An inductor and a resistor are connected in series. When...

Name: Problem 35, Chapter 21: College Physics
Uploaded: 2019-11-26T11:36:22-08:00
Duration: 2 min 42 s
Channel: Salamat Ali
Description: An inductor and a resistor are connected in series. When connected to a 60. - Hz, 90. - V (rms) source, the voltage drop across the resistor is found to be 50. V (rms) and the power delivered to the circuit is 14 W. Find (a) the value of the resistance and (b) the value of the inductance.

An inductor and a resistor are connected in series. When connected to a 60. - Hz, 90. - V (rms) source, the voltage drop across the resistor is found to be 50. V (rms) and the power delivered to the circuit is 14 W. Find (a) the value of the resistance and (b) the value of the inductance.

Key Concepts

AC Circuits and RMS Values

AC circuits operate with sinusoidally varying voltages and currents, and RMS (root mean square) values are used to express the effective or equivalent DC values of these signals. RMS values provide a measure of the energy-delivering capability of AC power, making them essential for power calculations in AC circuits.

Series RL Circuit

A series RL circuit is a fundamental configuration in AC circuit analysis where a resistor and an inductor are connected in a single loop. This arrangement results in a total impedance that combines both the resistance (real part) and the inductive reactance (imaginary part), leading to phase differences between the voltage and current which are critical in understanding circuit behavior.

Impedance in AC Circuits

Impedance is the generalized concept of resistance in AC circuits and accounts for both resistive and reactive elements. It is a complex quantity often expressed as Z = R + jX, where R represents resistance and X represents reactance, which can be inductive or capacitive. Analyzing the total impedance enables the determination of current flow and voltage drops within the circuit.

Power in AC Circuits

In AC circuits, power is often calculated using the relationship that takes into account both the voltage and current phase difference, with the average power given by P = V_rms × I_rms × cos(?), where cos(?) represents the power factor. For circuits like series RL circuits, only the resistive component dissipates real power, making it important to consider the resistor when performing power calculations.

Inductive Reactance

Inductive reactance is the property of an inductor that opposes changes in current, and it is frequency-dependent. It is given by the formula X_L = 2?fL, where f is the frequency of the AC signal and L is the inductance. This concept is vital in understanding how inductors affect the total impedance and phase relationships in an AC circuit.

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