An electric generator rotates at 60 Hz.

Question

It has 1000 turns and produces an rms voltage of 120 V.?

The area of each turn of the coil is . What is the generator’s magnetic field?

Update : the area of each turn of the coil is 10^-2m^2

 

Answer 1

Number of turns = 1000 turns.

Rms voltage Vm = 120 v

Frequency = 60 Hz

Area of the coil = 10^-2 m².

Induced EMF = Vm*sinωt

ω = 2πf

ω = 2π * 60

ω = 120π

Induced EMF = 120 sin(120πt).

We know that Induced EMF in the electric motor.

Induced EMF = -NA (dB/dt)

Induced EMF = - 1000 * 10^-2 * (dB/dt)

120 sin(120πt) = -10 * (dB/dt)

(dB/dt) = -12 sin(120πt)

Integrate with respect to t.

Magnetic Field = (12/120π) cos(120πt)

Magnetic Field = 0.0318 * cos(120πt)

Therefore Magnetic Field is 0.0318 cos(120πt).