An AC power source has an rms voltage of 120 V and operates...

Name: Problem 14, Chapter 21: College Physics
Uploaded: 2019-11-16T16:23:30-08:00
Duration: 2 min 18 s
Channel: Averell Hause
Description: An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 47 - H inductor, determine (a) the inductive reactance and (b) the rms current through the inductor.

An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 47 - H inductor, determine (a) the inductive reactance and (b) the rms current through the inductor.

Key Concepts

Inductive Reactance

Inductive reactance is the opposition that an inductor offers to the change in current in an AC circuit. It is calculated using the formula X_L = ?L, where ? is the angular frequency and L is the inductance. This concept is essential for understanding how inductors influence the amplitude and phase of currents in AC circuits.

AC Circuit Analysis

This concept involves understanding how alternating current (AC) circuits are analyzed. AC circuit analysis requires considering the sinusoidal nature of voltage and current, and the use of phasor representation to solve circuit problems that include resistors, capacitors, and inductors. It is essential for understanding how different circuit elements interact with a time-varying source.

Root Mean Square (RMS) Voltage

RMS voltage is a statistical measure of the magnitude of a varying voltage. It is particularly important in AC circuits since it gives a value equivalent to a DC voltage that would produce the same average power in a resistive load. Understanding RMS voltage is necessary when calculating current and power in AC circuits.

Frequency and Angular Frequency

Frequency, measured in Hertz (Hz), represents the number of cycles per second in an AC signal. Angular frequency, usually denoted by ?, is related to frequency by ? = 2?f. This conversion is crucial when calculating reactance in AC circuits, as many formulas, such as for inductive reactance, rely on angular frequency.

Ohm's Law in AC Circuits

Ohm's law for AC circuits relates the RMS voltage, current, and impedance (which may be a combination of resistance and reactance). In a purely inductive circuit, the impedance is equal to the inductive reactance. This relationship, given by I_rms = V_rms / X_L, is fundamental for analyzing current flow in AC circuits.

Transcript

Please give Ace some feedback