Question

Show work to receive full credit.

A human sized 'hamster wheel' of radius R= 6m is connected to a generator. The generator is made with a magnet producing 24000 Gauss magnetic field as a stator, 2000 coils of conductive wire with 4 cm² of area each for a rotor, wrapped around an iron core with relative permeability ?_R = 200. The generator doesn't have a commutator. The generator is connected to a 20 ohm heating element.

a. Is this generator a dynamo or an alternator?

b. What is the angular velocity of the wheel if a person runs 3 m/s?

c. What is the amplitude of the voltage and frequency of AC output of the generator?

d. What is the power output? Would changing the resistor to 2 ohms require more or less work to heat the element, assuming the runner maintains 3 m/s?

Answer 1

a) The generator is a alternator because the output will be an AC

b As given that the speed of the human is3 m/s and the radius r of hamster whell is 6m

As we knoe that V=

so

=V/r

=0.5

C) As we know that

according to faraday's Law of electromagnetic induction

V=

and =B*A

=> =2.4*4*

and T=

=>T=2*3.14/0.5

=>T=12.56

V=0.1528

and =0.5/s

d- as we know that

Power =

power =(0.1528*.1528)/20

Power =0.0011W

as R becomes 2

Power become 10 time the initial power output

Power(2 ohms)=0.011W