Drift of Electrons and the Origin of Resistivity

Consider the circuit in Figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?

No. Of electrons $n={10}^{29} m^{-3}$

Length of circuit $L=10cm$

Cross-section $A=1 m{m}^2$

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter $1\mathrm{mm}$. Conductor B is a hollow tube of outer diameter $2\mathrm{mm}$ and inner diameter $1\mathrm{mm}$. Find the ratio of resistance ${\mathrm{R}}_{\mathrm{A}}$to ${\mathrm{R}}_{\mathrm{B}}$.

The relaxation time $\tau$ is nearly independent of applied $E$ electric field whereas it changes significantly with temperature $T$. First fact is (in part) responsible for Ohm’s law whereas the second fact leads to variation of $\rho$with temperature. Elaborate why?

Which of the following characteristics of electrons determines the current in a conductor?
 

A metal rod of length $10 \mathrm{cm}$ and a rectangular cross-section of $1 \mathrm{cm}\times \frac{1}{2} \mathrm{cm}$ is connected to a battery across opposite faces. The resistance will be
 

Consider a current-carrying wire (current $I$) in the shape of a circle. Note that as the current progresses along the wire, the direction of $J$ (current density) changes in an exact manner, while the current $I$ remains unaffected. The agent that is essentially responsible for this is: