What Is the Maximum Induced EMF in the Inductor?

[Asmaa Mohammad]

Homework Statement

A generator consists of 500 turns each of surface area 7/11 m² . It rotates at rate of 50 revolutions per second (f =50 Hz), in a field of magnetic flux density of 5*10^-4 T, its terminals were connected in series with a capacitor (Xc=110Ω), an inductor (Xl=80Ω) and a resistor (R=40Ω).

Ignoring the internal resistance of the generator, the maximum induced emf in the inductor is:
a) 30V. b) 40V. c)50V. d) 60V

Homework Equations

emf= NBAω
emf(eff)= 1/√2 emf(max)
Z= √R²+(Xl-Xc)²

The Attempt at a Solution

Here is it, and the final solution I got is not any of the choices, so please correct me, and tell me where I am wrong.

 

[Asmaa Mohammad]

This thread has been marked solved, although the answer I got of my work is not any of the choices, and it is MCQ. So, is there any explanation here?

 

[cnh1995]

This thread has been marked solved, although the answer I got of my work is not any of the choices, and it is MCQ. So, is there any explanation here?

Your method looks correct but you have calculated the rms value of induced emf in the inductor.
But the peak value is also not in the options.

 

[gneill]

I wonder if the question was first formulated to ask for the maximum voltage across the resistor and was subsequently changed to be the inductor in order to make a "new" question, but whoever did it forgot to change the answer choices accordingly?

 

[gneill]

This thread has been marked solved

No, the thread has not been marked solved. Perhaps you saw the icon at the top right of the thread:

and concluded that it had been marked solved? That icon is actually a button for you to click on once you've decided that the problem has been solved to your satisfaction.

If the thread was actually marked solved then that button would read "MARK UNSOLVED", and you could retract the solved status by clicking on it. Hope that helps

 

[Asmaa Mohammad]

Your method looks correct but you have calculated the rms value of induced emf in the inductor.

Do you mean that I shouldn't calculate the rms of the induced emf of the generator? And hence I would get the correct value of the induced emf in the inductor?! Which would be 80V?

I wonder if the question was first formulated to ask for the maximum voltage across the resistor and was subsequently changed to be the inductor in order to make a "new" question, but whoever did it forgot to change the answer choices accordingly?

Gneill, actually that is how the question is found in my textbook.

and concluded that it had been marked solved? That icon is actually a button for you to click on once you've decided that the problem has been solved to your satisfaction.

Oops, how silly I am, I didn't even notice that it was a button, thank you gneill!

 

[cnh1995]

Do you mean that I shouldn't calculate the rms of the induced emf of the generator?

Yes, because you need the peak voltage.

Which would be 80V?

Yes, I think so.

Gneill, actually that is how the question is found in my textbook.

Might be a typo.

 

[Asmaa Mohammad]

Might be a typo.

Perhaps.

Yes, because you need the peak voltage.

OK, I will take your advice.

 

[rude man]

I'd go with 80 also.