Electrical Engineering ⇒ Topic : Effect of Temperature on Resistance

Effect of Temperature on Resistance

As already studied in Chap. , an increase in temperature increases the resistance of pure metals. If a conductor having a resistance of R_o at 0°C is heated to a temperature 1°C, its resistance increases. Let the new resistance be R_T. The net increase in resistance is (R_T - R₀). This can be written as:

                                              (R_T - R_O) = α R_O T                       .............. (1)

where, α (Greek symbol, Alpha) is a constant and is called the temperature coefficient of resistance of the material of the conductor. From Eq. (1) we find that

                                             R_T = R_O (l + αT)                            .............. (2)

where R_T is the final resistance, R_O is the initial resistance, T is the difference between the final and the initial temperatures and α is the temperature coefficient of resistance of the material.

The temperature coefficient of some metals which are widely used as conductor is given in Table (a).

                                 TABLE (a) Temperature coefficient of resistance of different metals

So far, we have assumed that a does not change with temperature, but in most metals it does change with temperature. If α₁ is the temperature coefficient at temperature T₁ and α₂ is the temperature coefficient at temperature T₂ and if we know α₁, T₁ and T₂, we can calculate α₂ from the following equation

                                                     .............. (3)

Similarly, resistivity or specific resistance of a metal also changes with temperature.The relationship between ρ_o and ρ_T, can be written as

                                                     ρ_T = ρ₀(l+ αT)                  ................. (4)      

Equations (2), (3) and (4) describe the variation of resistance, temperature coefficient and resistivity of a material with variation in its temperature

Effect of Temperature on Resistance

In general, the resistance of a material changes with the change in temperature. The effect of temperature upon resistance varies according to the type of material as discussed below

• The resistance of pure metals (e.g. copper, aluminium) increases with the increase of temperature. The change in resistance is fairly regular for normal range of temperatures so that temperature/ resistance graph is a straight line as shown in Fig. (a) (for copper). Since the resistance of metals increases with the rise in temperature, they have positive temperature co-efficient of resistance.
• The resistance of electrolytes,insulators (e.g. glass, mica, rubber etc.)and semiconductors (e.g. germanium,silicon etc.) decreases with the increase in temperature. Hence these materials have negative temperature co-efficient of resistance.
• The resistance of alloys increases with the rise in temperature but this increase is very small and irregular. For some high resistance alloys (e.g. Eureka, manganin, constantan etc.), the change in resistance is practically negligible over a wide range of temperatures.

                                                                       figure (a)

Figure (a) shows temperature/resistance graph for copper which is a straight line. If this line is extended backward, it would cut the temperature axis at 234.5°C. It means that theoretically, the resistance of copper wire is zero at 234.5°C. However, in actual practice, the curve departs (point A) from the straight line path at very low temperatures