An electric generator is designed to produce a maximum emf of 220 V while rotati

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 0.059 m2.

a.) If the magnetic field used in the generator has a magnitude of 0.050 T, how many turns of wire are needed?
197.82

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---

While the flux is decreasing, the induced current in the coils will make a B field which tries to  ---Select---

This generator will produce what kind of current? ---Select---

c.) The generator is connected to a resistor of R=150 ?, 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.)

Imax = 1.467 A
Pmax = 322.67 W
? = ???????degrees

Imin = 0 A
Pmin = 0 W
? = 0 degrees

Explanation / Answer

a. flux = B*A*cos(theta) , where theta is the angle between B and A.

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

= B*A*sin(theta)* omega

if, number of turns = n

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

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

Hence n = 220 /(0.05*0.59*3600*2*pi/60) = 197.82

b.  flux = B*A*cos(theta) , where theta is the angle between B and A.

-1 <= sin(theta) <=1

Hence, magnteic flux will increasing and decreasing over time ..

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

While the flux is decreasing, the induced current in the coils will make a B field which tries to reinforce.

Generator will produce Alternative current (AC).

c . Imax = Emax/R = 220/150 = 1.467

Pmax = Imax^2 * R = 322.66

Angle will be zero .

Imin = Emin/R = 0/150 = 0

Pmax = 0

Angle will be 90 degree .

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