How to find Pmax when you know voltage and current?

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Discussion Overview

The discussion revolves around determining the maximum power level (Pmax) delivered to a flashlight bulb, given the time-dependent current and voltage equations. The focus is on applying calculus to find the maximum power based on the provided equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant states the equations for current and voltage: i(t) = 2(1-e^(-10t)) A and v(t) = 12e^(-10t) V, and expresses uncertainty about how to proceed with finding Pmax.
  • Another participant suggests using differential calculus to find the maximum power.
  • A participant confirms they can use calculus but is unsure where to start.
  • A suggestion is made to derive the expression for power, p(t) = i(t) * v(t), to find its maximum.
  • One participant claims to have derived the expression and obtained a specific derivative but expresses confusion about how to find Pmax with only t=0 given.
  • Another participant advises checking the derivative and equating it to zero to find the maximum.
  • A participant asserts their derivative is correct and thanks others for their help, providing a final answer for t and Pmax.

Areas of Agreement / Disagreement

There is no consensus on the method to find Pmax, as participants express varying levels of confidence in their calculations and understanding of the process.

Contextual Notes

Participants do not clarify the assumptions behind their calculations or the conditions under which their results hold. The discussion includes unresolved steps in the mathematical process.

Justin26
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Homework Statement


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.

Homework Equations


i(t) = 2(1-e^(-10t)) A
v(t) = 12e^(-10t) V

The Attempt at a Solution


I know p(t) = i(t)*v(t) but that is where my knowledge of this stops
 
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Hi Justin26. Can you use differential calculus?
 
Yes i can. Just unsure on where to begin
 
Start with your expression for power, and find its derivative...
 
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.
 
Better check that derivative.

You are looking for a maximum, so equate your derivative to 0.
 
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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