# Resistance Variation with Temperature

on 24/2/2012 & Updated on 28/8/2018
If we take a piece of pure metal and make its temperature 0^{o} by means of ice and then increase its temperature from gradually from 0^{o}C to to 100^{o}C by heating it.

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During increasing of temperature if we take its resistance at a regular interval, we will find that electrical resistance of the metal piece is gradually increased with increase in temperature. If we plot the **resistance variation with temperature** i.e. resistance Vs temperature graph, we will get a straight line as shown in the figure below. If this straight line is extended behind the resistance axis, it will cut the temperature axis at some temperature, - t_{0}^{o}C. From the graph it is clear that, at this temperature the electrical resistance of the metal becomes zero. This temperature is referred as *inferred zero resistance temperature*.
Although zero resistance of any substance cannot be possible practically. Actually rate of **resistance variation with temperature** is not constant throughout all range of temperature. Actual graph is also shown in the figure below.
Let's R_{1} and R_{2} are the measured resistances at temperature t_{1}^{o}C and t_{2}^{o}C respectively. Then we can write the equation below,
From the above equation we can calculate resistance of any material at different temperature. Suppose we have measured resistance of a metal at t_{1}^{o}C and this is R_{1}.
If we know the inferred zero resistance temperature i.e. t_{0} of that particular metal, then we can easily calculate any unknown resistance R_{2} at any temperature t_{2}^{o}C from the above equation.

The resistance variation with temperature is often used for determining temperature variation of any electrical machine. For example, in temperature rise test of transformer, for determining winding temperature rise, the above equation is applied. This is impossible to access winding inside the an electrical power transformer insulation system for measurement of temperature but we are lucky enough that we have resistance variation with temperature graph in our hand. After measuring electrical resistance of the winding both at the beginning and end of the test run of the transformer, we can easily determine the temperature rise in the transformer winding during test run.

20^{o}C is adopted as standard reference temperature for mentioning resistance. That means if we say resistance of any substance is 20Ω that means this resistance is measured at the temperature of 20^{o}C.

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