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.

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aristeus aristeus · Answer 1 · 2019-09-12T09:29:46+02:00

Answer:

The amplitude of voltage source will be 662.799 volt

Explanation:

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

Capacitance [tex]C=9.8\mu F=9.8\times 10^{-6}F[/tex]

Frequency f = 60 Hz

Capacitive reactance [tex]X_C=\frac{1}{\omega C}=\frac{1}{2\times 3.14\times 60\times 9.8\times 10^{-6}}=270.80[/tex]

Impedance [tex]Z=\sqrt{R^2+X_C^2}=\sqrt{529^2+270.80^2}=594.288[/tex]

Power consumed by resistor = 658 W

We know that [tex]P=i^2R[/tex]

[tex]658=i^2\times 529[/tex]

i = 1.11528 A

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