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.

A wire of diameter $1 \mathrm{mm}$ has a resistance of $14 \mathrm{ohm}$. If the resistivity of its material is $44\times {10}^{-6}\mathrm{\Omega cm}$, calculate its length.

The current density in a cylindrical wire of radius $R=2 \text{mm}$ is uniform over the cross-section of the wire and is given by $J=2\times {10}^4 \mathrm{A}/{\mathrm{m}}^2$. Find the current through the outer portion of the wire between the radial distance $\frac{\mathrm{R}}{2}$ and $\mathrm{R}$.

(a) The current density in a cylindrical wire of radius $R=2 \text{mm}$ is uniform over the cross-section of the wire and is given by $J=2\times {10}^4 \mathrm{A}/{\mathrm{m}}^2$. Find the current through the outer portion of the wire between the radial distance $\frac{R}{2}$ and $R$.

(b) If $J=f\left(r\right)$ and is given by $J=f\left(r\right)$ where $J=b{r}^2$ where $b=3\times {10}^{10}\frac{\mathrm{A}}{\mathrm{m}}$ and $r$ is any radial distance in metres, find the current through the given portion as in(a)

The copper winding of a motor have a resistance of $50\Omega$ at ${20}^{°}\mathrm{C}$, when the motor is idle. After running for several hours, the resistance rises to $58\Omega$. Calculate the temperature of the windings at the end. ${\alpha }_{Cu}=3.93\times {10}^{-3} {\mathrm{K}}^{-1}$.