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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.

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ 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. $\endgroup$ – Jon Custer Sep 6 '17 at 15:58
  • $\begingroup$ 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. $\endgroup$ – ADIMAN Sep 6 '17 at 16:39
  • $\begingroup$ For a conductor, the valence band do overlap the conduction band already at normal conditions. $\endgroup$ – Physicpsycho Sep 6 '17 at 16:58
  • $\begingroup$ 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 $\endgroup$ – ADIMAN Sep 6 '17 at 17:30
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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 $I$).

You're also right that high fields can induce nonlinearities in the microscopic conductivity. Large voltages can excite electrons to different energies with different mobilities, they can distort lattices of certain materials in certain ways, and cause tunneling currents in narrow-gap semiconductors, among other things (Stark shifts, Franz-Keldysh effect, etc). Perhaps your example happens as well.

In short, Ohm's law is less of a law and more of a good approximation for many cases.

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    $\begingroup$ You might say "it is a law for linear materials". But all materials will be nonlinear at sufficiently high fields. $\endgroup$ – Floris Sep 6 '17 at 17:14

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