From what I have read about semiconductors, the reason their IV characteristic shows a decrease in resistance is because as voltage is increased, current is increased. However, the reason for the disproportionate increase in current is because any increase in current causes joule heating as describe by P = I^2R - current has a strong dependency on heating effect. This means the temperature increases. This causes more electrons to be freed as they have more energy (from the thermal energy) to cross the band gap. This causes a further increase in current than would occur with an ohmic conductor. This further increase in current reduces the resistance. Powerlines use this ohmic heating effect to there advantage by ramping up the voltage and therefore reducing the current so their is little joule heating. Could someone clarify if this logic is correct as this is what I have gathered from reading around various websites.
This brings up several problems for me: 1) Take a simple circuit with a loop of resistive wire, a transformer and a fixed power source. The power can either be put in as high current, low voltage or low current, high voltage. If the high voltage, low current combination causes less joule heating, where would the energy go in this circuit? 2) Ohmic conductors show that voltage is proportional to current and this holds across a range of temperatures. This means that if you increase the voltage, the current increases but the resistance remains constant. I don't get how this can happen? In a filament bulb, an increase in current causes a greater joule heating (and temperature rise) leading to an increase in resistance. What is it about an ohmic conductor that stops this from happening to it?