Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 29

Tim is using a cordless electric weed trimmer with a de motor to cut the long weeds in his back yard. The trimmer generates a back emf of \(18.00 \mathrm{V}\) when it is connected to an emf of \(24.0 \mathrm{V}\) de. The total electrical resistance of the electric motor is \(8.00 \Omega .\) (a) How much current flows through the motor when it is running smoothly? (b) Suddenly the string of the trimmer gets wrapped around a pole in the ground and the motor quits spinning. What is the current through the motor when there is no back emf? What should Tim do?

Short Answer

Expert verified
What should Tim do if there is no back emf due to the string of the trimmer being wrapped around a pole? Answer: When the motor is running smoothly, the current through it is 0.750 A. If there is no back emf and the current increases to 3.00 A, Tim should immediately turn off the trimmer, remove the string wrapped around the pole, and then restart the trimmer to avoid damaging the motor.

Step by step solution

01

Find the net emf in the motor when it is running smoothly

To find the net emf when the motor is running smoothly, we need to subtract the back emf from the total emf: Net emf = Total emf - Back emf Net emf = \(24.0 \mathrm{V} - 18.00 \mathrm{V}\) Net emf = \(6.00 \mathrm{V}\)
02

Calculate the current when the motor is running smoothly

Now, we can use Ohm's law to find the current flowing through the motor when it's running smoothly: I = Net emf / Resistance I = \(6.00 \mathrm{V} / 8.00 \Omega\) I = \(0.750 \mathrm{A}\) So, when the motor is running smoothly, the current through it is 0.750 A.
03

Find the current when there is no back emf

If the string of the trimmer wraps around a pole and the motor stops spinning, the back emf will be 0 V. In this case, we will use the initial total emf and the resistance to calculate the current: I_no_back_emf = Total emf / Resistance I_no_back_emf = \(24.0 \mathrm{V} / 8.00 \Omega\) I_no_back_emf = \(3.00 \mathrm{A}\) So, when there is no back emf, the current through the motor is 3.00 A.
04

Determine what Tim should do

The current through the motor increases significantly when there is no back emf (from 0.750 A to 3.00 A), which might indicate that the motor could be damaged with such high current. To avoid damaging the motor, Tim should immediately turn off the trimmer, remove the string that is wrapped around the pole, and then restart the trimmer.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

The magnetic field between the poles of an electromagnet is \(2.6 \mathrm{T} .\) A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance \(25 \Omega,\) radius $1.8 \mathrm{cm},\( and length \)12.0 \mathrm{cm} .$ When the current supply to the electromagnet is shut off, the total charge that flows through the coil is \(9.0 \mathrm{mC} .\) How many turns are there in the coil?
The alternator in an automobile generates an emf of amplitude $12.6 \mathrm{V}\( when the engine idles at \)1200 \mathrm{rpm}$. What is the amplitude of the emf when the car is being driven on the highway with the engine at 2800 rpm?
Two solenoids, of \(N_{1}\) and \(N_{2}\) turns respectively, are wound on the same form. They have the same length \(L\) and radius \(r\) (a) What is the mutual inductance of these two solenoids? (b) If an ac current $$I_{1}(t)=I_{\mathrm{m}} \sin \omega t$$ flows in solenoid $$1\left(N_{1} \text { turns }\right)$$ write an expression for the total flux through solenoid \(2 .\) (c) What is the maximum induced emf in solenoid \(2 ?[\text { Hint: Refer to Eq. }(20-7) .]\)
A \(0.30-\mathrm{H}\) inductor and a \(200.0-\Omega\) resistor are connected in series to a \(9.0-\mathrm{V}\) battery. (a) What is the maximum current that flows in the circuit? (b) How long after connecting the battery does the current reach half its maximum value? (c) When the current is half its maximum value, find the energy stored in the inductor, the rate at which energy is being stored in the inductor, and the rate at which energy is dissipated in the resistor. (d) Redo parts (a) and (b) if, instead of being negligibly small, the internal resistances of the inductor and battery are \(75 \Omega\) and \(20.0 \Omega\) respectively.
An airplane is flying due north at \(180 \mathrm{m} / \mathrm{s}\). Earth's magnetic field has a northward component of \(0.30 \mathrm{mT}\) and an upward component of \(0.38 \mathrm{mT}\). (a) If the wingspan (distance between the wingtips) is \(46 \mathrm{m},\) what is the motional emf between the wingtips? (b) Which wingtip is positively charged?
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Force

Read Explanation

Electric Charge Field and Potential

Read Explanation

Translational Dynamics

Read Explanation

Physical Quantities And Units

Read Explanation

Electromagnetism

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.

Sign-up for free