The relaxation time in conductors

Two wires $A$ and $B$ of the same material have lengths $L_A, L_B$ and radii $R_A, R_B$ and drift velocities $v_A, v_B$ respectively. Both wires carry the same current. If $L_A = L_B$ and $R_A = 2R_B$,then the value of $\left(\frac{v_A}{v_B}\right)$ is:

$A$ cylindrical resistor is connected across a battery $\varepsilon$. The cylinder has a uniform free electron density, and the middle part of the cylinder has a larger radius as shown in the figure. Which of the following graphs represents the variation of $V_d$ (drift velocity) with respect to $x$ (distance along the length of the resistor)?

Derive the equation of mobility in terms of electric current.

The current density in a solid cylindrical wire of radius $R$,as a function of radial distance $r$,is given by $J(r) = J_{0}(1 - \frac{r}{R})$. The total current in the radial region $r = 0$ to $r = \frac{R}{4}$ will be:

Is the motion of a charge across a junction momentum conserving? Why or why not?