# How does an increase in potential difference increase the resistance of a non-Ohmic conductor?

I am a little confused with the reasoning of why an increase in potential difference (P.D.) increases the resistance of a non-Ohmic conductor, namely a filament lamp.

From what I've seen this is the reason for why Temperature affects resistance

The increase in temperature increases the vibrational energy of the positive ions causing them to vibrate more vigorously causing the flowing electrons to collide with the ions more frequently, which causes more loss in kinetic energy of the electrons, which reduces the current.

Is it enough to say that an increase in P.D. simply increases the temperature of the conductors causing the effect as described above? or am I missing a few point?

• P.D. is short for what? – Pieter Mar 9 '18 at 23:30
• @Pieter -Its "potential difference" as defined in the first sentence, not "Privatdozent". – freecharly Mar 10 '18 at 0:45
• You have the basics in a simplified picture, except for one or two missing links. I find it more satisfying to say that the increased current causes the temperature to rise. More current means more collisions per second, meaning that the rate that energy is deposited into the lattice increases relative to the energy lost by such mechanisms as conduction, convection, and significantly for a filament, radiation. – garyp Aug 8 at 1:35

Independent of the resistance, the energy released by a current flow through a conductor per unit time (called power) is given by the the product of potential difference $V$ and current $I$: $$P=V\cdot I$$ This energy corresponds to the potential energy loss of the electrons going from high potential energy $e\cdot V$ at the negative contact of the resistor to zero potential energy at the positive contact of the resistor. This energy is converted into thermal energy (heat) of the conductor, which largely corresponds to the vibrational energy of the crystal lattice of the conductor characterized by its temperature. These lattice vibration in turn lead to an enhanced scattering of the electrons which enhances the resistance $R$ of the conductor reducing the current flow according to Ohm's law $$I=\frac {V}{R}$$ In the case if the filament, the increase of the applied voltage increases the the power released and thus the temperature of the wire which increases it's resistance $R$.