How Does Changing Wire Resistance Affect EMF in an AC Generator?

[bettysuarez]

Homework Statement

This is the solution to one of the problems I came across:
In an AC generator, a coil spins in a magnetic field. Of the following choices, circle the
one that will not cause an increase in the EMF generated in the coil?
a. replacing the coil wire with one of lower resistance.
b. spinning the coil faster.
c. increasing the magnetic field.
d. increasing the number of turns of wire on the coil.
e. all of the above actions will increase the EMF.

Explain your choice.
A is the correct answer
• Lower resistance wire will not affect the EMF, which is
proportional to the rate of change of flux.
• It would however, increase the current possible.

I would like to know if EMF is the same as V = IR (Ohm's law)? Hence if resistance decreases, then EMF would decreased since V is proportional to R. Why then do the answers to this question say that resistance will not affect the induced EMF?

Homework Equations

EMF = (change of flux)/ time
V = IR

The Attempt at a Solution

Please see above, part 1.

 

[kuruman]

Yes, it is like V = IR but you are confused about how to apply it. You can think of the induced emf as a battery the "voltage" of which depends on things like the frequency of rotation, magnetic field. etc. - there is a formula for this. Now if you take a 6 Volt battery and you hook it up to a wire, you will get a current. If now you hook up a wire of lower resistance, will the battery stop being a 6 Volt battery? No, it will just put out more current so that the product IR is constant. Same situation here.

 

[tomcue]

I would like to clarify that EMF (electromotive force) and V (voltage) are not exactly the same thing. While they are both measured in volts, EMF refers to the potential difference created by a changing magnetic field or a moving conductor, while V (voltage) is the potential difference between two points in a circuit.

In this context, the induced EMF in a coil is directly proportional to the rate of change of magnetic flux, as stated in the Faraday's law of induction. This means that any action that increases the rate of change of flux, such as spinning the coil faster or increasing the magnetic field, will result in an increase in the induced EMF.

On the other hand, resistance (R) is a property of the wire and does not directly affect the rate of change of flux. Therefore, replacing the coil wire with one of lower resistance will not have an impact on the induced EMF. It may, however, affect the current (I) in the circuit, as seen in Ohm's law (V=IR).

In summary, while EMF and voltage are related, they are not interchangeable terms. In the context of an AC generator, EMF is directly related to the rate of change of magnetic flux, and decreasing the resistance of the wire will not affect this relationship.