# Lesson : Power Law

The power law formula is used to calculate the power dissipate through a component. In this lesson, we will only calculate power dissipate through a resistor since it is a simple example. We will also mix Ohm’s law with the power law to get various formulas to calculate current, power, resistance and voltage. The power law is also known as Joule’s Law because the discovery was made by James Prescott Joule. The power law states that the power of a resistive component is proportional to the product of its resistance and the square of the current flowing through it. The unit of power is the Watt. One Watt is equal to 1 Joule per second.

$1) \ P = I^{2}\cdot R$

We can simplify 1) by using Ohm’s law:

From Ohm’s law:

$2) \ R = \cfrac{V}{I}$

We can replace R in 1) to get a different formula for power:

$3) \ P = V\cdot I$

Combining Joule’s law and Ohm’s law, we can get new formulas to find current, resistance, voltage and power. Below you can find a table with all the possible combination:

In real life applications, you will rarely use all of these formulas. Just remember the two below and you can figure out the rest by combining the two formulas if you ever needs to:

$3) \ P = V\cdot I$

$4) \ V = R\cdot I$

Below you will find an example of a very simple example on how to use power law.

Example 1: We want to calculate the power dissipate in the resistor of this circuit. If we look at table 1, we could use all three formulas in the power column since we have the voltage across the resistor, the current flowing through it and the resistance of the resistor. For this example, we will use formula 3.

$3) \ P = V\cdot I$

$P = V\cdot I$

$P = 12V\cdot 0.0025A=0.03W=30mW$

It is a very simple example but power law with resistor cannot get more complicated than this. The only thing that could change is the formula you need to use to calculate the power dissipate in the resistor. This complete the lesson on the power law. In the next lessons, we will analyze more complicated circuits with Ohm’s law. We will analyze circuits with multiples resistors connect in series and in parallel.