Question

A hollow cylinder of length $3\text{m}$ has inner and outer diameters of $4\text{mm}$ 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 $1.75\times {10}^{-3}\Omega$

$l=3\text{m};\rho =2.2\times {10}^{-8}\text{mm};r_1=\frac{4}{2}=2\text{mm}=2\times {10}^{-3}\text{m};r_2=\frac{8}{2}=4\text{mm}=4\times {10}^{-3}\text{m}$

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

$R=\frac{21\times {10}^{-9}}{12\times {10}^{-6}}=\frac{7}{4}\times {10}^{-3}\Omega$

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