# How are proportional relations derived in physics?

I would like to ask a simple question :How are proportional relationships in physics found?

To be more specific, let's consider a simple law, Ohm's law, which states $\Delta V\propto I$. Now, it seems intuitive that as the potential difference increases, the current must also increase. But it doesn't seem intuitive at all that it would increase by the same factor. So, how are laws like these established? Is it just empirical or is there a theoretical way to do this?

NOTE: I am considering that proportionality means the same in physics, i.e if $a \propto c$, then $a/c = constant$.

• Proportionals are derived by results of experiments regression. – lucas Apr 19 '16 at 12:40

In many cases, when one experimentally finds two quantities are related to each other like, say, Ohm's Law, $\Delta I \propto \Delta V$ (it is more reasonable to write this way around, since you can usually control the voltage and then measure the resulting change in current), it is an approximation. Actually Ohm's Law is probably one of the most famous cases of this .... it is not a law in the sense of being a fundamental relationship between current and voltage, rather it is a convenient approximation for many materials under constant physical condition.