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If we raise the temperature of any conductor the atom, free electrons starts vibrating There kinetic energy increases

If kinetic energy increase then , Current must be increase As current increase resistance must decrease

Then why positive coefficient of temperature exist. There must be only negative coefficient of temperature

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If kinetic energy increase then the current must be increase . . . . is not true.

You can think of the free (mobile) electrons as having two types of motion.
A random component due to their thermal energy and a directed component, often called the drift velocity, produced by the electric field and hence the flow of charges (current).

Increasing the temperature increases the thermal motion of not only the free electrons but the ions in the lattice of the material and for most materials results in a greater impediment to the drifting of the free electrons under the influence of the electric field, hence a greater resistance and a lowering of the current.

Here is a graph of current against time after a light bulb is switched on.

enter image description here

Note the initial rise in the current when the bulb is filament is cold (low resistance) and then the lowering of the current due to the increase in resistance as the bulb heats up.

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