Two wires $A$ and $B$ of circular cross-section are made of the same metal and have equal lengths, but the resistance of wire $A$ is four times greater than that of wire $B$. Find the ratio of their cross-sectional areas.

A sphere of radius $10 \mathrm{mm}$ that carries a charge of $8 \mathrm{nC}=8\times {10}^{-9}\mathrm{C}$ is attached at the end of an insulating string and is whirled in a circle. The rotation frequency is $100\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-1}$.

(a) What is the basic definition of current in terms of charge?

(b) What average current does this rotating charge represent?

A $2$ ampere current flows in a uniform conductor which has $1\times {10}^{24}$ free electrons per metre. What is their average drift velocity?

If the circuit is a $20$ feet long wire in your automobile, approximately how long would it take an electron to travel from the negative terminal to the positive terminal of the battery?

(b) We want to calculate how long it takes for an electron to get from a car battery to the starter motor after the ignition switch is turned. Assume that the current flowing is $115 \mathrm{A}$, and that the electrons travel through copper wire with cross-sectional area $31.2{ \mathrm{mm}}^2$ and length $85.5 \mathrm{cm}$. What is the current density in the wire? The number density of the conduction electrons in copper is $8.49\times {10}^{28} {\mathrm{m}}^{-3}$. Given this number density and the current density, what is the drift speed of the electrons? How long does it take for an electron starting at the battery to reach the starter motor? Assume no collision.

A $5.80 \mathrm{m}$ length of $2.0 \mathrm{mm}$ diameter wire carries a $750 \mathrm{mA}$ current when $22.0\mathrm{mV}$ is applied to its ends. If the drift speed is $1.7\times {10}^{-5} {\mathrm{ms}}^{-1}$, determine

(a) The resistance $R$ of the wire

(b) The resistivity $\rho$, and

(c) The number $n$ of free electrons per unit volume.