1. Let's start by stating the problem: You want to understand why the power dissipated is the same and whether it is because the power factor is the same. 2. Power dissipated in an electrical circuit is given by the formula $$P = VI \cos\phi$$ where: - $V$ is the voltage, - $I$ is the current, - $\cos\phi$ is the power factor (the cosine of the phase angle between voltage and current). 3. The power factor $\cos\phi$ represents the fraction of the total current that is doing useful work (real power). If the power factor is the same, it means the phase angle between voltage and current is the same. 4. If voltage $V$ and current $I$ remain constant and the power factor $\cos\phi$ is the same, then the power dissipated $P$ will be the same because all three factors in the formula are unchanged. 5. However, if either $V$ or $I$ changes, even with the same power factor, the power dissipated will change accordingly. 6. Therefore, the power dissipated is the same if and only if the product $VI \cos\phi$ remains the same, which can happen if the power factor is the same and voltage and current are unchanged. 7. In summary, the power factor being the same is a necessary condition for the power dissipated to be the same, but voltage and current values must also remain constant.