Formula for the average EMF of generator

[songoku]

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

 

[Gordianus]

Even if the generator had a rectified output, the average fem wouldn't match your notes. Can you check them?

 

[pbuk]

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

Because we are interested in the magnitude of the EMF.

 

[Gordianus]

What is (4NBA)/T suppose to mean? Peak? RMS? Half-cycle average?

 

[Steve4Physics]

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.

 

[songoku]

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.

Because we are interested in the magnitude of the EMF.

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.

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

 

[Steve4Physics]

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.