Question

A hollow cylinder of length $3\text{m}$ has inner and outer diameters are $4\text{mm}$ and $8\text{mm}$ respectively. The resistance of the cylinder is-

[specific resistance of the material $=2.2\times {10}^{-8}\Omega \text{m}$]

• A. $1.75\times {10}^{-3}\Omega$
• B. $1.25\times {10}^{-3}\Omega$
• C. $1.5\times {10}^{-3}\Omega$
• D. $1.95\times {10}^{-3}\Omega$

Answer 1

The correct option is A $1.75\times {10}^{-3}\Omega$

Given, $l=3\text{m};\rho =2.2\times {10}^{-8}\Omega \text{m}$

$r_{in}=2\text{mm}=2\times {10}^{-3}\text{m}$
$r_{out}=4\text{mm}=4\times {10}^{-3}\text{m}$

The resistance of the cylinder is,

$R=\frac{\rho l}{A}=\frac{\rho l}{\pi [r^2{}_{out}-r^2{}_{in}]}$

$R=\frac{2.2\times {10}^{-8}\times 3}{\frac{22}{7}\times [4^2-2^2]\times {10}^{-6}}$

$=\frac{21\times {10}^{-8}}{12\times {10}^{-5}}$

$R=1.75\times {10}^{-3}\Omega$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.