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Resistors

Resistors dissipate energy in electric circuits, but their behavior is found time and again in diverse phenomena from the flux of biomass in bacterial cells to the flow of cars on city traffic grids.

Ohm's Law - Microscopic

         

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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