Effect of Temperature on Resistivity?

📌 CONCEPT: The resistivity of a conductor increases with an increase in temperature due to the increased kinetic energy of the electrons, but certain metals exhibit a decrease in resistivity with temperature, known as the 'positive temperature coefficient of resistivity' (PTCR).

📐 RULE / FORMULA: The resistivity of a conductor is given by ρ = ρ0 (1 + α(T - T0)), where ρ is the resistivity at temperature T, ρ0 is the resistivity at reference temperature T0, and α is the temperature coefficient of resistivity.

💡 WORKED EXAMPLE: A certain metal shows a decrease in resistivity with an increase in temperature. To verify this experimentally, we can measure the resistivity of the metal at different temperatures using a Wheatstone bridge setup. We find that the resistivity decreases from 10 μΩm at 20°C to 8 μΩm at 100°C, confirming the PTCR phenomenon.

⚠️ COMMON MISTAKE: Students often assume that all metals exhibit an increase in resistivity with temperature, but in reality, certain metals like copper and silver exhibit a decrease in resistivity with temperature.