How to find Pmax when you know voltage and current?

[Justin26]

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

 

[NascentOxygen]

Hi Justin26. Can you use differential calculus?

 

[Justin26]

Yes i can. Just unsure on where to begin

 

[NascentOxygen]

Start with your expression for power, and find its derivative...

 

[Justin26]

Alright I get -240e^-10t+480e^-20t after i derive it but that does not give me the P_MAX of the equation when the only t that is given is t=0 current starts to flow.

 

[NascentOxygen]

Better check that derivative.

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

 

[Justin26]

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 P_MAX = 6