Temperature Coefficient of Resistance

Temperature coefficient of resistance, this is the factor that temperature does affect the value of resistance in a resistor or a conducting wire. All the resistors value of resistance is specified at specific temperature and that is 20 degree Celsius. If the temperature where resistor is placed is more or less than 20 degree Celsius, then the value of that specified resistor differs. That difference is obviously dependent on temperature coefficient of resistance.

Suppose we want to use a circuit having resistors in a compute which heats and inner temperature will be of course more than 20 degree Celsius. In this case, values of resistance changes and thus affect the system’s voltage and current controlling part of the circuit.  The influence of temperature on resistance is estimated using temperature coefficient.

Influence of Temperature on Resistance

The electric current is more than army of electrons which stimulates the atoms in a conductor. If a material (conductor) is heated, the atoms vibrate. This will make the free electrons to collide with the atoms. This creates more resistance in the movement of electrons through the conductor. The resistance will be more with rise in temperature. This feature is known as the temperature coefficient of resistance.

It is defined as the change in resistance per degree rise of temperature for every ohm of resistance. It is denoted by the symbol “alpha” (α). All the conductors have their specific temperature coefficient at 20 degree Celsius. For pure metals, temperature coefficient is positive that means their resistance will increase with increase in temperature. This is referred as positive temperature coefficient of resistance. While for some elements temperature coefficient is negative that means their resistance will decrease on increasing the temperature which is known as negative temperature coefficient of resistance.

For some very good conductors, the temperature coefficient is nearly zero, which means their resistance doesn’t change a lot with a change in temperature. This type of metals is generally used for making precision resistors. The change in resistance of resistors other than 20 degree Celsius can be given by this formula.

R=R₀ [1+α(T-T₀ )]

Where, R= Resistance at temperature ‘T’ R₀= Resistance at reference temperature, usually 20 degree Celsius. α = Temperature coefficient of material. T = Temperature T₀ = Reference temperature, usually 20 degree Celsius. Note: Sometimes the reference temperature can be 273K i.e. 0 degree Celsius instead of 20 degree Celsius. If the 20Ω resistor is at 40 degree Celsius. We can now determine its resistance at this temperature. The temperature coefficient of copper at 20 degree Celsius is 0.004041.

R=20[1+0.004041(40-20)]

∴R=20[1+0.08082]

∴R=20[1.08082]

∴R=21.6164Ω

Therefore, the value of resistance changed by 1.6Ω. This can bring a huge difference in circuit. To observe this difference lets us assume this resistor is connected to 12Vand we need to figure out the current. Then, if we do not consider effect of temperature, then current would be

I = 12/20 = 0.6A

And if we calculate keeping in mind the effects of temperature, current would be

I = 12/21.6164 = 0.55A

You can observe the difference we are getting. This difference can sometimes mislead and thus we have to keep in mind the effect of temperature on the value of resistance. The below table shows the temperature coefficient of resistance for various metals.

Metal	Temperature Coefficient
Copper	0.0039
Silver	0.0038
Aluminium	0.0036
Iron	0.0045
Tin	0.0045
Zinc	0.0037
Lead	0.004
Manganin	0.000015
Nichrome	0.0004
Constantan	0.000025

In some high power applications, current is dissipated in the form of heat and thus increases the temperature of the system inside the enclosure. In some units, fans are provided to regulate the temperature inside the enclosure. Thus, here the value of resistance changes greatly and thus precision resistors are used keeping in mind the effects of temperature.