Answer :
Final answer:
The statement "Problem 3: Consider a generator that rotates its 200 turn, 0.15 m diameter coil at 3700 rpm in a 0.95 T field" is a)True because according to Faraday's law, when a coil rotates in a magnetic field, it induces a voltage proportional to the rate of change of magnetic flux through the coil.
Explanation:
To determine the correctness of the statement, we need to calculate the induced voltage in the generator coil using Faraday's law of electromagnetic induction. The induced voltage (EMF) is given by the formula EMF = N * ΔΦ / Δt, where N is the number of turns in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time. Given that the coil has 200 turns, rotates at 3700 rpm (which is equivalent to 388.8 radians per second), and is in a magnetic field of 0.95 T, we can calculate the induced voltage. The change in magnetic flux (ΔΦ) can be calculated as ΔΦ = B * A * Δθ, where B is the magnetic field, A is the area of the coil, and Δθ is the change in angle. Substituting the given values, we find the induced voltage to be approximately 559.5 V.
The statement is true because, according to Faraday's law, when a coil rotates in a magnetic field, it induces a voltage proportional to the rate of change of magnetic flux through the coil. In this scenario, the coil rotates at a constant angular velocity in a magnetic field, resulting in a changing magnetic flux. As a result, an electromotive force (EMF) or voltage is induced in the coil. The magnitude of the induced voltage depends on factors such as the number of turns in the coil, the strength of the magnetic field, and the angular velocity of the coil. Therefore, the induced voltage in the given generator coil setup is indeed approximately 559.5 V.
This calculation demonstrates the fundamental principle underlying the operation of generators, where mechanical energy is converted into electrical energy through electromagnetic induction. The induced voltage generated in the coil drives an electric current when connected to a circuit, producing usable electrical power. Therefore, the statement is true, reflecting the physics of electromagnetic induction in rotating coil generators.
