# Why is electrical resistance of different materials different?

" Why is the electric resistance of different materials different " - Question

Maybe because objects have different densities ,since some objects are more tightly packed than other , there more likely to bump into other atoms than others slowing the flow of electrons ? - Hypothesis

Disproved by :

1. Rubber density - $$0.92 g/cm^3$$
2. Copper Density - $$8.92 g/cm^3$$ According to this copper should have more resistivity than rubber but that isn't so

So final question

1. what exactly is resistance?
2. why is it caused ?
3. And what exactly causes difference in electrical resistance from one material to another?

Electrical resistance $$R$$ depends on geometry as well as the electrical resistivity $$\delta$$ of the material. For a uniform column-resistor component with constant cross-sectional area $$A$$ and length $$L$$, it is calculated as:

$$R=\delta \frac LA.$$

Your question is to the resistivity $$\delta$$ specifically. Note that $$\delta$$ is the mathematical inverse of electrical conductivity, $$\sigma=1/\delta$$. This conductivity is "how freely charges can move about", so to speak, whereas resistivity is the opposite: "how hindered charges are from moving about".

Conductivity depends close-to linearly on the free charge-carrier concentration $$n$$ and the charge-carrier mobility $$\mu$$ (as well as the charge-carrier's charge $$e$$). In the case of wired circuits, the charge-carrier will most likely be the electron:

$$\sigma=e n\mu.$$

$$\mu$$ can be considered the "easiness" of the electrons' drift and thus increases with scattering time $$\tau$$ in the material structure, which is the averaged time between collisions that cause the drifting charges to scatter about, but decreases with the electron's effective mass $$m^*$$, since the "heavier", the less a particle is "disturbed" and scattered in a collision. Together, $$\mu$$ can thus be described by the relation:

$$\mu=\frac{\tau e}{m^*}.$$

In metals we find a huge number of free electrons (electrons in non-filled conduction bands), so a large concentration $$n$$. This gives metals some of the highest conductivities, typically in the range of $$\sigma=10^8 \frac{1}{\Omega m}$$, corresponding to very low resistivities closing in near zero. Insulators on the other hand will often show conductivities near or to all practical purposes at $$\sigma=0$$ due to a close-to non-existing concentration of free charges, corresponding to a to all practical purposes infinite resistivity. A non-perfect insulator is typically what we call a resistor where some hindering against charge flow is wanted but not full insulation.

A special type of insulators are what is called semiconductors. These show conductivities (often in the mid-range) when activated but act as insulators when not activated. This happens due to their narrow band-gabs that are easily jumped by an excited electron when a small amount of activation energy is applied, thus suddenly making them conductive and "freeing" their stored potential.

We can go deeper into band-gap theory at the Ångström-scopic level to investigate the atomic and soon quantum differences between materials which are rooted in various particle interactions. But the overall nano-scopic and microscopic property considerations described here do give some idea of why different materials come with different resistivities and thus, at the macro-scopic level, result in different resistances even when their geometries are the same. In electric circuits, wires are typically metallic (often Copper, Silver or Gold, which are particularly good conductors) while resistors are some kind of cheramic tweaked in material composition and shaped in geometry to achieve an exact resistance for a given purpose.