A 100 `muF` 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 the voltage maximum?

Explanation

`X_(C ) = ( 1)/( 2pi v C ) = ( 1)/( 2 xx 3.14 xx 60 xx 10^(-4)) ~~ 26.54 Omega`
`I_(m) = ( V_(m))/( |Z|)`
`= ( sqrt(2) V_(rms))/( sqrt( R^(2) + X_(C )^(2)))`
`= ( sqrt( 2) V_(rms))/( sqrt( R^(2) + ( 1)/( 4 pi ^(2) f^(2) C^(2))))` ....(1)
`:. I_(m ) = (( 1.414 ) ( 110))/( sqrt(( 40)^(2) + ( 1)/(( 26.54)^(2) ( 60)^(2) ( 100 xx 10^(-6))^(2))))`
`:. I_(m) = 3.24 A`