A circuit containing a 80 mH inductor and a 60 `muF` capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.
(a) Obtain the current amplitude and rms values.
(b) Obtain the rms values of potential drops across each element.
(c) What is the average power transferred to the inductor?
(d) What is the average power transferred to the capacitor?
(e) What is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’.]

Explanation

(a) For `V=V_(0)sin omega t`
`I=(V_(0))/(|omegaL-(1)/(omegaC)|) sin (omega t +(pi)/(2)), " if "R=0`
where - sign appears if `omegaL gt 1//omegaC`, and + sign appears if `omegaL lt 1//omegaC.`
`I_(0)=11.6A, I_("rms")=8.24A`
(b) `V_("Lrms")=207V, V_("Crms")=437V`
(c) Whatever be the current I in L, actual voltage leads current by `pi//2`. Therefore, average power consumed by L is zero.
(d) For C, voltage lags by `pi//2`. Again, average power consumed by C is zero.
(e) Total average power absorbed is zero.