An AC voltage of the form Δv = (65.0 V)sin(340t) is applied to a series RLC circuit. If R = 46.0Ω, C = 27.0 μF, and L = 0.300 H, find the following.

(a) impedance of the circuit

Ω

(b) rms current in the circuit

A

(c) average power delivered to the circuit

W

1 answer

a. Z = R + jXl + jXc = 46 + j340*0.3 - j1/340*27*10^-6 = 46 + j102 - j109,
Z = 46 - j7 = 46.5 Ohms[-8.65o].

b. Irms = Erms/Z = (65*0.707)/46.5[-8.65] = 0.988A[8.65o].

c. P = (Irms)^2 * R = (0.988)^2 * 46 = 44.9 Watts.