A simple dc generator in contact with a bicycle\'s tire can be used to generate

Question

A simple dc generator in contact with a bicycle's tire can be used to generate power for the headlight. The generator has 150 turns of wire in a circular coil of radius 1.8 cm. The magnetic field strength in the region of the coil is 0.20 T. When the generator supplies an emf of amplitude 4.2 V to the lightbulb, the lightbulb consumes an average power of 12.0 W.

What would the maximum power be if the bicycle moves half as fast? Assume that the resistance of the lightbulb does not change. Remember that the angular velocity affects the emf, which in turn affects the current. How does the power in the lightbulb depend on the bicycle's speed?

Explanation / Answer

Here,

N = 150

radius ,r = 1.8 cm = 0.018 m

magnetic field , B= 0.20 T

emf , V = 4.2 V

power , P = 12 W

for speed of bicycle half as fast

V1 = 4.2/2 = 2.1 V

as Power = V^2/R

the power will become 1/4 times

Power = 12/4 = 3 W

the new power will be 3 W

-----------------------------

as Voltage is directly dependent on u(speed of bicycle)

power in lightbulb will depend on u^2

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