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Homework Help: Current problem help

  1. Mar 9, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations



    3. The attempt at a solution

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

    Now im 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>
     
  2. jcsd
  3. Mar 9, 2010 #2

    ideasrule

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    Homework Helper

    Re: Current

    P is just I^2*R. You're thinking of energy.
     
  4. Mar 9, 2010 #3

    bon

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    Re: Current

    But I is a function of t, so don't you have to integrate over time? ahh no i guess not.
     
  5. Mar 9, 2010 #4

    bon

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    Re: Current

    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...
     
  6. Mar 9, 2010 #5

    bon

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    Re: Current

    anyone?
     
  7. Mar 9, 2010 #6

    bon

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    Re: Current

    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?
     
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