Question

$100mg$ mass of nichrome metal is drawn into a wire of area of cross-section $0.05{mm}^2$. Calculate the resistance of this wire. Given density of nichrome $8.4\times {10}^3$ $kg{m}^{-3}$ and resistivity of the material as $\rho =1.2\times {10}^{-6}\Omega m$.

Answer 1

$m=100mg=100\times {10}^{-6}kg$

$A=0.05{mm}^2=0.05\times {10}^{-6}{m}^2$
Density $D=8.4\times {10}^{3}kg{m}^{-3}$
$\rho =1.2\times {10}^{-6}\Omega m$
$D=\frac{mass}{volume}=\frac{m}{Al}$
$l=\frac{m}{D\times A}$
Resistance, $R=\rho \frac{1}{A}$
$R=\rho \left(\frac{m}{D\times A}\right)\frac{1}{A}=1.2\times {10}^{-6}\times \frac{100\times {10}^{-6}}{8.4\times {10}^3\times 0.05\times {10}^{-6}}\times \frac{1}{0.05\times {10}^{-6}}=5.72\Omega$