Question

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

Short answer

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

Step-by-step solution

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.

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.