A series ac circuit contains a 500 omega resistor a 150 mu F

A series ac circuit contains a 50.0 omega resistor, a 15.0 mu F capacitor. A 0.200.H inductor, and a 60.0-Hz generator that has an rms output of 90.0 v. Find the average power delivered to the circuit.

Solution

Inductive reactance

X_L=2pifL =2pi*60*0.2 =75.4 ohms

Capacitive reactance

X_C=1/2pifC =1/2pi*60*(15*10^-6) =176.84 ohms

Impedance

Z=sqrt[R²+(X_L-X_C)²]=sqrt[50²+(75.4-176.84)²]

Z=113.1 ohms

Rms Current

I=V/Z =90/113.1 =0.7958 A

Phase ang;e

o=tan^-1(X_L-X_C/R)=-63.76^o

Average power delivered is

P=VICos(o) =90*0.7958*Cos(-63.76)

P=31.67 Watts