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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.

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