Question

In the temperature range in which resistivity increases linear with temperature, the temperature coefficient of resistivity alpha is defined as the fractional increase in resistivity per unit increase in temperature......?

Answer 1

Answer:

Temperature coefficient of resistance is the measure of change in electrical resistance of any substance per degree of temperature change.

Let us take a conductor having a resistance of R0 at 0oC and Rt at toC respectively.

This αo is called temperature coefficient of resistance of that substance at 0oC.

From the above equation, it is clear that the change in electrical resistance of any substance due to temperature mainly depends upon three factors –

the value of resistance at initial temperature,

the rise of temperature and

the temperature coefficient of resistance αo.

This αo is different for different materials, so effect on resistance at different temperature are different in different materials.

So the temperature coefficient of resistance at 0oC of any substance is the reciprocal of the inferred zero resistance temperature of that substance. So far we have discussed the materials that resistance increases with increase in temperature, but there are many materials electrical resistance of which decreases with a decrease in temperature. Actually in metal if the temperature increases, the random motion of free electrons and interatomic vibration inside the metal increase which result in more collisions. More collisions resist the smooth flow of electrons through the metal, hence the resistance of the metal increases with the rise in temperature. So, we consider the temperature coefficient of resistance as positive for metal.

But in case of semiconductor or other non-metal, the number of free electrons increases with increase in temperature. Because at a higher temperature, due to sufficient heat energy supplied to the crystal, a significant number of covalent bonds get broken, and hence more free electrons get created. That means if temperature increases, a significant number of electrons comes to the conduction bands from valence bands by crossing the forbidden energy gap. As the number of free electrons increases, the resistance of this type of non-metallic substance decreases with an increase in temperature. Hence temperature coefficient of resistance is negative for non-metallic substances and semiconductors.

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