In a series `RC` circuit with an AC source, `R = 300 Omega, C = 25 muF, epsilon_0= 50 V` and `v = 50/(pi) Hz`. Find the peak current and the average power dissipated in the circuit.

Explanation

Given `R= 300 W`, `C= 25 muF`
`=25 xx 10^-6 F`,`E_0 = 50 V`,
`f_x = 50/ pi Hz`
`X_C = 1/(omegaC)`
`=(1)/(50//pi xx 2 pi xx 25 xx 10^-6)`
`=((10^4)/(25))^4`
`Z=sqrt(R^2 + X_(0)^2)`
`=sqrt((300)^2 + (10^4//25)^2)`
`sqrt( (300)^2 + (400)^2)`= 500
(a) Peak current ` E_0/Z= 50/500= 0.1A`
(b) Average Power dissipated
`=E_(rms)I_(rms)cosphi`.
`=E_0/sqrt2 xx E_0/sqrt(2Z)RZ`
`=(E_(0)^2)/(2Z)*R/Z`
`=(50 xx 50 xx 300)/(2 xx 500 xx 500)`
`=3/2 = 1.5W`