Question

Find the resistance of a hollow cylindrical conductor of length $1m$ with inner radius 1.0 mm and outer radius 2.0 mm respectively. The resistivity of the material is $2.0\times {10}^{-8}\Omega m$.

• A. $2.1\times {10}^{-3}\Omega$
• B. $1.3\times {10}^{-4}\Omega$
• C. $3.2\times {10}^{-4}\Omega$
• D. $4.6\times {10}^{-2}\Omega$

Answer 1

The correct option is A $2.1\times {10}^{-3}\Omega$

The area of cross section of hollow cylinder=$A=\pi (R^2-r^2)$

$=\pi (4^2-1^2)\times {10}^{-6}{m}^2$

The length of the cylinder=$1m$

Resistivity of material=$\rho =2\times {10}^{-8}\Omega m$

Hence resistance=$\frac{\rho l}{A}$

$=\frac{2\times {10}^{-8}\times 1}{\pi (4^2-1^2)\times {10}^{-6}}$

$=2.1\times {10}^{-3}\Omega$