## why do conductors have resistance?

Resistance in a conductor is caused by the collisions between electrons and the lattice structures (ions) of the material composing the conductor. The electrons in a conductor experience these collisions as they move through the material, which makes it more difficult for electric current to flow. This effect is known as electrical resistance.

The amount of resistance in a conductor depends on several factors, including:

- Material: The type of material the conductor is made of can affect its resistance. Some materials, such as copper and aluminum, are good conductors and have low resistance, while others, such as rubber and glass, are insulators and have high resistance.
- Temperature: Increasing the temperature of a conductor can increase its resistance. This is because the increased thermal energy of the material makes it more difficult for the electrons to flow freely.
- Length: The longer a conductor, the greater its resistance. This is because the electrons have a longer distance to travel and therefore experience more collisions with the lattice structures of the material.
- Cross-sectional area: The wider the cross-sectional area of a conductor, the lower its resistance. This is because a wider conductor allows more electrons to flow through it, which reduces the number of collisions they experience with the lattice structures of the material.

Overall, resistance in a conductor can be understood as a result of the interactions between the electrons and the lattice structures of the material composing the conductor.

## What is Electrical Resistivity of a Material?

Resistivity is a measure of a material’s opposition to electric current flow. The resistivity of a material is directly proportional to the amount of electrical resistance it exhibits and is inversely proportional to its conductivity. Materials can be classified as conductors, semiconductors, and insulators based on their resistivity. Conductors have low resistivity and high conductivity, allowing electric current to flow through them with little resistance. Examples include metals such as copper and aluminum. Semiconductors have intermediate resistivity and conductivity, and are used in electronic devices such as diodes and transistors. Insulators have high resistivity and low conductivity, and are used to electrically isolate other components. Examples include rubber and glass.

The Fermi level energy, temperature, charge carrier population, and electric potential all play a role in determining the resistivity of a material. The Fermi level is the highest energy state that an electron in a material can occupy at thermal equilibrium. The temperature affects the distribution of electrons in a material, with higher temperatures leading to higher electron populations. The charge carrier population affects the resistivity of a material, as more electrons available to carry current leads to lower resistivity. The electric potential affects the movement of electrons in a material, with higher potentials leading to greater electron movement.

Power dissipation, or the conversion of electrical energy into heat, is directly proportional to the square of the current and the resistance of the material.

The equation for resistivity, ρ, is given by:

where R is the resistance and A is the cross-sectional area of the material.

The equation for resistance, R, is given by:

where *l* is the length of the material.

## Resistivity and Fermi level energy Relation

The Fermi level energy is a crucial factor in determining the electrical resistance of a material. This is because the resistance of a material depends on the number of available states for electrons to occupy. The Fermi-Dirac distribution function can be used to calculate the number of states occupied by electrons at a given energy level. This is given by:

where *E* is the energy of the electron, *E _{F}* is the Fermi level energy,

*k*is Boltzmann’s constant, and

_{B}*T*is the temperature. As the number of occupied states increases, the resistance to the flow of electrons decreases, as there are more available states for the electrons to occupy. Conversely, as the number of occupied states decreases, the resistance to the flow of electrons increases, as there are fewer available states for the electrons to occupy. The absorption of energy to convert this energy into thermal energy and photons can also be described using thermodynamics. The energy absorbed is given by:

where Q is the energy absorbed, ΔU is the change in internal energy, *n* is the number of particles, C_{v} is the heat capacity at constant volume, and ΔT is the change in temperature. The energy absorbed can also be converted into thermal energy, which is given by:

where *C _{p}* is the heat capacity at constant pressure. Finally, the energy absorbed can also be converted into photons, which is given by:

where *E* is the energy of the photon, *h *is Planck’s constant, and *f *is the frequency of the photon.

Resistance in a conductor is primarily caused by the collisions between electrons and the lattice structures (ions) of the material composing the conductor. The lattice structures effectively act as obstacles that the electrons must overcome as they move through the material. These collisions cause the electrons to lose some of their energy, which makes it more difficult for electric current to flow. This effect is known as electrical resistance.

The energy level requirement of the electrons, on the other hand, refers to the amount of energy that an electron must have in order to occupy a higher energy level in an atom. This energy level requirement is related to the electron’s position within the material, as well as the potential energy of the surrounding lattice structures. The energy level requirement of the electrons is a fundamental property of the material and determines its electrical conductivity. However, it is not directly responsible for the resistance experienced by electrons in a conductor.