Statement I: Power = $\frac{V^2}{R}$ is used only when the potential difference across the resistors are constant.

Statement II: Power = $I^2$​R is used only when current in the resistors are constant.

The correct option is B

Both statements are true

Power = $\frac{V^2}{R}$ when V is constant. While Power = $I^2$​R when I is constant in the circuit. We try to minimize the number of variables in an equation.