# How to optimze a coil for needed voltage?

Faraday's law for a coil is :

V = A * M * N

Where: V = Peak output-voltage A = Area of the cross-section of the wire M = Rate of change of magnetic flux in the coil N = Number of turns of the coil

Question:

Whats happens when A gets very small and N very large? I expect that in that case internal resistance gets higher and the output voltage drops??

If that's true, there will be a certain combination of A and N that will be optimal for a needed V. Question: How to obtain this A and N ?

NB: By optimal I mean minimal space needed by the coil and minimal material costs for the wire.

edit: The coil is used as a generator like in a bike dynamo. So the coil is wound around a linear weak-iron core.

• Every single part of your question, including the parts you didn't ask, have the answer "it depends". And that law, while it may be true for specific cases, doesn't cover the realities of solenoidal coils or coils wound on cores. Please tell us what specifically you're trying to do, e.g. build a radio, build a switching power supply, tug Mars out of orbit, achieve world domination, etc. Commented Oct 16, 2018 at 19:46