Find it in phasor and time domain form Solutionby appliing b

Find i(t) in phasor and time domain form.

Solution

by appliing below equations .

circuit :

V(t) = 120 sinn( 377t + 60^o )

R = 20 ohm

L = 40 mH ,

C = 50 UF

Z_R = 20 ohm,

Z_L= wl < 90^o   =    314 * 40 * 10^-3 = 125.6

Z_c= 1/ wc < -90^o =   1/ 314 x 50 x 10-^-6 = 63.69

Series with resistance + inductor =   sqrt ( R² + XL² )=   (20 ²   + 125.6² )    =  sqrt (400 +15776.36) = 127.18

Z₁ = 127.18

Z₂= 63.69

Z = 63.69 x 127.18 /  63.69+ 127.18  =    8100.09 / 190.87 = 42.43   

I   =   V /Z    =   120 sin ( 377t + 60⁰) /42.43