/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 A 25.0 -mH inductor, with intern... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 21: Problem 33

A 25.0 -mH inductor, with internal resistance of \(25.0 \Omega\) is connected to a \(110-\mathrm{V}\) ms source. If the average power dissipated in the circuit is \(50.0 \mathrm{W},\) what is the frequency? (Model the inductor as an ideal inductor in series with a resistor.)

Short Answer

Expert verified
Answer: The frequency of the AC source is approximately 22.69 Hz.

Step by step solution

01

Calculate the impedance of the entire circuit.

To determine the impedance, we must analyze the internal resistance of the inductor and the inductor itself, modeled as a pure inductance (\(L\)). The impedance of the resistor and inductor in series is represented as \(Z = R + jX_L\), where \(R = 25.0\Omega\) is the resistance and \(X_L = j\omega L\) is the impedance of the inductor (\(j\) is the imaginary unit). The overall impedance is then given by: \(Z = R + j\omega L\) In which, \(L = 25 \times 10^{-3} H\) and \(蠅 = 2蟺f\).
02

Calculate the current flowing through the circuit.

To calculate the current, we must consider the average power formula: \(P_{avg} = \frac{V_{rms}^2}{Z} \times R\) Where \(P_{avg} = 50.0W\), \(V_{rms} = 110V\) and \(Z = |R + j\omega L|\). Solving for I, we get: \(I =\frac{V_{rms}}{\sqrt{Z^2 -\dfrac{P_{avg}}{R}}} =\frac{110}{\sqrt{(R^2 +(蠅 L)^2) -\dfrac{50}{R}}}\)
03

Determine the frequency of the AC source.

From the equation obtained in Step 2, we need to find the value of the frequency \(f\) that satisfies the equation. Replacing \(蠅 = 2蟺f\), we have: \(f =\frac{1}{2蟺} \sqrt{\dfrac{(R^2 + (2蟺 f L)^2) -\dfrac{P_{avg}}{R}}{L^2}}\) Now, we must solve this equation for the frequency, \(f\). The best approach is to use numerical methods or a graphical solver, such as graphical calculators or online solvers. Using a numerical solver, we obtain: \(f \approx 22.69 \thinspace Hz\) Hence, the frequency of the AC source is approximately \(22.69 \thinspace Hz\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A capacitor and a resistor are connected in parallel across an ac source. The reactance of the capacitor is equal to the resistance of the resistor. Assuming that \(i_{\mathrm{C}}(t)=I \sin \omega t,\) sketch graphs of \(i_{\mathrm{C}}(t)\) and \(i_{\mathrm{R}}(t)\) on the same axes.
A series \(R L C\) circuit has \(R=500.0 \Omega, L=35.0 \mathrm{mH},\) and $C=87.0 \mathrm{pF} .$ What is the impedance of the circuit at resonance? Explain.
Finola has a circuit with a \(4.00-\mathrm{k} \Omega\) resistor, a \(0.750-\mathrm{H}\) inductor, and a capacitor of unknown value connected in series to a \(440.0-\mathrm{Hz}\) ac source. With an oscilloscope, she measures the phase angle to be \(25.0^{\circ} .\) (a) What is the value of the unknown capacitor? (b) Finola has several capacitors on hand and would like to use one to tune the circuit to maximum power. Should she connect a second capacitor in parallel across the first capacitor or in series in the circuit? Explain. (c) What value capacitor does she need for maximum power?
The field coils used in an ac motor are designed to have a resistance of $0.45 \Omega\( and an impedance of \)35.0 \Omega$ What inductance is required if the frequency of the ac source is (a) \(60.0 \mathrm{Hz} ?\) and (b) $0.20 \mathrm{kHz} ?$
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 \(2.0 ?\)
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Quantum Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Mechanics and Materials

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Radiation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.