## Physics: Principles with Applications (7th Edition)

In the first power equation, $P=\frac{V^{2}}{R}$, to say that power decreases as resistance increases is to imply that the voltage stays constant. In the second power equation, $P=I^{2}R$, to say that power increases as resistance increases is to imply that the current stays constant. Both voltage and current cannot stay constant in any single situation if the resistance is changing; One must be changing. So in one of those equations the underlying assumption is not upheld, and there is no contradiction.