# How fast must the rotor of a generator rotate?

## Homework Statement

The maximum indicued emf in a generator is 205rpm is 43.0V. How fast must the rotor of the generator rotate if it's to generate a maximum inducded emf of 55.0V?

E= NBAsinwt

## The Attempt at a Solution

magnet field isnt given, so how can u solve this?

rl.bhat
Homework Helper

Check the formula for induced emf.

i did, but ur not given enough info to solve it, when u have E=-N ( magnetic flux)/ time or motion emf which is E= Blv

rl.bhat
Homework Helper

Formula for induces emf is E = NBAwsin(wt)

rl.bhat
Homework Helper

i did, but ur not given enough info to solve it, when u have E=-N ( magnetic flux)/ time or motion emf which is E= Blv

When a coil is moving in a magnetic field, E = -N( change in magnetic flux/time)
When a conductor is moving a magnetic field with a velocity v, E = Blv.
In your problem you hve to the first formula. At any instant th magnetic flux = NBA*cos(wt)

The eq for the induced emf is NBAwsin(wt). To max this eq out you have to realize the max value for the sin function is 1. Therefore, the max emf = NBAw. Since they give you what the max emf is for an w=205rev/min, you can simply solve for a value of (NBA). and use this same value for (NBA) in the eq 55V=(NBA)(w). You have to realize that the values for N, B, and A are not changing for this situation. You do not really have to change the w to SI units, or, 21.46 rad/sec. You can use the 205 rev/ min as the w to find a value for (NBA) and plug this into the eq 55V = (NBA)(w). Either way you get approx 262 rev/min.