# $V$-$I$ linear OR $V=IR$ is statement of Ohm's law?

What is the real statement of Ohm's Law: $V$-$I$ is linear OR $V=IR$?

Looks like V-I is linear is ohm's law and conductors don't alway obey ohm's law and R=V/I is a general definition of R wheather conductor obeys ohm's law or not

I confirm your statement (with the slight amendment that for Ohm's law the relationship is not just linear but proportional (as I = 0 when V =0)).

A trickier issue is whether Ohm's law states that...

for a conductor I is proportional to V, in which case the law has a lot of exceptions, because there are lots of non-linear conductors (e.g. silicon diodes),

OR that for homogeneous conductors (e.g. wires made of one metal) at constant temperature (and, strictly, constant pressure), I is proportional to V. In this case the law is obeyed pretty accurately with no exceptions except at very high currents, as far as I know.

I won't give an opinion on which is the better statement of Ohm's law, because I once got into a lot of trouble over the issue.

The equation $R=\frac{V}{I}$ defines resistance, $R$. The equation by itself doesn't tell us anything about how a conductor behaves. We can apply the equation to a silicon diode, for example, finding that (within a certain range of pds) the diode's resistance drops from immeasurably high to a lower and lower value as we increase the forward pd, V. The key thing about an ohmic conductor is that the resistance, as defined above, doesn't change as we change the applied pd.

• thx this is helpful. Just to make sure I am getting the distinction between I proportional to V and V=IR. 1st one says R is indepedant of V & I and 2nd one says R may depend on V and/or I and but at any time R=V/I is that fair.? and I think even V=IR is not always true. is that correct .? – user31058 Jun 17 '17 at 13:00
• Yes, that's it, though I'd argue with the bit after your last 'and'. The way I look at it is that $R=\frac{V}{I}$ defines $R$. So it's always right, (for the same reason that a bachelor is always an unmarried male) and can be applied to both ohmic and non-ohmic conductors. But for Ohmic conductors, $R$ is a constant. – Philip Wood Jun 17 '17 at 13:13