A material with a positive coefficient of temperature has resistance that increases with temperature.

A material with a positive coefficient of temperature has resistance that increases with temperature.

• A. Increases
• B. Decreases
• C. Stays constant
• D. Fluctuates

Answer: (A)

The concept being tested is the temperature coefficient of resistance. If a material has a positive coefficient, its resistance increases as temperature rises. This comes from the relation R = R0 [1 + α (T − T0)]. A small temperature increase ΔT leads to ΔR ≈ R0 α ΔT, which is positive when α > 0. Physically, higher temperatures make atoms vibrate more, causing more scattering of electrons by lattice vibrations (phonons) and thus higher resistivity. For metals, α is typically positive, so resistance climbs with temperature. In contrast, many semiconductors have a negative coefficient, so their resistance decreases as temperature increases. Therefore, a positive coefficient means the resistance increases with temperature.

The concept being tested is the temperature coefficient of resistance. If a material has a positive coefficient, its resistance increases as temperature rises. This comes from the relation R = R0 [1 + α (T − T0)]. A small temperature increase ΔT leads to ΔR ≈ R0 α ΔT, which is positive when α > 0. Physically, higher temperatures make atoms vibrate more, causing more scattering of electrons by lattice vibrations (phonons) and thus higher resistivity. For metals, α is typically positive, so resistance climbs with temperature. In contrast, many semiconductors have a negative coefficient, so their resistance decreases as temperature increases. Therefore, a positive coefficient means the resistance increases with temperature.