A `100 mu F` capacitor in series with a `40 Omega` resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit
(b) What is the time lag between the current maximum and voltage maximum ?

Explanation

Here,
(a) Capacitance `C = 100 muF`
Resistance, `R = 40 Omega`
Rms voltage `V_(rms) = 110 V`
Frequency, f = 60 Hz
Now, impendance, `Z=sqrt(R^(2)+X_(C)^(2))`
`=sqrt(R^(2)+((1)/(omegaC))^(2))=sqrt(R^(2)+((1)/(2pifC))^(2))`
`=sqrt((40)^(2)+((1)/(sqrt(2pixx60xx100xx10^(-6))))^(2))`
`= 47.9 Omega = 48 Omega`
`I_(0)=(e_(0))/(Z)=((110)sqrt(2))/(48)=3.2A`
(b) Here, tan `phi = (X_(C))/(R )`
`rArr tan phi=(((1)/(2pixx60xx100xx10^(-6))))/(40)`
`rArr tan phi = 0.66`
`rArr phi = 33.4^(@)`
`therefore` Time lag, `Delta t = (phi)/(omega)`
`=(33.4xxpi)/(180xx2pixx60)`
`1.54 xx 10^(-3) = 1.5ms`