Answer to Question 2

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A motor takes a current I, and the armature is placed in a magnetic field for flux density B.  The armature has N turns and is of length l and width w, rotating at a frequency f.

Show that the equations P = Fv and P = tw are consistent.  What is the final relationship between power and angular velocity?

Using P = Fv:

F = NBIl

v = 2p w/2 f = 2pwf

P = NBIl 2pwf

 

Since A = wl, we can write:

P = BANI 2pf

Since w = 2pf, we can write:

P = BANIw

Using P = tw

t = BANI

By definition:

w = 2pf

We can combine the two to give:

P = BANIw

The two results are the same, so each relationship is consistent with the other.  The final relationship is P = BANIw  or P = 2pBANIf