The picture shows the main idea behind a generator. Mechanical force or torque i

Question

The picture shows the main idea behind a generator. Mechanical force or torque is used to rotate a wire loop in a magnetic field. Here only a half loop is rotated. a) Find an expression for the induced current as a function of time if you turn the crank with frequency f. Assume that the semicircle is at its highest point (current position) at t = 0 s. b) With what frequency will you have to turn the crank to generate 4.0 w of electrical peak power? (Use the values corresponding to the amplitude of the ac current.) (Answer: 405 Hz, probably not doable by hand)

Explanation / Answer

a)Einduced = rate of change of Flux

= d[AB cos wt]/dt

= wAB sin wt

= 2pi f *pi(0.05^2)/2 *0.2* sin 2pift

Note: You have made a mistake in calculating the area, it is radius given not diameter.

b) For 4W power, V^2/R = 4

V^2 =4*1

V = 2

Einduced = 2V

Putting this value in earlier equation,

2 = 2pi f *pi(0.05^2)/2 *0.2* sin 2pift

for peak power sin 2pift = 1,

2 = 2pi f *pi(0.05^2)/2 *0.2

f = 2/[2pi f *pi(0.05^2)/2 *0.2]

= 405 Hz

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