Question

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V, a 529-Ω resistor, and a capacitor of capacitance 9.8 μF. What must be the source voltage amplitude V for the average electrical power consumed in the resistor to be 658 W? There is no inductance in the circuit.

Answer 1

The amplitude of voltage source will be 662.799 volt

Step-by-step explanation:

We have given the resistance of the circuit R = 529 ohm

Capacitance
`C=9.8\mu F=9.8* 10^(-6)F`

Frequency f = 60 Hz

Capacitive reactance
`X_C=(1)/(\omega C)=(1)/(2* 3.14* 60* 9.8* 10^(-6))=270.80`

Impedance
`Z=√(R^2+X_C^2)=√(529^2+270.80^2)=594.288`

Power consumed by resistor = 658 W

We know that
`P=i^2R`

`658=i^2* 529`

i = 1.11528 A

We know that voltage = current × impedance = 1.11528×594.288=662.799 volt