An inductor has a 54.0-Ωreactance when connected to a 60.0 -Hz source. The inductor is removed a

step 1 Here we are asked to find the i max in inductor, maximum current in inductor, inductor. We can f

An inductor has a 54.0-Ωreactance when connected to a 60.0...

An inductor has a $54.0-\Omega$ reactance when connected to a 60.0 -Hz source. The inductor is removed and then connected to a 50.0 - Hz source that produces a 100. - V rms voltage. What is the maximum current in the inductor?

Key Concepts

Inductive Reactance

Inductive reactance is the opposition that an inductor offers to the flow of alternating current. It is calculated using the formula X? = ?L, where ? is the angular frequency and L is the inductance. This concept is crucial in AC circuits as it determines how much the inductor will impede the current at a given frequency.

Angular Frequency

Angular frequency is a measure of the rate of change of the phase of a sinusoidal waveform. It is defined as ? = 2?f, where f is the frequency in hertz. This provides a bridge between the linear frequency and the reactive properties of circuit elements like inductors and capacitors.

Relationship Between RMS and Peak Values

In AC circuits, the root mean square (RMS) value of a voltage or current is a measure of its effective value, while the peak value refers to its maximum amplitude. For a sinusoidal waveform, the peak value is ?2 times the RMS value. This relationship is essential when converting between RMS values given by instruments and the peak values used in circuit analysis.

Maximum Current Calculation in AC Circuits

The maximum or peak current in an AC circuit can be determined by dividing the peak voltage by the total impedance of the circuit. When dealing solely with an inductor, the impedance is provided by the inductive reactance. Thus, knowing both the peak voltage and the reactance allows for the calculation of the maximum current flowing through the inductor.

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