Formula for the average EMF of generator

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Homework Help Overview

The discussion revolves around the average electromotive force (EMF) of a generator, specifically questioning the formula for calculating this average value. The subject area includes concepts from electromagnetism and alternating current (AC) theory.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the sinusoidal nature of the EMF and its average value, questioning how the average can be non-zero despite the sinusoidal graph suggesting otherwise.
  • There are inquiries about the meaning of the formula (4NBA)/T, including whether it refers to peak, RMS, or half-cycle average values.
  • Some participants suggest using calculus to find the average value of the sine function over a specific interval, indicating a mathematical approach to the problem.

Discussion Status

The discussion is active with multiple participants questioning the original poster's notes and offering insights into the average EMF calculations. There is no explicit consensus, but various interpretations and approaches are being explored, including the implications of rectification in the output.

Contextual Notes

Participants mention the average value of sin(x) over a half-cycle, which may influence the understanding of the average EMF calculation. There is also a reference to the context of simple DC generators and fully-rectified outputs of AC generators, indicating specific scenarios under discussion.

songoku
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Homework Statement
In my notes, the average emf of generator is given by ##\frac{4NBA}{T}##. I want to know how to derive this formula
Relevant Equations
##\varepsilon=\frac{4NBA}{T}##

##\varepsilon=NBA\omega \sin (\omega t)##
I know the formula of emf of generator is ##\varepsilon=NBA\omega \sin (\omega t)##. If I draw the graph of emf against time, the graph will be sinusoidal and if I find the average, the average will be zero.

How can the average emf of generator is ##\frac{4NBA}{T}##?

Thanks
 
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Even if the generator had a rectified output, the average fem wouldn't match your notes. Can you check them?
 
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songoku said:
How can the average emf of generator is ##\frac{4NBA}{T}##?
Because we are interested in the magnitude of the EMF.
 
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What is (4NBA)/T suppose to mean? Peak? RMS? Half-cycle average?
 
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songoku said:
How can the average emf of generator is ##\frac{4NBA}{T}##?
The formula is (I believe) correct when finding:

a) the average emf of a simple DC generator, or

b) the average emf for the fully-rectified output of a simple AC generator.

If you know a little calculus, find the average value of ##\sin x ## over, say, the positive half of a cycle; then the rest should be easy.
 
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Gordianus said:
Even if the generator had a rectified output, the average fem wouldn't match your notes. Can you check them?
I have checked, it is what I wrote.

pbuk said:
Because we are interested in the magnitude of the EMF.
Steve4Physics said:
The formula is (I believe) correct when finding:

a) the average emf of a simple DC generator, or

b) the average emf for the fully-rectified output of a simple AC generator.

If you know a little calculus, find the average value of ##\sin x ## over, say, the positive half of a cycle; then the rest should be easy.
I understand.

Gordianus said:
What is (4NBA)/T suppose to mean? Peak? RMS? Half-cycle average?
I suppose it would be half-cycle average

Thank you very much Gordianus, pbuk, Steve4Physics
 
Gordianus said:
Even if the generator had a rectified output, the average fem wouldn't match your notes. Can you check them?
For information, the average value of ##sin(x)## over a positive half-cycle is ##\frac 2{\pi}##.

With ##\mathscr E =NBA\omega \sin (\omega t)## and ##\omega = \frac {2 \pi}T##, this gives the OP's post #1 formula for the average value of a fully rectified output.
 
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