Find the total charge carried by the number of free electrons in a copper wire of length $1 \mathrm{m}$ and cross section $1.6 {\mathrm{mm}}^2$ if density of copper is $9\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ and its molecular mass is $63.5 {\mathrm{gmol}}^{-1}$. Assume valency of copper to be one.

A copper wire of radius $0.1 \mathrm{mm}$ and resistance $1 \mathrm{k\Omega }$ is connected across a power supply of $20 \mathrm{V}$. How many electrons are transferred per sec. between the supply and the wire at one end?

A copper wire of radius $0.1 \mathrm{mm}$ and resistance $1 \mathrm{k\Omega }$ is connected across a power supply of $20 \mathrm{V}$. Find the current density of the wire.

A wire of $2 \mathrm{mm}$ in diameter transfers a charge of $60 \mathrm{coul}.$ in $5 \mathrm{minutes}$. If the number density of electron in the wire is $5.8\times {10}^{28}$ per ${\mathrm{m}}^3$. Calculate the current in the wire.

A wire of $2 \mathrm{mm}$ in diameter transfers a charge of $60 \mathrm{coul}.$ in $5 \mathrm{minutes}$. If the number density of electron in the wire is $5.8\times {10}^{28}$ per ${\mathrm{m}}^3$. Calculate the electrons in the wire.

A copper wire of circular cross section has a radius of $1 \mathrm{mm}$. It carries a current of $0.5 \mathrm{A}$. If the resistivity of copper at room temperature is $1.724\times {10}^{-8} \mathrm{\Omega }.\mathrm{m}$, find the magnitude of current density in the wire and that of electric field intensity in it.

The conductivity of aluminium is $3.55\times {10}^7 {\mathrm{ohm}}^{-1}{\mathrm{m}}^{-1}$ at room temperature. Find the resistance of an aluminium wire of length $1 \mathrm{m}$ and diameter $2 \mathrm{mm}$.

Two wires of aluminium and copper have the same length and same resistance. Show by calculation which of them is lighter. Densities of copper and aluminium are $8.9\times {10}^3 \mathrm{Kg}/{\mathrm{m}}^3$ and $2.7\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ respectively. ${\rho }_{Cu}=1.724\times {10}^{-8}\mathrm{\Omega m}$ and ${\rho }_{Al}=2.824\times {10}^{-8}\mathrm{\Omega m}$.

Determine the resistance of a silver wire through which $360 \mathrm{coul}.$of charge flows in $2 \mathrm{minutes}$ under a potential difference of $30 \mathrm{V}$ between its ends.