Rotation Rate of a Generator Coil

[lampshader]

Homework Statement

If the rotation rate of a generator coil is doubled, what happens to the peak emf?

Homework Equations

The Attempt at a Solution

I think it stays the same. Am i right?

 

[xcvxcvvc]

Homework Statement

If the rotation rate of a generator coil is doubled, what happens to the peak emf?

Homework Equations

The Attempt at a Solution

I think it stays the same. Am i right?

no. look at the equation for induced emf...

 

[lampshader]

Ok so looking at Faraday's Law: http://physics.bu.edu/~duffy/py106/InducedEMF.html


The emf will be cut in half.

 

[xcvxcvvc]

Ok so looking at Faraday's Law: http://physics.bu.edu/~duffy/py106/InducedEMF.html


The emf will be cut in half.

No!

Use math, not intuition!

$$V_{induced}=\frac{d(BAcos(\omega t))}{dt}$$

 

[lampshader]

I don't even have a number in my word problem..How can I not use intuition..lol

 

[xcvxcvvc]

I don't even have a number in my word problem..How can I not use intuition..lol

by doing it symbolically, and you do have a number: 2

the new $$\omega$$ is twice that of the old $$\omega$$

$$V_{max}$$ is whenever the trig function on the right is equal to 1. Therefore, we can say this:
$$V_{oldmax}=\omega BA$$
$$V_{newmax} =2\omega BA$$
Do you see a substitution?
$$V_{newmax} =2V_{oldmax}$$