Question

n the circuit shown, the AC voltage source supplies an rms voltage of 156 V at frequency f. The circuit has R = 99 W, X_L = 190 W, and X_C = 93 W.

(a) Find the impedence of the circuit.

Z = W     

(b) Find the rms current flowing in the circuit.

I_rms = A     

(c) Find the phase angle in degrees between the current in the circuit and the voltage supplied by the AC source.

f = degrees     

(d) At the instant the voltage across the generator is at its maximum value, what is the magnitude of the current in the circuit?.

I = A     

Answer 1

voltage,v= 156 V

The circuit has Resistance,R = 99 W,

Inuctance Impedence,XL = 190 W,

Capacitive impedence, XC = 93 W.

Zt =sqrt(R²+(XL-XC)²)= [99 +j(190 - 93)]Ohm = [99 + j 97] = 138.60 Ohm

Angle=97/99=tan^-1(99/97)=44.41

i max = [(156)*(1.4142)]V/(138.6)Ohm = 1.591 Amps

I max trails V max by 44.41

V max occurs at angle 90

When V is at 90 the current will be at (90 -44.41) = 45.58

Therefore;

At each instant the Voltage across the generator is at it's maximum value the magnitude of the current will be (1.481A)*(sin 45.58) = 1.057 Amps