Compute the size of each of the inductors and capacitors Red

Compute the size of each of the inductors and capacitors. Redraw the circuit as one voltage source and an equivalent impedance. What are the Power, Reactive Power, and Apparent Power of the source

Solution

from the circuit w=942 rad/sec.

inductive reactance of j10 ohms=jwL=j10

942*L=10

L=(10/942)=0.0106 H.

capacitive reactance of -j2 ohms=-j2=1/(jwC)

2=1/(wC)

C=1/(942*2)=5.307*10^-4 F.

capacitive reactance of -j5 ohms=-j5=1/(jwC).

5=1/(wC)

C=1/(942*5)=2.123*10^-4 F.

EQUIVALENT IMPEDANCE:

Zeq=[(10+j10-j5)(j10-j2)]/[10+j10-j5+j10-j2]=(2.379+j4.907) ohms.

total load current I=[50<0/(2.379+j4.907)]=9.168<-64.13 amp.

active power=50*9.168*cos(64.13)=200 watts.

reactive power=50*9.168*sin(64.13)=412.462 VARS.

apparent power=50*9.168=458.4 VA.