A 20 mH inductor is connected across an AC generator that produces a peak voltage of 10.0 V. Wha

step 1 To solve for peak current for both part A and part B, we need to first access the formulation to

A 20 mH inductor is connected across an AC generator that...

$\mathrm{A} 20 \mathrm{mH}$ inductor is connected across an $\mathrm{AC}$ generator that produces a peak voltage of $10.0 \mathrm{V}$. What is the peak current through the inductor if the emf frequency is (a) $100 \mathrm{Hz}$ ?
(b) $100 \mathrm{kHz} ?$

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Key Concepts

Angular Frequency

Angular frequency is a measure of how quickly the current oscillates in an AC circuit, and it is related to the regular frequency by the equation ? = 2?f. It plays a key role in determining the inductive reactance, as higher angular frequencies lead to larger reactance values, thereby reducing the AC current through the inductor.

Ohm’s Law in AC Circuits

Ohm’s law for AC circuits relates the peak voltage, the peak current, and the impedance (in this case, the inductive reactance) through the equation I_peak = V_peak / XL. This principle allows us to compute the current flowing through an inductor by dividing the applied voltage by its frequency-dependent reactance.

Inductive Reactance

Inductive reactance is the opposition offered by an inductor to the change in current when subjected to an alternating current (AC). It is frequency dependent and is given by the formula XL = ?L, where ? is the angular frequency and L is the inductance. This concept is central to understanding how inductors behave differently at varying frequencies.

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