How does power change with voltage?

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Answer 1 · 2015-01-28T19:18:08

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

$P = V \cdot I$ $P = V * I$

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:

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

Voltage is defined as the amount of energy per charge:

$V = \frac{E}{Q}$ $V = E / Q$ 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:

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

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

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

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

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

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