Current vs. Time: Mathematical Expression for Hippolyte Pixii's Dynamo

[f77126]

Consider a simple alternating current generator such as Hippolyte Pixii's dynamo. The current generated by such dynamo can be described as simple oscillating cosine signal. Assuming for simplicity that the max current generated each time a pole of Pixii's magnet passed the coil is (2/pi)0.5 amperes and that the magnet rotate with a characteristic angular frequency ω0.

Write the mathmatical expression for the time-domain signal (current vs. time) from such AC generator. For simplicity, assume that the magnet was already spinning at the beginning of the observation and the magnet's poled happened to be just below the coils at time zero.

I am not really sure how to start, I just need know that I need something relate current with time and equation should have cosine.
Thanks for any help

 

[LowlyPion]

Maybe start here then?
http://en.wikipedia.org/wiki/Alternating_current#Mathematics_of_AC_voltages

 

[thomate1]

The mathematical expression for the time-domain signal (current vs. time) from Hippolyte Pixii's dynamo can be written as:

I(t) = (2/π)^0.5 cos(ω0t)

Where I(t) represents the current at time t, ω0 is the characteristic angular frequency of the magnet's rotation, and cos(ω0t) represents the cosine function that describes the oscillating current signal.

This expression assumes that the magnet was already spinning at the beginning of the observation and that the magnet's poles were just below the coils at time zero. The maximum current generated each time a pole of the magnet passes the coil is represented by (2/π)^0.5 amperes.

Overall, this mathematical expression accurately describes the simple alternating current generated by Hippolyte Pixii's dynamo, using the characteristics of the magnet's rotation and the cosine function to represent the oscillating current signal.