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How Is resistance determined by electron mobility for a given resistor or wire.

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The electron mobility μ is defined as

$v_{d}=\mu E$

There is a simple relation between mobility and electrical conductivity. Let n be the number density (concentration) of electrons, and let μe be their mobility. In the electric field E, each of these electrons will move with the velocity vector $mu _{e}\mathbf {E}$, for a total current density of $ne\mu _{e}\mathbf {E}$ (where e is the elementary charge). Therefore, the electrical conductivity σ satisfies:

σ = $ne\mu _{e}$

This formula is valid when the conductivity is due entirely to electrons. In a p-type semiconductor, the conductivity is due to holes instead, but the formula is essentially the same: If "p" is the concentration of holes and μh is the hole mobility, then the conductivity is

σ = $pe\mu _{h}$

If a semiconductor has both electrons and holes, the total conductivity is:

σ = e$(n\mu _{e}+p\mu _{h})$

Resistance is then, R=l/σA ,where l is the length of the conductor, σ is the conductivity and A is the area of cross-section of the conductor.

Using R=l/σA, use the value of σ for your type of conductor and then substitute the electron mobility in that formula to get an expression for resistance-electron mobility dependence.

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