Conductor Resistivity vs. Temperature Explained

Resistivity, often denoted by the Greek letter $\rho$, is a fundamental property of a material that measures how strongly it resists the flow of electric current. It's independent of the object's shape or size, unlike resistance.

Temperature Dependence of Resistivity in Conductors

For most metallic conductors (like copper, silver, aluminum), the resistivity increases as the temperature increases. This is a key characteristic behaviour for conductors.

Why Resistivity Increases with Temperature

• Atomic Vibrations: In a solid conductor, atoms are arranged in a lattice structure. At higher temperatures, these atoms vibrate more vigorously around their fixed positions.
• Electron Scattering: Electric current in metals is due to the movement of free electrons. As these electrons move through the conductor, they collide with the vibrating atoms (or lattice imperfections).
• Increased Collisions: When the temperature increases, the increased atomic vibrations lead to more frequent and energetic collisions between the electrons and the lattice atoms.
• Impeded Flow: These frequent collisions impede the smooth flow of electrons, effectively increasing the material's opposition to current flow. This opposition is quantified as increased resistance and, consequently, increased resistivity.

Mathematical Approximation

For many conductors, over a limited temperature range, the relationship between resistivity ($\rho$) and temperature ($T$) can be approximated by the formula:

$$ \rho \approx \rho_0 (1 + \alpha (T - T_0)) $$

Where:

• $\rho$ is the resistivity at temperature $T$.
• $\rho_0$ is the resistivity at a reference temperature $T_0$.
• $\alpha$ is the temperature coefficient of resistivity. For most metallic conductors, $\alpha$ is positive, confirming that resistivity increases with temperature.
• $T$ is the final temperature.
• $T_0$ is the reference temperature.

Analyzing the Options

Based on the physics of conductors:

• Option 1: increases - This aligns with the behaviour of conductors due to increased electron scattering at higher temperatures.
• Option 2: decreases - This is typically observed in semiconductors and insulators, not conductors.
• Option 3: remains the same - Resistivity is temperature-dependent for conductors.
• Option 4: becomes zero - Zero resistivity signifies superconductivity, a phenomenon occurring at very low temperatures under specific conditions, not a general response to increased temperature.

Therefore, the resistivity of a conductor increases with an increase in temperature.