For the circuit shown below, let vS(t) = 396 cos(2?60t - 30o) V, R1 = 15 ?, R2 = 35 ?, R3 = 46 ?, L1 = 33 mH, L2 = 63 mH, C = 126 ?F

Question

(a) Find impedances ZR1, ZR2, ZR3, ZL1, ZL2, ZC, and phasor VS for vS(t). (b) Find the equivalent impedance Zeq of parallel combination of ZR2 + ZC and ZR3 + ZL2. (c) Find the total impedance Zt seen from the voltage source. (d) Find the phasor for the current I. (e) Find the phasor for load voltage Vo. (f) Find the phasors for I1 and I2.

Answer 1

ZL1 = j?L1 = j12.4407 ?, ZL2 = j?L2 = j23.7504 ?
ZC = 1/(j?C) = -j21.0522 ?
Za = (R2 + ZC) || (R3 + ZL2) = 25.9642 - j2.558 ?
Zt = R1 + ZL1 + Za = 40.9642 + j9.8828 ?
I = Vs/Zt = 6.8094 - j6.4763 A
Vo = Za×I = 160.2351 - j185.5697 = 245.1762?-49.1902o V
vo(t) = 245.1762 cos(2?60t - 49.1902o) V
I1 = Vo/(R2 + ZC) = 5.7037 - j1.8713 = 6.0028?-18.1636o A
I2 = Vo/(R3 + ZL2) = 1.1057 - j4.605 = 4.7359?-76.4981o A

R1=15;R2=35;R3=46;L1=33e-3;L2=63e-3;C=126e-6;f=60;
w=2*pi*f
ZL1=j*w*L1
ZL2=j*w*L2
ZC=1/(j*w*C)
Vs=P2Rd(396,-30)
Za=P([R2+ZC,R3+ZL2])
Zt=R1+ZL1+Za
I=Vs/Zt
Ip=R2P(I)
Vo=Za*I
Vop=R2P(Vo)
I1=Vo/(R2+ZC)
I1p=R2P(I1)
I2=Vo/(R3+ZL2)
I2p=R2P(I2)