Find the reactances of the following capacitors and...

Find the reactances of the following capacitors and inductors in ac circuits with the given frequencies in each case: (a) $2-\mathrm{m} \mathrm{H}$ inductor with a frequency $60-\mathrm{Hz}$ of the ac circuit; (b) 2-mH inductor with a frequency 600-Hz of the ac circuit; (c) 20-mH inductor with a frequency 6-Hz of the ac circuit; (d) 20-mH inductor with a frequency 60-Hz of the ac circuit; (e) 2-mF capacitor with a frequency $60-\mathrm{Hz}$ of the ac circuit; and (f) 2 -mF capacitor with a frequency $600-\mathrm{Hz}$ of the AC circuit.

Key Concepts

Inductive Reactance

Inductive reactance is the opposition that an inductor presents to the change in current in an AC circuit. It is calculated using the formula X? = 2?fL, where f is the frequency and L is the inductance. This concept is crucial for understanding how inductors behave at different frequencies, affecting the phase and amplitude of the current.

Capacitive Reactance

Capacitive reactance is the opposition a capacitor provides to the change in voltage in an AC circuit. It is determined by the formula X_c = 1/(2?fC), where f denotes the frequency and C represents the capacitance. This concept is essential in AC circuit analysis as it influences how capacitors filter signals and manage phase relationships.

Angular Frequency

Angular frequency, denoted as ? and defined as ? = 2?f, is a fundamental concept in AC circuits. It converts the frequency of the AC signal into radians per second and is used in formulas to compute reactance, making it pivotal for exploring the temporal behavior of inductors and capacitors.

AC Circuit Analysis

AC circuit analysis involves studying the behavior of circuit components when subjected to alternating current. This includes calculating reactance, impedance, phase angles, and understanding the frequency-dependent characteristics of inductors and capacitors. Mastery of AC circuit analysis is essential for designing and analyzing practical electronic circuits.

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