The figure shows a conductor of length $l$ having a circular cross-section.

The radius of cross-section varies linearly from $a$ to $b$. The resistivity of the material is $\rho$. Assuming that $b-a\ll l$, find the resistance of the conductor.

(a) A steady current flows in a metallic conductor of the non-uniform cross-section. State which of the quantities, i.e., current, current density, electric field, and drift velocity remain constant?

(b) A steady current passes through a cylindrical conductor. Is there an electric field inside the conductor?

A potential difference $V$ is applied to copper wire of diameter $d$ and length $L.$ What will be the effect on the electron drift speed, by doubling:

(a) voltage $V$, 

(b) length $L$ and

(c) diameter $d$

The following table gives the length of three copper rods, their diameters and the potential differences between their ends. Rank the rods according to (a) the magnitude of the electric field within them, (b) the drift speed of electrons through them and (c) the current within them, greatest first.

The $V-I$ graph for a metallic wire at two different temperatures $T_1$ and $T_2$ is shown in the figure. Which of the two temperatures $T_1$ and $T_2$ is higher and why?