Question

An AC voltage of the form Av = 65 sin 305t where Av is in volts and t is in seconds, is applied to a series RLC circuit. If R = 38.0 12, C = 28.0 pF, and L = 0.280 H, find the following. (a) the impedance of the circuit 12 (b) the rms current in the circuit A (c) the average power delivered to the circuit W

Answer 1

Applied ac voltage, ΔV = 65 Sin 305 t. this equation is in the form ΔV = Vo Sin ωt.

Comparing the two equations we get,

Peak voltage, Vo = 65 V and angular frequency, ω = 305 rad/s

Given: R = 38 Ω; C = 28 x 10^-6 F; L = 0.28 H

Inductive reactance, X_L = ω L = 305 x 0.28 = 85.4 Ω

Capacitive, X_c = 1/ω C = 1/305 x 28 x 10^-6   = 117.1 Ω

(a)

Impedance of the circuit, Z = { R² + ( X_c - X_L )² }^1/2 = { 38² + ( 117.1 – 85.4 )² }^1/2 = 49.5 Ω

Impedance of the circuit, Z = 49.5 Ω

(b)

Rms current in the circuit, I_rms = V_rms/Z = Vo/1.41 Z = 65/1.41 x 49.5 = 0.93 A

Rms current in the circuit, I_rms = 0.93 A

(c )

Power factor of the circuit, Cos ɸ = R/Z = 38/49.5 = 0.767

Average power delivered to the circuit, P_ave = V_rms I_rms Cos ɸ = (65/1.41 ) x 0.93 x 0.767 = 32.9 W

Average power delivered to the circuit, P_ave = 32.9 W