# How to find Pmax when you know voltage and current?

1. Aug 31, 2016

### Justin26

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. Aug 31, 2016

### Staff: Mentor

Hi Justin26. Can you use differential calculus?

3. Aug 31, 2016

### Justin26

Yes i can. Just unsure on where to begin

4. Aug 31, 2016

### Staff: Mentor

5. Aug 31, 2016

### Justin26

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.

6. Aug 31, 2016

### Staff: Mentor

Better check that derivative.

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

7. Sep 1, 2016

### 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 PMAX = 6