A coil of negligible resistance is connected in series with a 90-Ωresistor across a 120-V, 60-Hz

step 1 Find the value of voltage drop across the inductor and the value of inductor. Solution. Some val

A coil of negligible resistance is connected in series with...

A coil of negligible resistance is connected in series with a $90-\Omega$ resistor across a 120-V, 60-Hz line. A voltmeter reads $36 \mathrm{~V}$ across the resistance. Find the voltage across the coil and the inductance of the coil.

Key Concepts

Phasor Relationships

Phasor analysis is a method of representing sinusoidally varying quantities as rotating vectors in a complex plane. This approach simplifies the analysis of AC circuits by converting differential equations into algebraic equations, making it easier to handle phase differences between voltage and current across reactive components like inductors.

Inductive Reactance

Inductive reactance is the opposition to the change in current offered by an inductor in an AC circuit. It is frequency-dependent and is calculated using the formula XL = 2?fL, where f is the frequency and L is the inductance. This concept is crucial in determining the effect of inductors in circuit calculations.

Voltage Division in AC Series Circuits

This principle describes how the total voltage in a series AC circuit is divided among the components according to their impedance. It allows for determining the voltage across an individual component when the total voltage and the impedances of all components are known.

AC Circuit Analysis

This concept involves examining circuits powered by alternating current, where voltages and currents vary sinusoidally with time. It includes the use of root mean square (RMS) values to represent effective voltages and currents, and requires understanding of how circuit elements behave under AC conditions.

Impedance

Impedance is the total opposition a circuit element presents to the flow of alternating current and is a combination of resistance and reactance. In an AC circuit, impedance replaces resistance in Ohm's law and is generally represented as a complex number, encapsulating both magnitude and phase information.

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