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. ${\alpha }_{Cu}=3.93\times {10}^{-3} {\mathrm{K}}^{-1}$.

A wire with a resistance of $6\Omega$ is drawn out so that its new length is thrice its original length. Find the resistance of the longer wire assuming that the resistivity and density of the material do not change during the process.

Find the resistance of $0.5 \mathrm{Kg}$ copper wire of diameter $0.008 \mathrm{m}$. Given that the density of copper$=8.9\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$. Use its value of resistivity from Table 5.1

Given: Table 5.1

A battery connected to a rheostat furnishes certain current. When a lamp of resistance $150\Omega$ is inserted in series, the current is reduced to one third of its former value. Find the resistance of the rheostat.

An electric lamp has a filament diameter of $0.525 \mathrm{mm}$. For $2.84$ ampere of current in the lamp, $1.37\times {10}^{22 }$electrons$/{\mathrm{m}}^3$ are found to flow through the wire, Calculate the average speed of the electrons in it.

A cylindrical metallic wire is stretched to increase its length by $10\%$. Calculate the percentage increase in resistance.