The resistivity of a metal increases as the temperature rises. This happens because, with increasing temperature, the metal atoms vibrate more intensely, leading to more frequent collisions between the free electrons (which carry current) and the vibrating atoms. These collisions increase resistance to electron flow, thus increasing the metal's resistivity. Metals generally have a positive temperature coefficient of resistivity, meaning their resistivity increases linearly with temperature over typical temperature ranges.

Explanation

• As temperature rises, atoms in a metal vibrate more vigorously.
• The increased atomic vibrations cause more collisions for free electrons traveling through the metal.
• This reduces the electrons' mean free path and mobility, raising resistivity.
• The relationship is often expressed as ρ=ρ0[1+α(T−T0)]\rho =\rho_0 [1+\alpha (T-T_0)]ρ=ρ0​[1+α(T−T0​)], where α\alpha α is a positive temperature coefficient for metals.

Thus, a rise in temperature causes the resistivity of metals to increase, making them less conductive at higher temperatures.