• # 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)  $270\,\Omega$

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: ${{R}_{eff}}=\frac{R'}{6}=\frac{45}{6}-7.5\Omega$