An AC generator with an output rms voltage of 36.0 V at a...

An AC generator with an output rms voltage of 36.0 V at a frequency of 60.0 Hz is connected across a $12.0-\mu \mathrm{F}$ capacitor. Find the (a) capacitive reactance, (b) rms current, and (c) maximum current in the circuit. (d) Does the capacitor have its maximum charge when the current takes its maximum value? Explain.

Key Concepts

RMS and Peak Values

The rms value of an AC voltage or current represents its effective value in terms of power delivery, while the peak (or maximum) value indicates the highest instantaneous value reached by the waveform. The relationship between them is given by a factor of ?2, with the peak value being ?2 times the rms value.

Phase Relationships in AC Circuits

In AC circuits with capacitors, there is an inherent phase difference between current and voltage; specifically, the current leads the voltage by 90 degrees. This phase shift means that the maximum current occurs a quarter cycle before the voltage (or capacitor charge) reaches its maximum, which is important when analyzing the timing of current flow and capacitor charging.

AC Circuits

AC circuits involve alternating currents and voltages that vary sinusoidally with time. Key parameters such as frequency and amplitude are used to describe these periodic signals, and concepts like the root mean square (rms) value are essential for analyzing the effective magnitudes of voltage and current in such circuits.

Capacitive Reactance

Capacitive reactance is the measure of a capacitor's opposition to AC current and is determined by the capacitance and the frequency of the applied AC voltage. It is calculated using the formula X_C = 1/(2?fC), indicating that higher frequency or larger capacitance results in lower reactance, allowing more AC current to flow.

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