Question

In the circuit shown, the AC voltage source supplies an rms voltage of 142 V at frequency f. The circuit has R = 106 W, X_L = 186 W, and X_C = 92 W.

(a) Find the impedence of the circuit.

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

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

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

Answer 1

Rms voltage, V_rms = 142 V

Resistance, R = 106 Ω

Inductive reactance, X_L = 186 Ω

capacitive reactance, X_c = 92 Ω

(a)

Impedance of the circuit, Z = {R² + ( X_L - X_C )²}^1/2 = {106² + (186 - 92 )²}^1/2 = 157.2Ω

(b)

Rms current in the circuit, I_rms = V_rms /Z = 142 /157.2 = 0.903 A

( c)

If ɸ is the phase angle between current and voltage then,

Cosɸ = R/Z = 106/157.2 = 0.8015

ɸ = Cos^-1 0.8015 = 36.7⁰

is the phase angle between current and voltage, ɸ = 36.7⁰

( d)

The maximum current in the circuit, I_m = I_rms = 1.41 x 0.903 = 1.27 A