Consider resistor of uniform cross-sectional area connected to a battery of internal resistance zero. If the length of the resistor is doubled by stretching it, then

A current of $7.5 \mathrm{A}$ is maintained in a wire for $45 \mathrm{s}$. In this time,

(a) how much charge and

(b) how many electrons flow through the wire?

A wire has a resistance $R.$ What will be its resistance if

$\left(\mathrm{a}\right)$ it is double on itself and

$\left(\mathrm{b}\right)$ it is stretched so that
$\left(\mathrm{i}\right)$ its length is doubled and $\left(\mathrm{ii}\right)$ its radius is halved.

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.