Physics

Physics

Problem

An RR–CC series circuit consists of a 200 Ω200\,\Omega resistor and a 10 μF10\,\mu\text{F} capacitor connected to a 110 V110\,\text{V} (rms), 60 Hz60\,\text{Hz} AC source. a. (i) Calculate the capacitive reactance. b. (ii) Determine the impedance of the circuit. c. (iii) Find the rms current in the circuit. d. (iv) Compute the phase angle between voltage and current, indicating whether the current leads or lags. e. (v) Obtain the average power consumed and the power factor of the circuit.
Intuitive explanation

In an AC circuit with resistance and capacitance, the key is recognizing that the capacitor's opposition to current—its reactance XC=1/(2πfC)X_C = 1/(2\pi f C)—depends on frequency, unlike a resistor's fixed resistance. The total impedance ZZ combines RR and XCX_C as perpendicular components (using the Pythagorean theorem), and the phase angle between voltage and current tells you whether the circuit is more resistive or capacitive. This impedance then determines both the current magnitude and how voltage divides across each component.

Intuitive explanation

In an AC circuit with resistance and capacitance, the key is recognizing that the capacitor's opposition to current—its reactance XC=1/(2πfC)X_C = 1/(2\pi f C)—depends on frequency, unlike a resistor's fixed resistance. The total impedance ZZ combines RR and XCX_C as perpendicular components (using the Pythagorean theorem), and the phase angle between voltage and current tells you whether the circuit is more resistive or capacitive. This impedance then determines both the current magnitude and how voltage divides across each component.

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