Induced Emf, Contributing factors

[K3nt70]

Homework Statement

A generator is constructed by rotating a coil of N turns in a magnetic field B at a frequency f. The internal resistance of the coil is R and the cross sectional area of the coil is A.
Which of the following statements are true? (Give ALL correct answers, i.e., B, AC, BCD...)

A) The maximum induced EMF occurs when the coil is rotated about an axis parallel to the magnetic field lines.
B) The average induced EMF doubles if the area A is doubled.
C) The average induced EMF doubles if the frequency f is doubled.
D) The average induced EMF doubles if the resistance R is doubled.
E) The maximum induced EMF occurs when the coil is rotated about the axis of the coil.
F) The average induced EMF doubles if the magnetic field B is doubled.

Homework Equations

$$|\epsilon| = I R$$
$$|\epsilon| = NA\frac{\Delta B}{\Delta t}$$

The Attempt at a Solution

Well, I am fairly sure A is false, B is true, E is true and F is true. I think D is false, and i can't find any expressions in my book relating frequency to emf. I don't really know the relationship between frequency and induced emf.

 

[Defennder]

The frequency tells you the rate of change of area of the coil in the magnetic field. You can start by imagining the coil rotating from its maximum exposed area to the B-field to zero flux of the B-field passing through the coil. You are given the angular frequency of rotation, so you can write an expression for the time taken for it to go from max B flux to zero B flux through the coil. From this just make use of your second equation to come up with a rough expression for emf induced throughout that quarter cycle of rotation.

 

[baba89]

I would like to clarify that the correct answers are B, C, E, and F.

Explanation:

A) The maximum induced EMF occurs when the coil is rotated about an axis parallel to the magnetic field lines. This statement is false. The maximum induced EMF occurs when the coil is rotated perpendicular to the magnetic field lines, as this maximizes the change in magnetic flux through the coil.

B) The average induced EMF doubles if the area A is doubled. This statement is true. This is because the induced EMF is directly proportional to the number of turns in the coil and the change in magnetic field, which is represented by the cross-sectional area.

C) The average induced EMF doubles if the frequency f is doubled. This statement is true. According to Faraday's law, the induced EMF is directly proportional to the rate of change of magnetic flux, which is represented by the frequency.

D) The average induced EMF doubles if the resistance R is doubled. This statement is false. The induced EMF is independent of the resistance in the circuit. However, the current produced by the induced EMF may be affected by the resistance, but this does not change the EMF itself.

E) The maximum induced EMF occurs when the coil is rotated about the axis of the coil. This statement is true. This is because the maximum change in magnetic flux occurs when the coil is rotated along its axis, as this maximizes the change in magnetic field through the coil.

F) The average induced EMF doubles if the magnetic field B is doubled. This statement is true. According to Faraday's law, the induced EMF is directly proportional to the change in magnetic field, so doubling the magnetic field will result in doubling the induced EMF.