Solving Electric Circuit Current & Power: Peak & Min Values

[bon]

Homework Statement

Given that the current in an electric circuit is I = Iocoswt and that the current passes through a resistance R

1) give an expression for P(t) power dissipated in the resistance. What are the peak and minimum values of P?

Then it defines the time average over 1 cycle as 1/T (integral from 0 to T) of f(t) dt where T=2pi/w

It asks us to find time average of I and P and illustrate the relevant integrals graphically

Homework Equations

The Attempt at a Solution

Ok so I think P(t) = integral from 0 to t of R Io^2 cos^2wt dt?

Now I am stuck :P How do i find maximum and minimum values of P?

to i differentiate using fundamental theorem to say that P'=RIo^2cos^2 wt?

Then find where this is maximum and minimum?

Also any ideas for the next part? thanks>

 

[ideasrule]

P is just I^2*R. You're thinking of energy.

 

[bon]

But I is a function of t, so don't you have to integrate over time? ahh no i guess not.

 

[bon]

Ok great. Thanks for your help...

So could you verify that the power is at max/min where sin2wt = 0...so this implies that t=0,pi/2w, pi/w etc...

so maximum value of power is Io^2 R

minimum is 0?

thanks...

 

[bon]

anyone?

 

[bon]

Ok all this done now :)

Just on the last part of the q..

asks me to work out the time average of <I V' > where V' is the voltage across an inductance L i.e. L dI/dt..

I get the solution to be 0..

why is this?