/*! 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 71 The field coils used in an ac mo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 21: Problem 71

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) $0.20 \mathrm{kHz} ?$

Short Answer

Expert verified
Answer: (a) 1.66 H (b) 0.055 H

Step by step solution

01

Calculate the inductive reactance at each frequency

First, we need to calculate the inductive reactance (\(X_L\)) for both frequencies using the formula: $$X_L = \sqrt{Z^2 - R^2}$$ For (a): $$X_{L1} = \sqrt{(35.0\,\Omega)^2 - (0.45\,\Omega)^2}$$ For (b): $$X_{L2} = \sqrt{(35.0\,\Omega)^2 - (0.45\,\Omega)^2}$$ Notice that the given impedance and resistance are the same for both frequencies, so our calculation for both \(X_{L1}\) and \(X_{L2}\) is the same.
02

Calculate the inductance for each frequency

Now that we have the inductive reactance at each frequency, we can use the formula that relates frequency, inductance, and inductive reactance: $$X_L = 2\pi f L$$ We will solve for \(L\) at each frequency: For (a): $$L_1 = \frac{X_{L1}}{2\pi f_1}$$ For (b): $$L_2 = \frac{X_{L2}}{2\pi f_2}$$
03

Plug in the values and compute the results

Now we will plug in the values for the inductive reactance and frequency, and compute the inductance for both cases: For (a): $$L_1 = \frac{\sqrt{(35.0\,\Omega)^2 - (0.45\,\Omega)^2}}{2\pi (60.0\,\mathrm{Hz})}$$ For (b): $$L_2 = \frac{\sqrt{(35.0\,\Omega)^2 - (0.45\,\Omega)^2}}{2\pi (0.20\,\mathrm{kHz})}$$ Solving for \(L_1\) and \(L_2\), we get the required inductance for each frequency: $$L_1 = 1.66 \,\mathrm{H}$$ $$L_2 = 0.055 \,\mathrm{H}$$

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 television set draws an rms current of \(2.50 \mathrm{A}\) from a \(60-\mathrm{Hz}\) power line. Find (a) the average current, (b) the average of the square of the current, and (c) the amplitude of the current.
An ac circuit contains a \(12.5-\Omega\) resistor, a \(5.00-\mu \mathrm{F}\) capacitor, and a \(3.60-\mathrm{mH}\) inductor connected in series to an ac generator with an output voltage of \(50.0 \mathrm{V}\) (peak) and frequency of \(1.59 \mathrm{kHz}\). Find the impedance,
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?
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 capacitor is connected across the terminals of a 115 \(\mathrm{V}\) rms, \(60.0-\mathrm{Hz}\) generator. For what capacitance is the rms current \(2.3 \mathrm{mA} ?\)
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Torque and Rotational Motion

Read Explanation

Physics of Motion

Read Explanation

Atoms and Radioactivity

Read Explanation

Thermodynamics

Read Explanation

Fields in Physics

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.