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) Given `L=80MH, C=60(mu)F, E_(v)=230V, f=50Hz`
Since the circuit has no resistance, so impedance of the circuit is equal to its reactance.
`Z=X=X_(C)_X_(L)=(1)/(100 pi C)-100pi L=28 (Omega)`
Current amplitude is `I_(0)=(E_0)/(Z)=(230 sqrt(2))/(28)=11.6A`
(b) The rms volatge across capacitor is
`V_(Lv)=I_(v)X_(L)=(111.6//sqrt(2))100 (pi)L=206 V`
(c ) Average power transferred to inductor and capacitor will be zero because whatever energy is used in building up of charges on capacitor (current in case of inductor ) is returned in discharging the capacitor (decay of current in case of inductor).
(d) As there is no resistance in the circuit, power factor of hte circuit is `cos(phi) =R//Z=0`. Hence, no power is absorbed by the circuit.