Magnetic field and generator power output

[dansmith170]

TL;DR Summary

Could decreasing the magnetic field increase a generator's power output?

Hi,

I am confused about whether decreasing the magnetic field used for a generator could increase the generator's power output.

I used four equations:

1. Torque = Force x radius
2. Torque = NIAB (N = number of turns, I = current, A = area of armature, B = magnetic field).
3. emf = NAB(2*pi*f) (emf = electromotive force, f = frequency of rotation of armature.
4. I = emf / R (R = resistance)

Using these equations, I found that frequency is inversely proportional to magnetic field ("f" is proportional to "1/B^2"). If that is the case, then decreasing magnetic field should actually increase frequency, correct?

A generator should produce more power when the frequency is greater. Well then, a generator with lower magnetic field, provided that it has greater frequency, should produce more power.

I get the feeling that I made a mistake somewhere in my math or reasoning, would someone please help me out on this?

Thanks.

Citations to sources for relevant equations:
https://courses.lumenlearning.com/suny-physics/chapter/23-5-electric-generators/
http://spiff.rit.edu/classes/phys213/lectures/amp/amp_long.html

 

[osilmag]

To keep a constant emf, if the B field is lower, the frequency has to be increased. The frequency compensates for a low B field in order to maintain an emf. The power is not greater.

 

[dansmith170]

To keep a constant emf, if the B field is lower, the frequency has to be increased. The frequency compensates for a low B field in order to maintain an emf. The power is not greater.

osilmag, thanks for your response. Suppose I do not want to keep a constant emf, but I do want to keep a constant torque. In that case, would lowering the B field mean increasing frequency (f) in a way that increases total power output of the generator?

 

[osilmag]

If you wanted a constant torque when your B field lowered, your current would have to increase. That has to come from your current source. Is the current in equation 2 the same as in equation 4?

 

[dansmith170]

If you wanted a constant torque when your B field lowered, your current would have to increase. That has to come from your current source. Is the current in equation 2 the same as in equation 4?

Yeah, same current (I) in both equations.

The current source is, I think, from the mechanical force that is spinning the generator's armature (maybe it is a wind-powered generator). In that case, the generator's armature spin, measured in frequency (f) should determine the current (I) magnitude.

In other words, given that current (I) is proportional to (B) times (f) (see equations 3 and 4), if I decrease (B) but (I) increases, then (f) must increase by a greater amount than (B) has decreased by.

Agree?

 

[osilmag]

Agree