In most conductive materials, resistance increases with temperature. This is due to the increased thermal agitation of atoms at higher temperatures, which causes more collisions between electrons and atoms, impeding the flow of electrical current.
For metals, the resistance \( R \) can be approximated by the equation:
\[ R(T) = R_0 [1 + \alpha (T - T_0)] \]
where:
- \( R(T) \) is the resistance at temperature \( T \),
- \( R_0 \) is the resistance at a reference temperature \( T_0 \),
- \( \alpha \) is the temperature coefficient of resistance, which is positive for metals.
In contrast, for semiconductors and insulators, resistance typically decreases with increasing temperature. This is because the number of charge carriers increases with temperature, leading to improved conductivity.