Bicycle headlights are often powered by a generator, with the rim of the generator's shaft rolling against the tire's rim.
In one such generator, the coil has 125 turns of wire and a cross-sectional area of 0.0010 m², immersed in a field of magnitude 0.080 T. At the area of contact with the tire, the rim of the generator's shaft has a radius of 1.25 cm. The tire's diameter is 66 cm.
(a) If the lightbulb in the headlight needs 5.0 W of average electrical power, corresponding to a voltage amplitude of 4.0 V, to produce a decent amount of light, calculate the linear speed of the bicycle needed, assuming no slipping anywhere in the problem.
(b) Calculate the torque that must be supplied by the bicycle wheel to produce the required average electrical power for the bulb. State briefly two other simplifying assumptions that must be made.
(c) What is the amplitude of the current induced in the coil under these conditions?
(d) To the extent that the lightbulb obeys Ohm's Law, and that its resistance is constant, by what factor would the power delivered to the bulb increase if the cyclist tripled the bicycle's speed (presumably downhill or at the Tour de France)?