A resistor and capacitor are connected in parallel to a 277-V, 60-Hz power source. The resistor

step 1 So for this point, we're again considering a series RLC circuit, and the circuit is such that it

A resistor and capacitor are connected in parallel to a...

A resistor and capacitor are connected in parallel to a $277-\mathrm{V}, 60-\mathrm{Hz}$ power source. The resistor has a value of $50 \Omega$ and the capacitor has a value of $40 \mu \mathrm{F}$. What is the circuit power factor?

Key Concepts

Power Factor

Power factor is defined as the ratio of real power, which performs useful work, to apparent power in an AC circuit. It is also equivalent to the cosine of the phase angle between the voltage and current waveforms. A high power factor indicates efficient utilization of electrical power, whereas a low power factor suggests the presence of significant reactive power, leading to inefficiencies.

Capacitive Reactance

Capacitive reactance quantifies the opposition offered by a capacitor to the flow of AC due to its ability to store and release energy in the electric field. It is inversely proportional to both the frequency of the AC signal and the capacitance of the capacitor, and introduces a phase shift where the current leads the voltage by 90 degrees.

AC Circuit Analysis

AC circuit analysis encompasses the study of circuits powered by alternating current, where voltage and current vary sinusoidally with time. This field involves understanding the phase relationships between voltage and current, and employing phasors and complex numbers to represent these quantities for simplified circuit analysis.

Impedance and Admittance

Impedance is the complex measure of opposition a circuit offers to the flow of AC, combining resistance and reactance. In parallel circuits, it is often more convenient to work with admittance, the reciprocal of impedance, which allows for the direct addition of the contributions from individual circuit elements like resistors and capacitors.

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