Question

Why does the resistance increase on increasing temperature

Answer 1

Although the resistance of a conductor changes with the size of the conductor (e.g. thicker wires have less resistance to current flow than thinner wires), the resistance of a conductor also changes with changing temperature. This may be expected to happen because, as temperature changes, the dimensions of the conductor will change as it expands or contracts.
However, materials that are classed as CONDUCTORS tend to INCREASE their resistance with an increase in temperature. INSULATORS however are liable to DECREASE their resistance with an increase in temperature. Materials used for practical insulators (glass, plastic etc.) only exhibit a marked drop in their resistance at very high temperatures. They remain good insulators over all temperatures they are likely to encounter in use.
These changes in resistance cannot therefore be explained by a change in dimensions due to thermal expansion or contraction. In fact for a given size of conductor the change in resistance is due mainly to a change in the resistivity of the material, and is caused by the changing activity of the atoms that make up the material.
Temperature and Atomic Structure
The reasons for these changes in resistivity can be explained by considering the flow of current through the material. The flow of current is actually the movement of electrons from one atom to another under the influence of an electric field. Electrons are very small negatively charged particles and will be repelled by a negative electric charge and attracted by a positive electric charge. Therefore if an electric potential is applied across a conductor (positive at one end, negative at the other) electrons will "migrate" from atom to atom towards the positive terminal.
Only some electrons are free to migrate however. Others within each atom are held so tightly to their particular atom that even an electric field will not dislodge them. The current flowing in the material is therefore due to the movement of "free electrons" and the number of free electrons within any material compared with those tightly bound to their atoms is what governs whether a material is a good conductor (many free electrons) or a good insulator (hardly any free electrons).
The effect of heat on the atomic structure of a material is to make the atoms vibrate, and the higher the temperature the more violently the atoms vibrate.
In a conductor, which already has a large number of free electrons flowing through it, the vibration of the atoms causes many collisions between the free electrons and the captive electrons. Each collision uses up some energy from the free electron and is the basic cause of resistance. The more the atoms jostle around in the material, the more collisions are caused and hence the greater the resistance to current flow.
In an insulator however, there is a slightly different situation. There are so few free electrons that hardly any current can flow. Almost all the electrons are tightly bound within their particular atom. Heating an insulating material vibrates the atoms, and if heated sufficiently, the atoms vibrate violently enough to actually shake some of their captive electrons free, creating free electrons to become carriers of current. Therefore at high temperatures the resistance of an insulator can fall, and in some insulating materials, quite dramatically.
In a material where the resistance INCREASES with an increase in temperature, the material is said to have a POSITIVE TEMPERATURE COEFFICIENT.
When resistance FALLS with an increase in temperature, the material is said to have a NEGATIVE TEMPERATURE COEFFICIENT.
In general, conductors have a POSITIVE temperature coefficient, whilst (at high temperatures) insulators have a NEGATIVE temperature coefficient.
Different materials within either group have different temperature coefficients. Materials chosen for the construction of the resistors used in electronic circuits are carefully selected conductors that have a very low positive temperaturecoefficient. In use, resistors made from such materials will have only very slight increases in resistivity, and therefore their resistance. Using such materials for the manufacture of resistors creates components whose value changes only slightly over a given range of temperature.
Materials chosen as insulators will have a very low NEGATIVE TEMPERATURE COEFFICIENT over their working range of temperature.