A 120-V, 60 -Hz power source is connected across an 800-Ωnoninductive resistance and an unknown

step 1 we have to find the value of reactants and voltage drop across the capacitor solution some value

A 120-V, 60 -Hz power source is connected across an...

A $120-\mathrm{V}, 60$ -Hz power source is connected across an $800-\Omega$ noninductive resistance and an unknown capacitance in series. The voltage drop across the resistor is $102 \mathrm{~V} .(a) \mathrm{What}$ is the voltage drop across the capacitor? (b) What is the reactance of the capacitor?

Key Concepts

Frequency Dependence in Reactance

The reactance of capacitors (and inductors) in AC circuits is not constant but varies with the frequency of the applied voltage. In the case of capacitors, as frequency increases, the reactance decreases, and vice versa. This frequency dependence is critical for understanding the dynamic behavior of AC circuits and designing circuits that operate correctly at specific frequencies.

Voltage Division in AC Series Circuits

Voltage division in a series AC circuit occurs when the total voltage of the source is divided among components in proportion to their impedances. This principle allows for determining the voltage across any element by using the ratio of its impedance to the total impedance of the circuit. It is a fundamental tool for solving problems involving multiple series components.

Capacitive Reactance

Capacitive reactance is the opposition that a capacitor offers to the flow of AC current, and it depends on both the frequency of the AC source and the capacitance. It is given by the formula XC = 1/(2?fC), where f is the frequency and C is the capacitance. This concept is essential for analyzing the behavior of capacitors in AC circuits, particularly in calculating voltage drops and phase shifts.

Impedance and Ohm’s Law in AC Circuits

In AC circuits, impedance generalizes resistance by incorporating both the resistive and reactive effects of circuit elements. Ohm’s law in the AC context is expressed as V = IZ, where V and I are phasors and Z represents the complex impedance. This concept enables the calculation of voltage drops across individual components when the circuit’s impedance is known.

Series AC Circuit Analysis

AC circuits in series involve components such as resistors, capacitors, and inductors connected along the same path. In these circuits, the same current flows through all components, and the total impedance is the vector sum of the individual impedances. Understanding series circuits is crucial for analyzing how voltages and currents distribute in AC systems.

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