Ohmic and Non-Ohmic devices

Question

Why do some conductors follow Ohm's law and some do not? Isn't there any universal law that can explain the flow of current?

Answer 1

Physics does not contain any truly 'universal' laws yet. Ohm's law like any other within physics relies on context for validity. $V=IR$ is implicitly only valid in simple circuit theory, in field theory it has the form $J=\sigma E$ as seen in the wiki article.

Variations from Ohm's law are due to electrical properties of the conductor/medium under inspection. The 'law' or equation to be used will be determined by pragmatic concerns of usefulness.

Answer 2

Ohm's law is an assumption that the value of resistance for a resistor is independent of the magnitude and polarity of an applied potential difference. Many conductors, like a diode, depend on the polarity of the applied potential difference-- e.g. you must apply a positive or negative voltage to get a current to move across the conductor.

An ohmic resistor on the other hand, will have a current that is linearly dependent on potential-- so as a larger positive voltage is applied to the resistor, there will be a correspondingly larger positive current through the resistor. Since R = V/I in a circuit, if both V and I are scaling up or down at a constant, linearly proportional rate, R will be constant since the factors that scale the numerator and denominator cancel each other out... and this is what it is meant by a resistor to be ohmic.

Most conductors change their resistance as their temperature change, and like a diodes, some conductors have completely non-linear relationships between current and voltage. Because Ohm's law isn't really a law, a more consistent way to look at a material is to consider it's "instantaneous" resistance, or it's resistivity (a property of a material as opposed to a geometry of a material):

$\rho$=$\frac{E}{J}$

$\rho$ is defined as the resistivity -- this is given by the electric field, $E$, divided by the current density $J$, (the current per cross-sectional area). So intuitively, a material with a high resistivity has a low current density motivated by a large electric field (remember, e-fields are proportional to the force on a particle), and a material with a low resistivity has a large current density motivated by a low electric field...

In any case, the salient thing to take away from this is that Ohm's law is only a "law" because of historical reasons-- in reality Ohm's law describes a special subgroup of conductors that have a linear relationship between current and voltage, but there are many conductors which don't fit this constraint.