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A motor has coils with a resistance of $30 . \Omega$ and operates from a voltage of 240 V. When the motor is operating at its maximum speed, the back emf is 145 V. Find the current in the coils (a) when the motor is first turned on and (b) when the motor has reached maximum speed. (c) If the current in the motor is 6.0 A at some instant, what is the back emf at that time?

a. 8.0 A

b. 3.2 \mathrm{A}

c. 60 \mathrm{V}

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University of Michigan - Ann Arbor

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Hope College

McMaster University

for part A were asked to find the current when the motor is first turned off. So the current here I is equal to the change in the e m f divided by resistance. This is just using owns law here. Of course. Well, they change in the IMF. If the motors turned off, there's no back current. So that's just going to be the potential 240 volts divided by 30 owns. So playing those values and you find that this is just equal to 8.0 and pierce so we can box said it is their solution for part A for part B, it says, Okay, we're gonna go ahead and turn it on. So now there is a back current. So now I Excuse me, Uh, there is a ah ah, there is a back e m f not about current. So now eyes equal toe absolute bias. Absolute sub d, which is the back, uh, back e m f divided by the resistance playing those values. And we find that this is equal to three point to amperes box. That is solution for B and lastly part. See, here we were asked to consider Ah, situation when Where the current in the motor is six and peers at some point. And it says, What's the backing of meth at this time? Well, okay, we're just gonna kind of reverse that equation. That equation there. So now we saw for the back GM. If we find that this is equal to the IMF minus the current I times the resistance are so playing in that six amperes for the current, we find that the back you meth is 60 volts. Chloe can go ahead and box that in as the solution for part C.