# How does power change with voltage?

Jan 28, 2015

Power $P$ is related to voltage $V$ and current $I$ as:

$P = V \cdot I$

So the power will increase proportionally with the voltage if I is constant.

This is because power is defined as energy consumed per second as stated in the equation:

$P = \frac{E}{t}$ where E is energy and t is time.

Voltage is defined as the amount of energy per charge:

$V = \frac{E}{Q}$ where Q is the amount of charge in Coulumbs and E is the amount of energy in Joules.

Current is defined as the the flow of charge per unit time:

$I = \frac{Q}{t}$

So when we multiply $V \cdot I$ we get:

$V \cdot I = \frac{E}{Q} \cdot \frac{Q}{t} = \frac{E}{t} = P$

We can also find Power from voltage and resistance because we know from Ohm's law that:

$I = \frac{V}{R}$ and so electric power can be related to voltage and resistance as:

$P = V \cdot I = V \cdot \frac{V}{R} = {V}^{2} / R$