The rms current in an R C circuit is 0.72 A. The capacitor...

The rms current in an $R C$ circuit is 0.72 A. The capacitor in this
circuit has a capacitance of 13$\mu F$ and the ac generator has a fre-
quency of 150 $\mathrm{Hz}$ and an $\mathrm{rms}$ voltage of 95 $\mathrm{V}$ . What is the resis-
tance in this circuit?

Key Concepts

Impedance in Series RC Circuits

Impedance in a series RC circuit is the combined effect of resistance and capacitive reactance, expressed as a complex quantity. It determines the overall opposition to current flow in the circuit and is calculated as the square root of the sum of the squares of the resistance and the capacitive reactance.

Capacitive Reactance

Capacitive reactance is the opposition offered by a capacitor to the change in voltage in an AC circuit. It is inversely proportional to both the frequency of the AC source and the capacitance, and it determines how much the capacitor impedes the AC current.

Ohm's Law for AC Circuits

In AC circuits, Ohm's Law is extended to account for impedance rather than just resistance. The relationship V_rms = I_rms * Z is used, where Z is the total impedance, linking the effective voltage and current and allowing the determination of unknown circuit parameters when others are known.

AC Circuits

AC circuits involve current and voltage that alternate polarity and magnitude over time. Understanding AC circuits is fundamental as they operate under different principles compared to DC circuits, involving sinusoidal signals, phase differences, and impedance rather than simple resistance.

RMS Values

RMS (root mean square) values provide a measure of the effective or equivalent constant value of an alternating current or voltage. They are crucial in AC circuit analysis because they allow comparisons to DC circuits by representing the amount of work that AC can perform as if it were DC.

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