A wind turbine generates electric power by powering a turbine though the mechani

Question

A wind turbine generates electric power by powering a turbine though the mechanical motion of a very large conducting loop in a giant magnetic field. Assume the coil/loop inside the generator can rotates at 1800 rotations per minute, it has coils of radius of 2 meters, which rotate in a magnetic field of 1.4 Tesla Assume that the instantaneous angle the normal to the coil makes with the magnetic held is theta = omega t What is the angular velocity omega in radians/second of the wind turbine? What is the flux passing through the coil (as a function of the time?) What is the induced voltage provided (EMF) by the generator? Looking at the expression in ) What is the maximum magnitude of the induced voltage ? What is the minimum magnitude of the induced voltage? Assume that the homes that are powered by one turbine are represented by an equivalent 36 k Ohm resistor connected to the turbine. What is the maximum power that is supplied by the turbine to the houses?

Explanation / Answer

a)

The angular velocity is given by w =2npi/t =2pi*1800/60s =188rad/s

b)

Flux =BAN =pir2BN =pi (2m)2(1.4T)(1) =17.59Wb

c)

Now magnitude of induced emf is given by e =BANw =(17.59Wb)(188rad/s) =3306.92V

d) The maximum induced emf is given by emax =3306.92V

   The minimum induced emf is given by emin =0V

e)

Power consumed is given by

P =e2/R =(3306.92V)2/36*103ohm=303.769W

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