(a) Sketch the phasor diagram for an ac circuit with a 105-Ωresistor in series with a 22.5 -mH i

step 1 In the first item of this problem, we have to do a sketch of the phaser diagram for that circuit

(a) Sketch the phasor diagram for an ac circuit with a...

(a) Sketch the phasor diagram for an ac circuit with a $105-\Omega$
resistor in series with a 22.5 -mH inductor. The frequency of the
generator is 60.0 $\mathrm{Hz}$ (b) If the rms voltage of the generator is 120 $\mathrm{V}$ ,
what is the average power consumed by the circuit?

Key Concepts

Phasor Diagram

A phasor diagram represents sinusoidally varying quantities as vectors in the complex plane, showing their magnitudes and phase angles. This concept helps in visualizing how voltages and currents add up in AC circuits and how their phase relationships affect overall circuit behavior.

AC Circuit Analysis

AC circuit analysis involves studying circuits in which the voltage and current vary sinusoidally. This analysis requires understanding the behavior of different circuit elements, such as resistors and inductors, particularly focusing on how they influence the magnitude and phase of the current relative to the applied voltage.

Inductive Reactance

Inductive reactance is the opposition that an inductor offers to the change in current, and it is given by the formula X_L = ?L, where ? is the angular frequency (2? times the frequency) and L is the inductance. This concept is essential for understanding how inductors behave at different frequencies in AC circuits.

Impedance

Impedance is the comprehensive measure of opposition to current flow in an AC circuit, combining both resistance and reactance as a complex quantity. In a series circuit with resistors and inductors, the impedance is expressed as Z = R + jX_L, which determines the overall current magnitude and phase relative to the input voltage.

Average Power

Average power in an AC circuit is the rate at which energy is consumed over a full cycle. It considers both the RMS (root mean square) values of voltage and current, as well as the phase difference between them. For circuits with purely resistive losses, the average power is calculated using P = I_rms^2 * R or by considering the voltage across the resistive component.

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