A circuit consisting of a capacitor and an active resistance `R=110 Omega` connected in series is fed an alternating voltage with amplitude `V_(m)=110V`. In this case the amplitude of steady `-` state current is equal to `I_(m)=0.50 A`. Find the phase difference between the current and the voltage fed.

Explanation

Here, `V=V_(m) cos omegat`
`I=I_(m) cos ( omegat+varphi)`
where `I_(m)=(V_(m))/(sqrt(R^(2)+((1)/(omegaC))^(2))) tan varphi=(1)/( omega RC)`
Now `R^(2)+(1)/((omegaC)^(2))=((V_(m))/(I_(m)))^(2)`
`(1)/(omegaRC)=sqrt(((V_(m))/(RI_(m)))-1)`
Thus the current is ahead of the voltage by
`varphi=tan^(-1)((1)/(omegaRC))=tan^(-1)sqrt(((V_(m))/(RI_(m)))-1)=60^(@)`