# Heat Energy $\propto 1/R$ or $\propto R$?

I know that heat energy can be calculated by $$I^2 R t$$. Therefore, it's directly proportional to resistance.

However,

$$I^2 R t = \frac{V^2}{R}t$$

In this case, won't the heat energy be inversely proportional to the resistance? Won't these 2 statements contradict each other?

You are implicitly assuming that $$I$$ and $$V$$ are constant quantities. If one says that $$x$$ is proportional to $$y$$, it means $$x = ay$$ where $$a$$ is a constant.
But consider what happens when you change $$R$$: either $$V$$ or $$I$$, or both, change. They are not constant.
I think it would be better to say that power is proportional to $$I^2$$, with coefficient of proportionality $$R$$, and power is also proportional to $$V^2$$, with coefficient of proportionality $$1/R$$. Changing $$I$$ or $$V$$ does not affect the value of $$R$$ (not in simple analyses anyway).