A `200muF` capacitor is in series with a `50Omega` resistor and is connected to a 220 V, 50 Hz ac source
(i) What is the maximum current in the circuit
(ii) What is the difference in time when the current and the voltage attain maximum values?

Explanation

Angular frequency of the source,
`omega=2pif=2times3.14times50Hz`
`C=200muF=2times10^-4F`
Maximum current through the circuit ,
`I_0=V_0/(sqrt(R^2+1/(C^2omega^2)))`
`=(sqrt2times220)/(sqrt((50)^2+1/((2times10^-4)^2times4times(3.14)^2times(50)^2)))`
Now if`theta` is the phase angle then
`tantheta=1/(omegaCR)=1/(2pifCR)=1/(2times3.14times50times2times10^-4times50)`
=0.3185
or, `theta=tan^-1(0.3185)=17.67^@=(17.67timespi)/180rad`
If the voltage and the current attain maximum value at a time difference of t, then
`theta=omegat`
or,`t=theta/omega=(17.67timespi)/(180times2pitimes50)=9.82times10^-4s`