A series circuit consisting of a capacitor `X_(C) =80 Omega` and a coil with active resistance `R =300 Omega` and inductance `X_(L) =40 omega` is connected to a source of alternating voltage with amplitude `V_(0) =200 V` Find
(a) the current amplitude in the circuit
(b) the phase difference between the current and voltage
(c) the amplitudes of voltage across the capacitor and the coli .

Explanation

Impedance `Z = sqrt(R^(2) + (X_(C) -X_(L))^(2)`
`sqrt( (30)^(2) + (80 -40))^(2) =50 Omega`
`i_(0) = (V_(0))/(Z) = (200)/(50) =4A`
`tan phi = (X_(C) -X_(L))/(R) = (80 -40)/(30) = (4)/(3) implies phi =53^(@)`
Currnet leads the voltage
`(c) (V_(C))_(0) =i_(0) X_(C) =4xx 80 =320V`
`(V_(coil))_(0) = i_(0) sqrt(R^(2) + X_(L)^(2)) = 4xx sqrt((30)^2) + (40)^(2)` ltbegt `4 xx 50 = 200 V`
.