# Ohm's law at high voltages [closed]

Ohm's law in its original form:

The conductivity is constant for a given conductor at a given temperature.(Taken from H.C.Verma).

My Question: When high voltages are impressed across a conductor, valence band starts to overlap with conduction band. On further increasing the voltage, not only the electrons in the conduction band speed up (thereby increasing the current) but also the electrons from the valence band starts conducting (thereby increasing the current). Doesn't this phenomenon violate ohm's law? Because now a small increase in voltage will increase current by a larger factor than with the case when valence band didn't yet overlap with the conduction band.

## closed as unclear what you're asking by Jon Custer, Yashas, Bill N, Wolpertinger, honeste_vivereSep 8 '17 at 13:44

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• Why will electrons in a valence band in a metal start to conduct? Or are you talking about a semiconductor? Or are you concerned about high voltage breakdown regimes? Unclear question. – Jon Custer Sep 6 '17 at 15:58
• No.I am saying that as we increase the voltage,valence band starts to overlap with the conduction band.I am talking about CONDUCTORS only. – ADIMAN Sep 6 '17 at 16:39
• For a conductor, the valence band do overlap the conduction band already at normal conditions. – Physicpsycho Sep 6 '17 at 16:58
• Oh sorry!I would have said electrons from lower energy levels with energy lower than valence band will jump to conduction/valence band (since it is a conductor).I apologize for what i did.Sorry – ADIMAN Sep 6 '17 at 17:30

Yes, I believe you are coming to an important realization: that Ohm's law is an approximation, and only appropriate in certain circumstances. Ohm's law is a linear relation (macroscopic $V=IR$ and microscopic $J=\sigma E$), which works well for general conduction in metals, semiconductors, etc when nothing funny is going on. That is, it is appropriate for linear materials and systems. But there are many examples of devices which are nonlinear, including diodes and transistors (for which $V$ is not simply proportional to $I$).