Temperature affects every material you can think of and resistors are no exceptions. The resistance of a resistor can change considerably over a range of temperature. Thus  it is quite important to take the effect of temperature into consideration while designing a circuit. The behavior of circuit might change considerably due to changes in resistance with temperature. The goal of this section is to quantitatively analyse how much change the resistance will undergo with the change in temperature. The factor which describes how much change the resistance will undergo as a function of temperature is called temperature coefficient.

In simple terms, temperature coefficient can be thought of as a parameter which describes the relative changes in resistance with temperature. You know from basics that the resistance of a simple conductor increases with temperature. This is due to the collisions taking place between vibrating atoms and free electrons. But while designing a circuit, this information is insufficient. We need some numbers which describes how much variation occurs in resistance with temperature. This figure is called temperature coefficient.

Temperature coefficient – Mathematical equation

Temperature coefficient can be mathematically described by the following equation.equation of temperature coefficient of resistors

Here the term α is called temperature coefficient. The term ΔR represents change in resistance as a result of change in temperature  ΔT . If we indicate the room temperature as T0, then the resistance at room temperature is indicated by R0. Now let us suppose that the temperature changes by  ΔT and the temperature becomes T, the corresponding resistance will now be R.

Hence  ΔT = T – T0

and  ΔR = R – R0.

Putting the value of  ΔT and  ΔR in equation (1), we get

simplified equation of temperature coefficientThus if we know the value of resistance R0 at temperature T0, we can calculate the value of resistance R at a given temperature T. Keep in mind that the above equation is valid only for  small changes in temperature. For large changes in temperature, more detailed calculations must be followed. Also note that the value of  α is different for different temperatures. Hence care must be taken to ensure that the correct value of α is used in the calculation.

Temperature coefficient has the unit 1/K or K-1. In practical applications, α is often described as ppm/°C. ppm means parts per million. Let us take an example to understand what it means by ppm/°C. Suppose a typical resistor has temperature coefficient of 100 ppm/°C. 100 ppm means one hundred parts for every one million parts. Hence for a 1°C change in temperature, the resistance will change by 100 ohms if the nominal value of resistance is 1 MΩ (one million ohms). If the resistor value is 100kΩ, the 100 ppm/°C will indicate a change in 10 Ω for every 1 °C change in temperature. You can use the following ppm/°C calculator to quickly calculate how much change occurs in resistance with temperature.

 

Temperature coefficient can be either a positive or negative value. Positive temperature coefficient indicates increase in resistance with temperature whereas negative temperature coefficient indicates decrease in resistance with temperature.