Electrical resistance represents the opposition a material presents to the flow of electric current. This resistance is influenced by external factors, with temperature being one of the most significant. For pure metals used as conductors, an increase in temperature leads to a direct increase in their electrical resistance.
The Mechanism of Resistance Increase in Conductors
Metallic conductors consist of a lattice of fixed, positively charged ions surrounded by a “sea” of mobile, free electrons, which are the charge carriers. Electrical resistance arises from the interference these flowing electrons encounter from the positive ions within the lattice structure.
When the temperature increases, thermal energy causes the fixed positive ions to vibrate more intensely around their lattice positions. These increased thermal oscillations mean the ions occupy a larger effective volume and move more erratically.
The path of the free electrons moving through the lattice becomes significantly more obstructed by these vibrating ions. The moving electrons are more likely to collide with the vigorously oscillating ions, a process known as electron scattering, which deflects the electron from its intended path and reduces its forward momentum. This increased frequency of scattering events directly impedes the collective flow of charge, resulting in a higher measured electrical resistance for the conductor. The concentration of free electrons does not change substantially with temperature, meaning the effect of enhanced scattering remains the dominant factor.
Quantifying Resistance Change with Temperature
A measurable change in resistance is quantified using the Temperature Coefficient of Resistance (TCR), symbolized by \(\alpha\). The TCR is a material property that defines how much the resistance changes for a given temperature change. For conductors like copper and gold, this coefficient is positive, confirming that resistance increases with rising temperature.
For small temperature changes, the relationship is approximated using the linear equation: \(R = R_0[1 + \alpha(T-T_0)]\). In this formula, \(R\) is the final resistance at the new temperature \(T\), and \(R_0\) is the initial resistance measured at a reference temperature \(T_0\). The term \((T-T_0)\) represents the temperature difference, and \(\alpha\) is the material’s TCR value, typically expressed in units of per degree Celsius or Kelvin.
This linear approximation provides a sufficiently accurate tool for calculating resistance changes in metals over a limited temperature range. For example, if the initial resistance of a copper wire at \(20^\circ\text{C}\) is known, this formula allows engineers to predict the new resistance at a higher operating temperature. The specific value of \(\alpha\) is unique to each material, making it a property used to select appropriate conductors for applications where temperature stability is a concern.
The Opposite Effect in Semiconductors and Insulators
Not all materials exhibit an increase in resistance with rising temperature; semiconductors and insulators demonstrate the opposite behavior, known as a negative temperature coefficient of resistance. This contrasting effect is driven by a different dominant physical mechanism related to the availability of charge carriers.
Unlike conductors, semiconductors and insulators have few free charge carriers at room temperature because their electrons are tightly bound in covalent bonds. Increasing the temperature adds thermal energy sufficient to break some of these bonds. Breaking a covalent bond releases an electron into the conduction band, simultaneously creating a positively charged “hole.” Both the newly freed electron and the resulting hole become mobile charge carriers capable of conducting current.
Although increased temperature still causes scattering, the number of new charge carriers created by thermal excitation increases exponentially. This exponential increase dramatically outweighs the resistance-increasing effect of scattering, leading to a net decrease in the material’s electrical resistance. This distinct behavior is exploited in specialized components like thermistors, which are designed to exploit this predictable change in resistance with temperature.