Question

The external diameter of a $314\, m$ long copper tube is $1.2\, cm$ and the internal diameter is $1 \,cm$. Calculate its resistance if the specific resistance of copper is $ 2.2\times {{10}^{-8}}\Omega -m $

• A. $ 5.0\times {{10}^{-2}}\Omega $
• B. $ 4.4\times {{10}^{-2}}\Omega $
• C. $ 3.14\times {{10}^{-2}}\Omega $
• D. $0.2\,\Omega $

Answer 1

Answer: (D)

Given, length $ l=314m $
Specific resistance $ p=2.2\times {{10}^{-8}}\Omega -m $
External diameter $ {{D}_{1}}=1.2\times {{10}^{-2}}m $
Internal diameter $ {{D}_{2}}=1\times {{10}^{-2}}m $
As resistance of tube
$ R=\frac{\rho l}{A} $
Or $ R=\frac{\rho l}{\pi [D_{1}^{2}-D_{2}^{2}]} $
$ [\because A=\pi {{r}^{2}}] $
Or $ R=\frac{4\times 2.2\times {{10}^{-8}}\times 314}{\pi [{{(1.2)}^{2}}-{{(1.0)}^{2}}]\times {{10}^{-4}}} $
$ =0.2\,\Omega $