The armature of a simple ac generator has 20 circular loops...

The armature of a simple ac generator has 20 circular loops of wire, each with a radius of $10 \mathrm{~cm} .$ It is rotated with a frequency of $60 \mathrm{~Hz}$ in a uniform magnetic field of $800 \mathrm{mT}$. (a) What is the maximum emf induced in the loops? (b) How often is this value attained? (c) If the time period in part (b) were cut in half, what would be the new maximum emf value?

Key Concepts

Impact of Frequency Changes on Induced EMF

The magnitude of the induced emf in a generator is directly proportional to the angular frequency, meaning that any change in rotation frequency will affect the emf. For instance, halving the time period (or doubling the frequency) leads to a proportional increase in the maximum induced emf.

Angular Frequency and its Relation to Frequency

Angular frequency (?) represents the rate of change of the angular position of a rotating object and is directly related to the conventional frequency (f) by the equation ? = 2?f. This concept is crucial when linking the speed of rotation to the induced emf in generators.

Faraday's Law of Electromagnetic Induction

Faraday's law states that a change in the magnetic flux through a circuit induces an electromotive force (emf) in the circuit. This principle underlies the operation of generators and is mathematically expressed by the relationship between emf and the rate of change of magnetic flux.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is determined by both the strength of the magnetic field and the area of the loop that the field penetrates, playing a central role in calculating the induced emf in a coil.

Alternating Current (AC) Generation

AC generation involves producing an alternating voltage and current by rotating a coil within a magnetic field. As the coil's orientation with respect to the field changes periodically, the magnetic flux through the coil varies, resulting in an emf that alternates in magnitude and direction.

Transcript

Please give Ace some feedback