Question

An ac series circuit consists of a voltage source of frequency f = 60 Hz and voltage amplitude V, a resistor of resistance R = 593 Ω, and a capacitor of capacitance C = 2.8×10−6F. What must the source voltage amplitude V be for the average electrical power consumed in the resistor to be 382 watts? There is no inductance in the circuit.

Answer 1

Here, for the impedance in the circuit is Z

Z = sqrt(593^2 + (1/(2pi * 60 * 2.8 *10^-6))^2)

Z = 1117.6 Ohm

for the average power consumed

P = (V/Z)^2 * R

let the amplitude of the volage is V

as Vrms = V/sqrt(2)

382 = (V/(sqrt(2) * 1117.6))^2 * 593

solving for V

V = 1270 V

the voltage source amplitude is 1270 V