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Electricity and Magnetism

# Ohm's law (microscopic interpretation)

Suppose that the number of conduction electrons per unit volume in a certain metal is $$n=1.23 \times 10^{29} \text{ m}^{-3}$$ and the mean free time between collisions for the conduction electrons in that metal is $$\tau=3.42 \times 10^{ -15} \text{ s}.$$ What is the resistivity $$\rho$$ of that metal?

The elementary charge is $$e=1.60 \times 10^{-19}\text{ C}$$ and the mass of electron is $$m=9.11 \times 10^{-31}\text{ kg}.$$

If the number of conduction electrons per unit volume in copper is $$8.47 \times 10^{28}\text{ m}^{-3}$$ and the resistivity of copper is $$1.61 \times 10^{-8}\,\Omega\cdot\text{m},$$ what is the mean free time $$\tau$$ between collisions for the conduction electron in copper?

The elementary charge is $$e=1.60 \times 10^{-19}\text{ C}$$ and the mass of electron is $$m=9.10 \times 10^{-31}\text{ kg}.$$

If the mean free time between collisions for the conduction electrons in copper is $$\tau=2.5 \times 10^{-14}\text{ s}$$ and their effective speed $$v_{\text{eff}}$$ is $$1.5 \times 10^6\text{ m/s},$$ what is the mean free path $$\lambda$$ for the conduction electron in copper?

The measured resistivity of aluminium at $$25\,^\circ\text{C}$$ is $$2.72 \times 10^{-8}\,\Omega\cdot\text{m}.$$ The valency, density, and the atomic mass of aluminium are $$3,$$ $$2.68\text{g/cm}^3,$$ and $$27,$$ respectively. Assuming that each aluminium atom contributes three free conduction electrons to the metal, what is the mean free time between collisions for the conduction electrons in aluminium at a temperature of $$25\,^\circ\text{C}?$$

The elementary charge is $$e=1.602 \times 10^{-19}\text{ C}.$$
The mass of electron is $$m=9.109 \times 10^{-31}\text{ kg}.$$
The Avogadro constant is $$N_A=6.022 \times 10^{23}\text{ mol}^{-1}.$$

The measured electron drift mobility in silver is $$57\text{ cm}^2\text{V}^{-1}\text{s}^{-1}$$ at $$27\,^\circ\text{C}.$$ The atomic mass and density of silver are $$107.87\text{ g/mol}$$ and $$10.70\text{ g/cm}^3,$$ respectively. Assuming that each silver atom contributes one conduction electron, what is the resistivity of Ag at $$27\,^\circ\text{C}?$$

The elementary charge is $$e=1.602 \times 10^{-19}\text{ C}.$$
The mass of electron is $$m=9.109 \times 10^{-31}\text{ kg}.$$
The Avogadro constant is $$N_A=6.022 \times 10^{23}\text{ mol}^{-1}.$$

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