Question

The motor in a toy car operates on 6.00 V, developing a 4.50 V back emf at normal speed. If it draws 3.00 A at normal speed, what current does it draw when starting?

Final Answer

$12.0\textrm{ A}$

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 23, Problem 42 (Problems & Exercises)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A toy car is operated by a 6.00 volt battery and when it's running at its normal speed, it has a back

*emf*of 4.50 volts and a current of 3.00 amps and the question is when it's first starting, what current does it draw? So we need to know what the resistance of the motor is inside this car and so we'll take the normal voltage as the normal current times resistance and this normal voltage is the difference between the source*emf*provided by the battery and the back*emf*that it generates when it's running at normal speed and we'll solve this for*R*by dividing both sides by the current when operating at normal speed and so resistance is source*emf*minus back*emf*divided by the normal current. Now the source*emf*is going to equal the initial current times the resistance because in this case, the total voltage in the circuit will be just that of the battery— there's no back*emf*when it's initially turned on— so we can solve this for*I initial*by dividing both sides by this resistance and so we have the initial current then is the source*emf*divided by the resistance and we have a formula for resistance here and since we are dividing by this fraction, I am going to instead multiply by its reciprocal so I am multiplying by the normal current divided by the difference between the source and the back*emf*and so we have 6.00 volts times 3.00 amps over 6.00 volts minus 4.50 volts and that is 12.0 amps of current drawn initially when the car is first turned on.