Question

If resistance of a wire formed by $1cc$ of copper be $2.46ohm$. The diameter of wire is $0.32mm$. Then the specific resistance of wire will be :

• A. $1.59\times {10}^{-6}$ohm.cm
• B. $2.32\times {10}^{-6}$ohm.cm
• C. $3.59\times {10}^{-6}$ohm.cm
• D. $1.59\times {10}^{-8}$ohm.cm

Answer 1

Answer: (A)

$1.59\times {10}^{-6}$ohm.cm

Given volume $=1cc=1\times {10}^{-6}{m}^3$ and $diameter=0.32\times {10}^{-3}m⟹Area\left(A\right)=\frac{\pi \times (0.32\times {10}^{-3}m{)}^2}{4}=0.25\times {10}^{-6}$

Use $R=\frac{\rho \times L}{A}=\frac{\rho \times L\times A}{A^2}=\frac{\rho \times Volume}{A^2}$

Substituting respective values,

$2.46=\frac{\rho \times 1\times {10}^{-6}{m}^3}{{(0.25\times {10}^{-6})}^2}⟹\rho =1.59\times {10}^{-8}\Omega m=1.59\times {10}^{-6}\Omega cm$