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MGIMS WARDHA MGIMS WARDHA Solved Paper-2005

  • question_answer
    An electrical cable of copper has just one wire of radius 9 mm. Its resistance is 5\[\Omega .\] the single wire of the cable is replaced by 6 different well insulated copper wires each of radius 3 mm. The total resistance of the cable will now be equal to :

    A) 27\[\Omega \]                                 

    B) 90 \[\Omega \]

    C) 4\[\Omega \]                                    

    D) 7.5 \[\Omega \]

    Correct Answer: D

    Solution :

    Resistance\[R\propto \frac{1}{{{r}^{2}}}\] \[\frac{{{R}_{1}}}{{{R}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\Rightarrow \frac{5}{{{R}_{2}}}={{\left( \frac{3}{9} \right)}^{2}}\] \[{{R}_{2}}=5\times {{(3)}^{2}}=5\times 9=45\,\Omega \] The equivalent resistance of 6 wires of resistance\[{{R}_{2}}\]each connected in parallel order \[=\frac{{{R}_{2}}}{6}=\frac{45}{6}=7.5\,\,\Omega \]


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