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Introduction:
In this question, we are asked to determine the effect of an increase in temperature on the resistance of a conductor. Resistance is a property of a conductor that opposes the flow of electric current. It is influenced by various factors, including temperature.

Explanation:
When the temperature of a conductor increases, the resistance also increases. This phenomenon is known as the positive temperature coefficient of resistance. It can be explained by the following points:

1. Atomic Vibrations: At higher temperatures, the atoms in a conductor vibrate with greater amplitude. This increased thermal agitation disrupts the flow of electrons, leading to an increase in resistance. The increased atomic vibrations cause more collisions between the electrons and the atoms, hindering the flow of current.

2. Increased Electron-Atom Collisions: As the temperature rises, the speed of electrons also increases. However, the increased atomic vibrations make it more likely for the electrons to collide with the atoms. These collisions scatter the electrons and impede their movement, resulting in an increased resistance.

3. Effect on Electron Mobility: Temperature affects the mobility of electrons within a conductor. At higher temperatures, the lattice structure of the conductor may expand, leading to a decrease in the mean free path of the electrons. This reduced mobility of electrons further contributes to an increase in resistance.

4. Temperature Coefficient: Different materials have different temperature coefficients of resistance. Some materials have a higher positive temperature coefficient, meaning their resistance increases significantly with temperature. Others may have a smaller coefficient, resulting in a relatively smaller increase in resistance.

5. Exceptions: There are a few materials, such as thermistors, which exhibit a negative temperature coefficient of resistance. These materials experience a decrease in resistance with an increase in temperature. However, such materials are not commonly used in everyday conductors.

Conclusion:
In conclusion, an increase in temperature generally leads to an increase in the resistance of a conductor. This can be attributed to the increased atomic vibrations, electron-atom collisions, and the effect on electron mobility. It is important to consider the temperature coefficient of resistance when analyzing the behavior of different materials.