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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# The power dissipated in a resistor is given by ${\mathbit{P}}{\mathbf{=}}{{\mathbit{V}}}^{{\mathbf{2}}}{\mathbf{/}}{\mathbit{R}}$, which means power decreases if resistance increases. Yet this power is also given by ${\mathbit{P}}{\mathbf{=}}{{\mathbit{I}}}^{{\mathbf{2}}}{\mathbit{R}}$, which means power increases if resistance increases. Explain why there is no contradiction here.

There is no contradiction because $V$and $I$ are not always constants and are dependent on one another.

See the step by step solution

## Step 1: Definition of Resistance

In an electrical circuit, resistance is a measure of the resistance to current

flow. The Greek letter omega (Ω) is used to represent resistance in ohms.

## Step 2: Explanation of the contradiction

There is no inconsistency because $V$and $I$ are not always constants and are dependent on one another.

By Ohm's law,

$V=IR$

$V$ , $I$ , and $R$ are connected to each other.

It is possible to convert one power equation to another.