DC generator: Induced EMF of a single coil armature

[kidsasd987]

Hi.

I am reading a textbook about simple DC generator. The situation is if we are rotating a single armature coil within a constant field B,
the induced emf will be (if we are to only think about the magnitude), emf= B*l*W*omegaB = magnetic field
l = length of the coil
W = width of the coil
omega = angular velocity of the coil However, if we are re-writing that equation in terms of RPS (Rotation per second)
we get


emf = B*I*v v = pi*D*n
D = Diameter which is equal to W.
n = Rotation per second


However, these two equations are not the same because


B*l*W*omega = B*I*v

-> W*omega = v
-> W*omega = pi*D*n

using n = omega / 2pi

-> W*omega = W/2 * omega
-> W = W/2This is a contradiction so I am not sure at what point I got these equations wrong.

 

[cnh1995]

emf = B*I*v

Think carefully about this equation and seek the hidden factor of 2 .

 

[kidsasd987]

Think carefully about this equation and seek the hidden factor of 2 .

Thanks. I was thinking that D is actually r. then it makes sense but since I was given with the equation

pi*D*n
D = 2r = W

I am confused.

 

[cnh1995]

emf= B*l*W*omega

This is the emf induced in one "loop".

emf = B*I*v

This is the emf induced in ...?