# Is there a relationship between voltage and resistance?

I was getting a bit confused with Ohm's law, and the relationship between the current, resistance and voltage/potential difference?
From my understanding, current and voltage both increase or decrease together, while current and resistance do the opposite?
I was then wondering if there was any relationship between the voltage and resistance, or did I get everything wrong?
Thanks!

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BvU
Homework Helper
2019 Award
relationship between the voltage and resistance
there is: it's called Ohms law. We write V = I R as if it were a 'law'. In reality it is a (generally very good) first approximation.

For a given resistance, if you double the voltage, the current doubles too.
For a given resistance, if you double the current, the voltage drop over the resistance doubles too.

For a given voltage, if you double the resistance, the current halves.
For a given voltage, if the current doubles, the resistance has halved.

For a given current, if you double the resistance, the voltage doubles too.
For a given current, if the voltage doubles, the resistance must have doubled.

 nice of you to like it, but I still must iron out some mistakions...

Cheesycheese213
BvU
Homework Helper
2019 Award
current and voltage both increase or decrease together
when the resistance is constant, yes.
while current and resistance do the opposite?
Yes: when the voltage is constant, the product of current and resistance is constant too.

sophiecentaur
Gold Member
when the resistance is constant, yes.
Yes: when the voltage is constant, the product of current and resistance is constant too.
etc. etc.
All this is just effectively re-arranging a mathematical equation. "Ohm's Law" is not so much a "Law" of Nature (as with Newton's Laws of Motion, which apply usefully in all cases until the conditions get extreme). We can measure the V and I of a component (something in a black box) and assign a value for R but there's absolutely no reason to assume that the R value will stay the same for another value of supply V. That would have to assume that the component actually followed Ohm's Law. We usually assume that a "resistor" out of the drawer will have a constant R (given by the coloured bands along the side) but it is only an assumption.
A Light Bulb Filament is Metal (Tungsten) and would follow Ohm's Law if you could find a way to keep the filament at a constant temperature. But it can get hot (by design, of course) and its Resistance will vary by a factor of about Ten between cold (off) and hot (full volts applied). Using the term Ohm's Law is, to my mind, just confusing but it is perfectly valid to measure the Volts and Current and to give it an instantaneous value of Resistance. Light bulbs and many other components are referred to as non-Ohmic conductors but they can all be assigned an instantaneous value of R, according to the volts applied.

Despite what is written in many text books and even in Wikipedia, I strongly feel that the relationship R=V/I and Ohm's Law should be treated as two distinct ideas.
Do we have a "Speed Law" to describe Distance / time = speed? No; that's just a relationship between two variables.

Nugatory
Mentor
I was getting a bit confused with Ohm's law, and the relationship between the current, resistance and voltage/potential difference?
Any two of them determine the third.

sophiecentaur
Gold Member
Any two of them determine the third.
That's the Maths of the situation. The Resistance is not readily changeable for the same physical entity, though. Changing the resistance would actually involve changing, say, the length of a rheostat wire so it is no longer the same entity.

BvU