Question

A circuit containing an `80mH` inductor and a `60muF` capacitor in series is connected to a `230V-50Hz` Supply. The resistance in the circuit is negligible .
(a) Obtain the current amplitude and rms currents.
(b) Obtain the rms values of voltage across inductor and capacitor.
(c ) What is the average power transferred to the inductor and to the capacitor?
(d) What is the total power absorbed by the circuit?

Answer 1

Here, `L = 800 mH = 800 xx 10^(-3) H`
`C = 60 mj F = 60 xx 10^(-6) F , R = 15 ohm`
`E_(v) = 230 V ,v = 50 hz`
`X_(L) = omega L = 2 pi v L`
`= 2 xx (22)/(7) xx 50 xx 800 xx 10^(-3) = 251.43 Omega`
`X_(C ) = (1)/(omega C) = (1)/(2 pi v C)`
` = (1)/( 2 xx (22)/(7) xx 50 xx 60 xx 10^(-6)) = 53.03 ohm`
`Z = sqrt(R^(2) + (X_(L) = X_(C ))^(2))`
`= sqrt(15^(2) + (251.43 - 53.03)^(2))= 198.97 ohm`
`I_(v) = (E_(v))/(Z) = (230)/(198.97) = 1.156 A`
Average power tranferred to resistance
`P_(R ) = I_(v)^(2) xx R = (1.156)^(2) xx 15 = 20.05` watt
Average power transferred to Inductor `P_(L) = 0`
Average power transferred to Capacitor `P_(C ) = 0`
Total power absorbed `E_(v) I_(v) cos phi`
`P = E_(v) I_(v) (R//Z)`
`P = (230 xx 1.156 xx 15)/(198.97) = 20.05` watt.