relationship between voltage and current

I know that this question had been asked many times but I think it will be a new info in Ohm’s law: $$R = V/I$$ So Voltage is directly proportional to Current

In Electric Power’s law: $$P = VI$$ so Voltage is inversely proportional to Current. I am very confused about this. I made many researches in many sites and here but no results.

• What is confusing about that to you? There doesn't seem to be a specific question here. – Brionius Aug 24 '15 at 18:57
• If you hold power FLAT and increase current, voltage would have to decrease. Similarly, if you hold resistance flat and increase current, voltage would have to increase. In practical terms, to hold power flat while you decrease voltage, you would have to be adjusting resistance down to increase current. – kbelder Aug 24 '15 at 19:06
• Those are two different constraints. Holing resistance constant versus power constant is apples and oranges. – paparazzo Aug 24 '15 at 19:20

If you keep the resistance constant, then $V=IR$ means that voltage is directly proportional to current.
If you keep the power constant, then $V=\frac{P}{I}$ means that voltage is inversely proportional to current.
However, because $V=IR$, we can write that $P=I^2R$. Therefore, if we say resistance is constant, then power must change with current, which means that voltage is no longer inversely proportional to current.