Question

When the resistance of copper wire is $0.1\Omega$ and the radius is $1mm$, then the length of the wire is (specific resistance of copper is $3.14\times {10}^{-8}ohm\times m$)

• A. $10cm$
• B. $10m$
• C. $100m$
• D. $100cm$

Answer 1

Answer: (B)

$10m$

Given,

$Radius=1\times {10}^{-3}m⟹Area\left(A\right)=\pi \times (1\times {10}^{-3}m{)}^2=3.14\times {10}^{-6}$

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

Substituting respective values,

$0.1=\frac{3.14\times {10}^{-8}\times L}{3.14\times {10}^{-6}}⟹L=\frac{0.1\times 3.14\times {10}^{-6}}{3.14\times {10}^{-8}}=10m$