A) \[7.5\Omega \]
B) \[45\,\Omega \]
C) \[90\,\Omega \]
D) \[270\,\Omega \]
Correct Answer: A
Solution :
For first Case : For one wire electrical cube of copper wire resistance is: \[R=\frac{\rho l}{A}=\frac{\rho l}{\pi {{r}^{2}}}\] Given, \[R=5\Omega ,\,\,r=9mm\] \[5=\frac{\rho l}{\pi \times {{(9\times {{10}^{-3}})}^{2}}}\] ??(i) For second case: For another electrical cable of 6 copper wire (each of radius \[r=3mml,\] then resistance of each wire, \[R'=\frac{\rho l}{\pi {{(3\times {{10}^{-3}})}^{2}}}=9\times \frac{\rho l}{\pi {{(9\times {{10}^{-3}})}^{2}}}\] ??(i) From equation (i) we get, \[R'=9\times 5=45\Omega \] As, the 6 wires are in parallel their effective resistance will be: \[{{R}_{eff}}=\frac{R'}{6}=\frac{45}{6}-7.5\Omega \]
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