As we know that

1. Metallic conductor :In Metals, the number of free electron is fixed, as the temperature increase, the amplitude of vibration of the atoms increases. The collisions of the electrons with these atoms becomes more frequent. The relaxation time decreases. Hence the resistivity of a metallic conductor increases with the increase in temp.
2. Semiconductor:  in case of semiconductor, the relaxation time does not changes with temperature but the number density of free electrons increases exponentially with the increase or resistivity decrease exponentially with the increase in temp.
3. Ionic Temperature: as ionic conductor has both positive and negative ions as the charge carriers. As the temperature increases. The ions are move freely and so the conductivity increases or resistivity decreases.
4.  Electrolyte : as the temp. increases, the ions move more freely so the conductivity increases or resistivity decreases.

Temperature coefficient of resistivity:

The temperature coefficient of resistivity may be defined as the increase in resistivity per unit resistivity per degree rise in temperature. It is given by

thus the resistivity at new temperature T will be

Hence the above equation may be written as

The unit of α is ⁰C^-1.

• For metal α is positive , i.e. resistance of metals increases with rise in temperature
•  For semiconductor and insulator, α is negative, i.e. their resistance decreases with the increase in temperature.
• For alloys like constantan and manganin , the temperature coefficient of resistance α is very small. So they used for making standard resistors.

Ques.    Why alloys like constantan or manganin are used in making standard resistance coils:

Ans:

1. These alloys have high value of resistivity.
2. They have very small temperature coefficient. So their resistance does not change appreciable even for several degree rise in temp.
3. They are least affected by atmosphere conditions like air, moistures etc.
4. Their contact potential with copper is small.