EFFECT OF TEMPERATURE ON RESISTANCE: 101 COMPREHENSIVE GUIDE

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

EFFECT OF TEMPERATURE ON RESISTANCE OF PURE METALS

The effect of temperature on resistance is such that the resistance of pure metals (e.g. copper, aluminum) increases with the increase of temperature. The change in resistance is fairly regular for a normal range of temperatures so the temperature-resistance graph is a straight line as shown in Fig, it shows the 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 a 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.

Since the resistance of metals increases with the rise in temperature, they have a positive temperature coefficient of resistance.

EFFECT OF TEMPERATURE ON RESISTANCE OF INSULATORS

The effect of temperature on 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.

EFFECT OF TEMPERATURE ON RESISTANCE OF ALLOYS

However, the effect of temperature on resistance in the case of alloys is such, that 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.

Temperature Coefficient of Resistance

Consider a conductor having resistance R₀ at 0°C and R_t at t °C. It has been found that in the normal range of temperatures, the increase in resistance (i.e. Rt − R0) is directly proportional to the initial resistance i.e. R_t − R₀ ∝ R₀

The increase in resistance is directly proportional to the rise in temperature i.e.

 R_t − R₀ ∝ t

The increase in temperature on resistance also depends upon the nature of the material.

Therefore, by combining the first two, we get,

R_t − R₀ ∝ R₀ * t

or R_t − R₀ = α₀ * R₀ * t, where α₀ is a constant and is called the temperature coefficient of resistance at 0°C. Its value depends upon the nature of the material and temperature.

Rearranging the above equation we get,

 R_t = R₀ (1 + α₀ t)

= Increase in resistance/ohm original resistance/°C rise in temperature.

Hence, the temperature coefficient of resistance of a conductor is the increase in resistance per ohm original resistance per °C rise in temperature.

A little reflection shows that the unit of α will be ohm/ohm°C i.e./°C. Thus, copper has a temperature coefficient of resistance of 0.00426/°C. It means that if a copper wire has a resistance of 1 Ω at 0°C, then it will increase by 0.00426 Ω for a 1°C rise in temperature i.e. it will become 1.00426 Ω at 1°C. Similarly, if the temperature is raised to 10°C, then resistance will become 1 + 10 × 0.00426 = 1.0426 ohms.

Important points to be noted:

Those substances (e.g. pure metals) whose resistance increases with rise in temperature are said to have a positive temperature coefficient of resistance. On the other hand, those substances whose resistance decreases with an increase in temperature are said to have a negative temperature coefficient of resistance.

If a conductor has a resistance R₀, R₁ and R₂ at 0^o C, t₁ ^o C and t₂ ^o C respectively, then,

R₁ = R₀ (1 + α₀ t₁), and R₂ = R₀ (1 + α₀ t₂)

This relation is often utilized in determining the rise of the temperature of the winding of an electrical machine. The resistance of the winding is measured both before and after the test run. Let R₁ and t₁ be the resistance and temperature before the commencement of the test. After the operation of the machine for a given period, let these values be R₂ and t₂. Since R₁ and R₂ can be measured and t₁ (ambient temperature) and a₀ are known, the value of t₂ can be calculated from the above equation. The average rise in temperature of the winding will be (t₂ − t₁) ° C.

The life expectancy of an electrical device is limited by the temperature of its insulation, the higher the temperature, the shorter the life. The useful life of electrical apparatus reduces approximately by half every time the temperature increases by 10°C. This means that if a motor has a normal life expectancy of eight years at a temperature of 100°C, it will have a life expectancy of only four years at a temperature of 110°C, two years at a temperature of 120°C and only one year at 130°C.

Graphical Determination of Thermal Coefficient of resistance,α

The value of the temperature coefficient of resistance can also be determined graphically from the temperature-resistance graph of the material. Fig. below shows the temperature/resistance graph for a conductor.

The graph is a straight line AX as is the case with all conductors. The resistance of the conductor is R₀ (represented by OA) at 0°C and it becomes R_t at t°C. By definition,

But R_t − R₀ = BC

and t = rise in temperature = AB and α₀ = BC / (R₀ * AB)

But, BC/AB is the slope of the temperature-resistance graph. Therefore, α₀ = Slope of the graph / original resistance.

Hence, the temperature coefficient of resistance of a conductor at 0°C is the slope of the temperature-resistance graph divided by resistance at 0°C (i.e. R₀).

Important points to be noted:

The value of α depends upon temperature. At any temperature, a can be calculated by using

α₀ = Slope of the graph / original resistance (R₀) and

α_t = Slope of the graph / original resistance (R_t).

The value of α₀ is maximum and it decreases as the temperature is increased. This is clear from the fact that the slope of the temperature on resistance graph is constant and R₀ has the minimum value.

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