# How greatly can heat increase resistance?

A conductor has a resistance of 0.001 Ohms, at room temperature, by increasing the heat x100 degrees Celsius how greatly would that effect the conductor's resistance? I'm trying to find the correlation of heat and wire resistance.

• moving from 1 C to 100 c is NOT a 100X increase in temperature. It only a 36% increase in temperature. 373 Kelvin vs. 273 Kelvin. Sep 18, 2014 at 17:49
• If the resistor burns out, the resistance could be increased practically to infinity. Oct 14, 2014 at 19:30

It depends dramatically on the material of the wire. A temperature coefficient for resistance can be calculated. See here.

Elemental metals (e.g. Copper) generally increase in resistance at about +0.4% per Kelvin near room temperature. Alloys are often less. For hundreds of degrees C the temperature coefficient will not be a constant and you'll need to find tables or graphs to get an accurate answer for the particular material.

Typically, for a conductor, the coefficient that relates the resistivity of the material with temperature is positive. This means that when the temperature increases, the resistivity increases as well.
Here you can find a table with various coefficients, and an online calculator.

The relationship can be described by

$$\Delta\rho = \alpha\cdot \Delta T + \rho_0$$

where $\Delta\rho$ is the resistivity variation, $\alpha$ is the thermal coefficient for the material, $\Delta T$ is the temperature increase and $\rho_0$ is the original resistivity.

The resistance of a conductor is

$$R = \rho\cdot\dfrac{L}{A}$$

where $R$ is the resistance, $\rho$ the resistivity, $L$ the length of the conductor and $A$ the cross-section area.

The temperature linearly increases the resistivity of the materials assuming it doesn't get to cold or becomes so hot the material begins to liquify (as shown in figure below)

Lets say the resistivity of a material is given by $$\rho_{Total} = \rho_{T} + \rho_1 \\ where ~ \rho_T ~ is~equal~to~resistivity~due~to~temperature~ and~\rho_1 ~is ~the ~normal ~resistivity$$

since resistivity is inverse proportional to the mobility of a material $$\rho_{T}= \frac{1}{\sigma_T}=\frac{1}{en\mu_d}$$ where $\sigma$ is conductivity, n is free electrons per unit volume, and $\mu$ is the mobility of material

The key point is that $$\mu_d ~inversely~ proportional ~to~temperature ~$$ which then implies that the resisitivity is directly proptional to temperture.

$$\rho_T = AT$$ where A is a constant. Different materials of course will have different constants for A, but the underlying theory that temperature increases resistivity still holds

Here is a picture showing what I mean It depends on the material of the wire. Resistivity tables showing how the resistance of various materials vary with temperature are readily available online.