How to find Pmax when you know voltage and current?

In summary, the conversation discusses determining the maximum power level delivered to a flashlight based on the current and voltage equations provided. The individual is able to use differential calculus to find the derivative of the power equation and solve for the maximum power level of 6.798588112 watts at t = 0.0693147181 seconds.
  • #1
Justin26
4
1

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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  • #2
Hi Justin26. Can you use differential calculus?
 
  • #3
Yes i can. Just unsure on where to begin
 
  • #4
Start with your expression for power, and find its derivative...
 
  • #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.
 
  • #6
Better check that derivative.

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

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

1. How do I calculate Pmax when I know voltage and current?

To calculate Pmax, or the maximum power output, you can simply multiply the voltage by the current. The formula for power is P = V x I, where P is power in watts, V is voltage in volts, and I is current in amps. This will give you the maximum power output in watts.

2. What units should I use for voltage and current when calculating Pmax?

Voltage should be measured in volts (V) and current should be measured in amps (A) when calculating Pmax. Using the correct units is important to ensure accurate calculations.

3. Can Pmax be greater than the product of voltage and current?

No, Pmax cannot be greater than the product of voltage and current. This is because power is directly proportional to both voltage and current, so the maximum power output will always be the product of the two values.

4. How does the value of Pmax change with voltage and current?

The value of Pmax will increase as either voltage or current increases. This is because power is directly proportional to both values. For example, if you double the voltage, Pmax will also double.

5. What is the significance of calculating Pmax?

Calculating Pmax is important in understanding the maximum power output of a circuit or device. This information can be used to determine the efficiency of a system and make improvements for optimal performance. It is also useful in determining the power requirements and limitations for different applications.

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