Temperature coefficient of resistivity

Not only resistance but resistivity of a substance is also effected by the temperature , and in the case of conductors ( mostly metallic conductors) the resistivity increases with the increase in it’s temperature and decreases with the decrease in temperature.Temperature coefficient of resistivity  can be defined as the rate of change of Resistivity per degree change in the temperature from a substance’s original temperature.

The resistivity of metallic conductors vary almost linearly with temperature over normal temperature and becomes non-linear both at very high and very low temperatures , Or in other words metallic conductors have positive temperature coefficient of resistivity. ( If the substance’s resistivity decreases with increase in temperature the substance is said to have a negative temperature coefficient of resistivity.) , as shown in the figure below:

Temperature coefficient of resistivity
Temperature coefficient of resistivity

 

Formula for temperature coefficient of resistivity:

The formula for temperature coefficient of resistivity can be derived as follows:

Let us suppose:

\rho _1 = Resistivity of a conductor at temperature t_1 ^o C

\rho _2 = Resistivity of the conductor at temperature t_2 ^o C

m = slope of the linear part of the curve of the resistivity line in the graph Resistivity versus Temperature as shown above.

Then,

\rho = \dfrac{\rho _2 - \rho _1}{t_2 - t_1}

or, \rho _2 = \rho _1 + m (t_2 - t_1)

or, \dfrac{m}{\rho _1} = \dfrac{(\rho_2 - \rho_1)}{\rho_1 \times (t_2 - t_1)}

The term: \dfrac{m}{\rho_1} is called the temperature coefficient of resistivity and is defined numerically as the fractional change in \rho _1 fer ^o C change in the temperature from t_1 ^o C.

Note: In most cases the numerical value of Temperature coefficient of resistance and Temperature coefficient of resistivity is almost equal.