What is the relationship between magnetic flux, voltage, induced current and time in a simple AC generator?

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If you're referring to point 4 in the wiki article, read it again and you'll see that it's not giving the induced current, i.e. that resulting from the emf. To find the induced current you use $I=\frac{V}{R}$ as you suggested.

[A small point: it's bad to write things like $\Phi= \text{sin}\ \theta$. For one thing the units don't match. You mean $\Phi= \Phi_{max}\ \text{sin}\ \theta$.]

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Archipelago2000
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Archipelago2000

Updated on August 01, 2022

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  • Archipelago2000
    Archipelago2000 over 1 year

    I've tried deriving the equations for voltage and magnetic flux over the angle between the rotating coil and the magnetic field vectors in this picture.

    enter image description here

    But for the induced AC current generated by this rotating coil, how do I derive it's equation over time?

    If I use P = VI, I get asymptotes from the resulting equation: I = -k*sec(theta).

    If I use V = IR, I get the equation: -k*cos(theta) which contradicts this Wikipedia page: https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Induction/Worked_Solutions

    I really could use some explanation as to how and why the AC current generated behaves the way it does.