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How to find Pmax when you know voltage and current?

  1. Aug 31, 2016 #1
    1. The problem statement, all variables and given/known data
    After t=0, the current entering the positive terminal of a flashlight bulb is given by:
    i(t) = 2(1-e^(-10t)) A
    and the voltage across the bulb is v(t) = 12e^(-10t) V.
    Determine the maximum power level delivered to the flashlight.

    2. Relevant equations
    i(t) = 2(1-e^(-10t)) A
    v(t) = 12e^(-10t) V
    3. The attempt at a solution
    I know p(t) = i(t)*v(t) but that is where my knowledge of this stops
     
  2. jcsd
  3. Aug 31, 2016 #2

    NascentOxygen

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    Staff: Mentor

    Hi Justin26. Can you use differential calculus?
     
  4. Aug 31, 2016 #3
    Yes i can. Just unsure on where to begin
     
  5. Aug 31, 2016 #4

    NascentOxygen

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    Staff: Mentor

    Start with your expression for power, and find its derivative....
     
  6. Aug 31, 2016 #5
    Alright I get -240e^-10t+480e^-20t after i derive it but that does not give me the PMAX of the equation when the only t that is given is t=0 current starts to flow.
     
  7. Aug 31, 2016 #6

    NascentOxygen

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    Staff: Mentor

    Better check that derivative.

    You are looking for a maximum, so equate your derivative to 0.
     
  8. Sep 1, 2016 #7
    Well the derivative is right. I even double checked it online. That being said thanks for your help. I really appreciated!!!!!

    Final answer broken down is t = 0.0693147181 and PMAX = 6
     
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