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Chapter 28: Problem 4

Why does it make sense that inductive reactance increases with frequency?

Short Answer

Expert verified
Inductive reactance increases with frequency, due to the formula used to calculate inductive reactance (\(X_L = 2\pi fL\)). In this formula, frequency (f), inductance (L), and the constant \(2\pi\) are multiplied together. This means, for a fixed inductance, as frequency (the number of cycles per second) increases, the inductive reactance also increases, showing a direct proportionality.

Step by step solution

01

Understanding Inductive Reactance

Inductive reactance is given by the product of the frequency (f), inductance (L) and the constant \(2\pi\). This relationship is represented by the equation \(X_L = 2\pi fL\).
02

Understanding Frequency

Frequency refers to the number of cycles a signal makes in a second. Frequency is a key element that comes to play in the equation for inductive reactance.
03

Analyze The Relationship

From the inductive reactance formula, it's clear that as frequency (f) increases, the inductive reactance \(X_L\) also increases as they are directly proportional to each other. This relationship shows why an increase in frequency results in an increase in inductive reactance.

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Most popular questions from this chapter

The applied voltage in a series \(R L C\) circuit lags the current. Is the frequency above or below resonance?

Much of Europe uses AC power at \(230 \mathrm{V}\) rms and \(50 \mathrm{Hz}\). Express this AC voltage in the form of Equation \(28.3,\) taking \(\phi_{V}=0\)

A series \(R L C\) circuit has \(R=18 \mathrm{k} \Omega, C=14 \mu \mathrm{F},\) and \(L=0.20 \mathrm{H}\) (a) At what frequency is its impedance lowest? (b) What's the impedance at this frequency?

Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a 5.0 -kg mass is connected to a spring with \(k=1.44 \mathrm{kN} / \mathrm{m} .\) This is then modeled by an \(L C\) circuit with \(L=2.5 \mathrm{H} .\) What should \(C\) be in order for the \(L C\) circuit to have the same resonant frequency as the mass-spring system?

(a) A \(2.2-\mathrm{H}\) inductor is connected across \(120-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) power. Find the rms inductor current. (b) Repeat if the same inductor is connected across the \(230-\mathrm{V}\) rms, \(50-\mathrm{Hz}\) power commonly used in Europe.
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