Question regarding resistance

[Rasmus Keis Neerbek]

Simple school project: We're looking at a model of a generator. We have an iron core, spools of cobber wire and a rotating magnet.

First we just test how much voltage is generated using different spools with different amount of coils - more coils equals higher voltage.

Now we test which setup are most efficient in making a small bulb glow. It turns out, that 400 coils are more efficient than both 200 and 1600 coils. Reason of course, because the spools are of same size, so the diameter of the copper wire is different, and 1600 coils gives a very thin wire with high resistance.

Person A claims, that the thin copper wire is also longer, and that will naturally increase the resistance also (although the diameter is the most significant factor)

Person B claims, that the length in the copper wire has no effect in this case, because the rotating magnet gives an alternating current, and therefore it is only the diameter that counts (if we had a direct current things would be different)

Who is right?

Rasmus (hope its clear - english is not my first language)

[Enthalpy]

Hi Rasmus, welcome here!

AC and DC work the same here, at small frequencies. Since R varies like L/S, both L and S are equally important. Coils are usually compared at identical volume, that is, proper design stuffs as much copper as possible in the available room, and the copper volume is L*S not forgetting a fill factor.

This means also that the designer can adapt a coil to the load voltage and current. For a given magnetic circuit hence available room and shape of the coil, the coil L varies as the number of turns N and the wire section S inversely, so the resistance changes like L². The produced voltage varies like N and the current at identical power like 1/N, so the lost RI² does not depend on N. You can design the magnetic circuit for a fictive coil with 1 turn, and later adapt N to the load.

In your project, you supposed that the coil resistance is the only limit to the output power, but generators have other limits. Especially, the current in the coil creates a magnetic field that reduces (but doesn't directly subtract, it's more complicated) from the inductor, maybe a permanent magnet. This effect can be more or less important than the resistance losses. With more turns, the same output current creates more of the unwanted magnetic field, so at some point more turns reduce the output current.

[Rasmus Keis Neerbek]

Thank you very much, that was really helpfull.

 Rasmus