When the temperature of metallic conductor increases, the velocity of free electrons increases but it also cause increase in amplitude of vibration of metallic atoms (kernels) which cause some extra hindrance or resistance in the path of free electron. Hence resistance increases in investing the temperature.

Explanation:
When the temperature of a conductor increases, the kinetic energy of the electrons in the conductor also increases. Due to this increase in kinetic energy, the electrons collide more frequently with the atoms in the conductor, resulting in an increase in the resistance of the conductor. This can be explained by the following points:

Ohm's Law:
Ohm's law states that the current passing through a conductor is directly proportional to the voltage applied across it, provided the temperature and other physical conditions remain constant. This law is expressed as I = V/R, where I is the current, V is the voltage, and R is the resistance of the conductor.

Effect of Temperature on Resistance:
The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. However, the resistance of a conductor also depends on its temperature. When the temperature of a conductor increases, the atoms in the conductor vibrate more vigorously, resulting in an increase in collisions between the electrons and the atoms. This increase in collisions results in a decrease in the mean free path of the electrons, which in turn increases the resistance of the conductor.

Temperature Coefficient of Resistance:
The temperature coefficient of resistance (α) is defined as the rate of change of resistance with respect to temperature. For most conductors, the temperature coefficient of resistance is positive, which means that the resistance of the conductor increases with an increase in temperature. The temperature coefficient of resistance can be expressed as α = (1/R)(dR/dT), where R is the resistance of the conductor, T is the temperature, and dR/dT is the rate of change of resistance with respect to temperature.

Conclusion:
In conclusion, with an increase in temperature, the resistance of a conductor increases. This phenomenon is due to the increase in collisions between the electrons and the atoms in the conductor, resulting in a decrease in the mean free path of the electrons and an increase in resistance.

Answer: The resistivity of conductors increases with rise in temperature. As the temperature of the conductor increases, the average speed of the electrons acting as the current carriersincreases. This in result increases the number of collisions and the average time of collisions decreases withtemperature.