Question

A bicycle generator rotates at 1875 rad/s, producing an 18.0 V peak emf. It has a 1.00 by 3.00 cm rectangular coil in a 0.640 T field. How many turns are in the coil?

a) 300 turns
b) 375 turns
c) 450 turns
d) 525 turns

Answer 1

To find the number of turns in the coil of a bicycle generator, Faraday's law is applied with the given values for peak emf, coil dimensions, magnetic field strength, and angular velocity. The calculations yield approximately 375 turns for the coil. Therefore, the correct answer is b) 375 turns.

Step-by-step explanation:

The student's question is about determining the number of turns in the coil of a bicycle generator that produces an 18.0 V peak emf with a given rotational speed in a magnetic field.

To solve this, we can use Faraday's law which states that the induced emf (ε) in a coil is equal to the rate of change of magnetic flux, ε = NABωsin(ωt), where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity.

To find N, we rearrange the equation to N = ε / (ABω), given that ε = 18.0 V, A = 1.00 cm x 3.00 cm = 3.00 x 10^-4 m^2, B = 0.640 T, and ω = 1875 rad/s. Substituting these values in, N is calculated to be around 375 turns, which is option b).