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Chapter 21: Problem 24

At what frequency is the reactance of a \(20.0-\mathrm{mH}\) inductor equal to \(18.8 \Omega ?\)

Short Answer

Expert verified
Answer: The frequency is approximately 150.38 Hz.

Step by step solution

01

Write down the reactance formula for an inductor

To find the frequency, we will use the formula for the reactance of an inductor: \(X_L = 2\pi fL\), where \(X_L\) is the reactance, \(f\) is the frequency, and \(L\) is the inductance.
02

Substitute the given values into the formula

We know the reactance \(X_L = 18.8\Omega\) and the inductance \(L = 20.0mH = 0.020H\). Now, we can substitute these values into the formula: \(18.8 = 2\pi f (0.020)\).
03

Solve the equation for the frequency \(f\)

To find the frequency \(f\), we need to isolate \(f\) on one side of the equation. First, divide both sides by \(2\pi(0.020)\): \(f = \frac{18.8}{2\pi(0.020)}\).
04

Calculate the frequency

Now, we can calculate the frequency by plugging the numbers into the formula: \(f = \frac{18.8}{2\pi(0.020)} \approx 150.38 Hz\).
05

State the final answer

The frequency at which the reactance of a \(20.0mH\) inductor is equal to \(18.8\Omega\) is approximately \(150.38 Hz\).

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Most popular questions from this chapter

An alternator supplics a peak current of \(4.68 \mathrm{A}\) to a coil with a negligibly small internal resistance. The voltage of the alternator is \(420-\mathrm{V}\) peak at \(60.0 \mathrm{Hz}\) When a capacitor of $38.0 \mu \mathrm{F}$ is placed in series with the coil, the power factor is found to be \(1.00 .\) Find (a) the inductive reactance of the coil and (b) the inductance of the coil.
A large coil used as an electromagnet has a resistance of \(R=450 \Omega\) and an inductance of \(L=2.47 \mathrm{H} .\) The coil is connected to an ac source with a voltage amplitude of \(2.0 \mathrm{kV}\) and a frequency of $9.55 \mathrm{Hz}$. (a) What is the power factor? (b) What is the impedance of the circuit? (c) What is the peak current in the circuit? (d) What is the average power delivered to the electromagnet by the source?
A series \(R L C\) circuit has a \(0.20-\mathrm{mF}\) capacitor, a \(13-\mathrm{mH}\) inductor, and a \(10.0-\Omega\) resistor, and is connected to an ac source with amplitude \(9.0 \mathrm{V}\) and frequency \(60 \mathrm{Hz}\) (a) Calculate the voltage amplitudes \(V_{L}, V_{C}, V_{R},\) and the phase angle. (b) Draw the phasor diagram for the voltages of this circuit.
A variable inductor with negligible resistance is connected to an ac voltage source. How does the current in the inductor change if the inductance is increased by a factor of 3.0 and the driving frequency is increased by a factor of \(2.0 ?\)
A solenoid with a radius of \(8.0 \times 10^{-3} \mathrm{m}\) and 200 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of \(15 \mathrm{V}\) ms at \(22 \mathrm{kHz}\), an \(\mathrm{rms}\) current of \(3.5 \times 10^{-2} \mathrm{A}\) is measured. Assume the resistance of the solenoid is negligible. (a) What is the inductive reactance? (b) What is the length of the solenoid?
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