Does an increase in the temperature of a metal conductor cause the positive metal ions to vibrate more hence increasing the resistivity or does an increase in the vibrational energy (from an increase in current in a circuit for example) cause an increase in temperature of the metal conductor?
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2 Answers
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This question doesn't make sense, really, since temperature and vibrational energy are almost the same thing. The temperature of a material is just a measurement that's proportional to the average kinetic energy of that materials molecules. Saying that temperature causes an increase in kinetic energy is kind of like saying an increase in weight causes an increase in mass. The two quantities are inextricably linked. The temperature of, for example, an ideal gas is just the average kinetic energy of the molecules multiplied by $2/k_b$ for every degree of freedom in the molecules' motion.
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Ok, first of all an increase in temperature doesn't always mean there will be an increase in resistance. That is only true in the case of conductors, where there is already a sufficient amount of free electrons inside the material.
What happens then is that as the temperature of the material rises its atoms vibrate violently disrupting the flow of electrons, therefore increasing its electric resistance. So, resistance inside a conductor creates heat and the heat increases resistance.
Now, in the case of an insulator it isn't the same. There is not enough free electrons to begin with inside it so there is no current flow. But when it's heated after some point the violent vibrations of its atoms will cause them to "release" some electrons. The amount of free electrons will become bigger so resistance will drop. This is negligible as far as I am concerned in everyday conductors, let's say plastic for example.
Edit: I know you said conductor but I wasn't aware if you knew the difference.
