Question

An electric generator is designed to produce a maximum emf of 220 V while rotating with an angular speed of 3600 rpm. Each coil of the generator has an area of 0.027 m².

a.) If the magnetic field used in the generator has a magnitude of 0.050 T, how many turns of wire are needed?


b.) During the rotation of the coils, the magnetic flux through the coils will alternately be increasing and decreasing. (Why?)

While the flux is increasing, the induced current in the coils will make a B field which tries to  ---Select--- oppose reinforce none of the above not enough info the external B field.
While the flux is decreasing, the induced current in the coils will make a B field which tries to  ---Select--- oppose reinforce none of the above not enough info the external B field.
This generator will produce what kind of current?  ---Select--- DC (direct current) AC (alternating current) none of the above not enough info

c.) The generator is connected to a resistor of R=250 Ω, and the magnitude of current passing through it and its rate of power dissipation are measured over time. What are the extremes of the measured values?
Also, give the angle between the normal vector to the loops and the magnetic field when these extremes occur. (If ambiguous, state the smallest angle.)

I_max =  A
P_max =  W
θ =  degrees

I_min =  A
P_min =  W
θ =  degrees

Answer 1

A). flux = B*A*cos(theta) [ here theta is the angle between B and A]

emf = -d(flux)/dt = B*A*sin(theta)* d(theta)/dt

= B*A*sin(theta)* omega

Here n is the number of turns

emf = n*B*A*sin(theta)*omega

Therefore, max. emf = n*B*A*omega

Hence n = 220 /(0.05*0.027*3600*2*pi/60) = 432.27

B) flux = B*A*cos(theta) [ here theta is the angle between B and A]

-1 <= sin(theta) <=1

Therefore, the magnetic flux will be increasing and decreasing over time

the induced current in the coils will make a field B which tries to oppose when the flux is increasing,

Also, the induced current in the coils make a field B which tries to reinforce while the flux is decreasing,

The generator will produce Alternative current

C) Imax = Emax/R = 220/250 = 0.88

Pmax = Imax^2 * R = 193.6

Here angle = 0

Imin = Emin/R = 0/250 = 0

Pmax = 0

So angle will be 90 degrees.