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why does resistance increase at high voltages
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I think this is making it too complicated. To get a certain power, then an increase in voltage would require a reduced current. However, power output isn't something you can keep constant whilst increasing the voltage unless you increase the resistance in order to reduce the current. This goes against the original question which, we assume, refers to the same resistance component throughout.
stanleyman
You have raised an important question for which providing an appropriate answer will hopefully satisfy a requirement imposed by the way the question generating this thread was phrased. Does everyone have their thinking cap in place?
When electrical current flows through a resistance some heat is generated. Under normal circumstances, even a conductor will exhibit a relatively small value of resistance.
In a well designed circuit the resistance of a resistor or conductor will not be significantly effected by the normal operating current flowing through it. However, if the current through it increases to a level that approaches or exceeds its designed current carrying capacity it will no longer be able to dissipate heat as quickly as it is generated. As temperature increases the resistance will increase in some materials. The combined increase of heating and resistance may lead to a failure of a conductor or resistor. This is what causes fuses to blow when excessive current flows through them; they melt or vaporize depending on how strong the current is.
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Sorry Mib but I dropped off before getting to the end of that :) The question was, why does resistance increase at high voltages? It doesn't, voltage is irrelevant, resistance remains constant and is only relevant to the current flowing through it.
If the questioner means why does the resistance increase when the voltage increases then as I think everyone understands, the current also increases causing the load to heat and increase the resistance as per the first answer by dynamicduo.