NEET Sample Paper NEET Sample Test Paper-27

  • question_answer An electrical cable of copper has just one wire of radius 9mm. Its resistance is\[5\Omega \]. The single copper wire of the cable is replaced by different well insulated copper wires each of radius 3mm. The total resistance of the cable will now be equal to:

    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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