Define resistance and resistivity and also give the relation between them. Explain the dependence of resistance on temperature.

Resistance is a property of a material that opposes the flow of electric current. It is measured in ohms (Ω) and is denoted by the symbol R. Resistance can be thought of as the friction that hinders the movement of electrons through a conductor.

Resistivity, on the other hand, is a characteristic property of a material that determines its resistance. It is denoted by the symbol ρ (rho) and is measured in ohm-meters (Ω·m). Resistivity is a measure of how strongly a material resists the flow of electric current.

The relation between resistance (R), resistivity (ρ), and the dimensions of a conductor can be given by the formula:

R = ρ * (L/A)

where R is the resistance, ρ is the resistivity, L is the length of the conductor, and A is the cross-sectional area of the conductor.

Now, let's discuss the dependence of resistance on temperature. In most conductors, as the temperature increases, the resistance also increases. This is known as positive temperature coefficient of resistance. The increase in resistance with temperature can be attributed to the increased collisions between the electrons and the lattice ions of the conductor.

According to the Drude model of electron motion, as the temperature rises, the lattice ions vibrate more vigorously, leading to an increased number of collisions with the electrons. These collisions impede the flow of electrons, resulting in an increase in resistance.

However, there are some materials, such as semiconductors, that exhibit negative temperature coefficient of resistance. In these materials, as the temperature increases, the resistance decreases. This behavior is due to the increase in the number of charge carriers (electrons or holes) with temperature, which enhances the conductivity of the material.

In summary, resistance is a property that opposes the flow of electric current, while resistivity is a characteristic property that determines the resistance of a material. The resistance of a conductor depends on its length, cross-sectional area, and the resistivity of the material. Additionally, the resistance of most conductors increases with temperature due to increased collisions between electrons and lattice ions.