Question

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V, a 194-Ω resistor, and a capacitor of capacitance 8.2 μF. What must be the source voltage amplitude V for the average electrical power consumed in the resistor to be 416 W? There is no inductance in the circuit.

Express your answer using two significant figures.

Answer 1

we are given the power absorbed by the resistor (416 watts in a 194 Ohm Resistor)

Lets Calculate the current required using P=I^2 R,

Current = I = sqrt ( P/R) = sqrt(416/194) =1.464 Amps

we can now calculate the voltage across the resistor E=IR , E = 1.464*194 = 284.08 Volts

Xc = 1/(2*pi*f*C)

Xc = 1/ (2*3.14*60*8.2*10^-6)

Xc = 323.649 Ohms

Voltage across Capacitor, V = i*Xc = 323.649*1.464 = 473.8 V

source voltage is square root of (473.8^2+284.08^2) = 552.4 Volts~ 55*10^2 V