A 120-V (rms), 60 -Hz power supply is connected to an R L C...

A $120-V$ (rms), 60 -Hz power supply is connected to an $R L C$ series circuit with $R=150 \Omega, L=1.20 \mathrm{mH},$ and $C=33.5 \mu \mathrm{F}$ Find (a) the reactance of the capacitor and inductor, (b) the circuit impedance, and (c) the peak current.

Key Concepts

Peak Current

Peak current is the maximum instantaneous value of the current in an AC circuit. It can be computed by first finding the peak voltage (which is related to the RMS voltage by a factor of ?2) and then dividing it by the circuit's impedance. This concept is important for understanding the extremes of current flow in AC power systems.

Impedance

Impedance is the total opposition to the flow of alternating current in a circuit, combining both resistance and reactance. In a series circuit, it is calculated using the formula Z = ?(R² + (X_L - X_C)²). Impedance, expressed as a complex number in many analyses, is vital for determining current and voltage relationships in AC circuits.

RMS Voltage

RMS (root mean square) voltage is a statistical measure of the effective value of a time-varying voltage. It is equivalent to a constant DC voltage that would deliver the same power to a load. RMS values are crucial in power calculations for AC circuits.

AC Circuit Analysis

AC circuit analysis deals with circuits powered by alternating current sources. It encompasses concepts such as frequency, phase, and sinusoidal waveforms, which are essential for understanding how voltage and current vary over time. This analysis is foundational for calculating circuit parameters like reactance, impedance, and current in AC circuits.

Reactance

Reactance refers to the opposition that inductors and capacitors present to AC current due to their energy storage properties. It is frequency-dependent, with inductive reactance given by X_L = ?L and capacitive reactance by X_C = 1/(?C), where ? is the angular frequency. This concept is central in analyzing the behavior of reactive components in AC circuits.

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