Question

A wire having a mass of $0.45kg$ possesses a resistance of $0.0014\Omega$. If the specific resistance of a material of wire is $1.78\times {10}^{-8}\Omega m$. Calculate its length and radius, given that the density of the material of wire $8.93\times {10}^{3}kg/m^3$.

Answer 1

Volume, $V=\frac{m}{d}$ ($d=$density)
$V=$volume, $A=$area, $l=$length
$\begin{array}{c}V=Al\Rightarrow l=\frac{V}{A}\end{array}$
$R=$Resistance
$\begin{array}{c}R=\rho \frac{l}{A}=\rho \frac{V}{A^2}=\rho \frac{m}{d{A}^2}\\ A^2=\frac{\rho m}{Rd}\Rightarrow A=\sqrt{\frac{\rho m}{Rd}}\\ A=\sqrt{\frac{1.78\times {10}^{-8}\times 0.45}{0.0014\times 8.93\times {10}^3}}\\ A=0.454\times {10}^{-4}{m}^2\\ l=\frac{V}{A}=\frac{m}{Ad}=\frac{0.45}{0.454\times {10}^{-4}\times 8.93\times {10}^3}\\ l=1.11m\end{array}$