# 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. 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. Aug 24 '15 at 19:06
• Those are two different constraints. Holing resistance constant versus power constant is apples and oranges. 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.

There is no contradiction here, you simply need to be mindful of what you are holding constant and ask yourself if you are being consistent

• Ok . i want to ask you . Is Ohm’s law working in life? can we make R constant or what Aug 24 '15 at 19:29
• Yes, resistors have practically constant resistance. Ohm's Law works just fine
– Jim
Aug 24 '15 at 19:34
• So now Voltage is directly proportional to Current? Aug 24 '15 at 19:37
• @Ahmed: only for voltage across a fixed-value resistor - not for other types of device. And only within certain limits of current, temperature and so on. Aug 24 '15 at 20:07