Temperature coefficient and metallic conductors If a metallic conductor exhibits a positive temperature coefficient of resistance, how does its resistance change as temperature increases?

Introduction / Context:
Most metals have a positive temperature coefficient of resistance (TCR). Understanding TCR is important for sensor design, power electronics, and precision measurement because temperature changes alter circuit behavior and can require compensation.

Given Data / Assumptions:

• Material is a typical metallic conductor (e.g., copper, aluminum).
• Temperature changes within normal operating ranges.
• No phase changes or extreme cryogenic effects.

Concept / Approach:
In metals, increased temperature causes more lattice vibrations (phonons). These increase electron scattering, which raises resistivity. The resistance approximately follows R(T) ≈ R0 * [1 + α * (T − T0)], where α > 0 for metals. Therefore, as temperature rises, resistance increases.

Step-by-Step Solution:
Start with R(T) = R0 * [1 + α * (T − T0)] for α > 0.If T increases, (T − T0) increases.Since α is positive, the product α * (T − T0) is positive, so R(T) > R0.Thus, resistance increases with temperature.

Verification / Alternative check:
Observe practical devices: incandescent filaments (tungsten) have much higher resistance hot than cold, explaining inrush current behavior.

Why Other Options Are Wrong:
Resistance decreases with temperature: true for many semiconductors or carbon, not metals.As current increases, resistance decreases: mixes variables; TCR is about temperature, not current directly.As voltage increases, current increases: that is Ohm’s law, not TCR behavior.

Common Pitfalls:
Confusing metallic behavior with NTC thermistors or semiconductor resistivity trends, which often show negative TCR.

Final Answer:
as temperature increases, resistance increases