question_answer

In an electrical cable there is a single wire of radius 9 mm of copper. Its resistance is \[5\,\Omega \]. The cable is replaced by 6 different insulated copper wires, the radius of each wire is \[3\,mm\]. Now the total resistance of the cable will be [CPMT 1988]

A)            \[7.5\,\Omega \]                

B)            \[45\,\Omega \]

C)            \[90\,\Omega \]                 

D)            \[270\,\Omega \]

Correct Answer: A

Solution :

                   Initially : Resistance of given cable \[R=\rho \frac{l}{\pi \times {{(9\times {{10}^{-3}})}^{2}}}\]                                       ... (i) Finally : Resistance of each insulated copper wire is \[R\,'=\rho \frac{l}{\pi \times {{(3\times {{10}^{-3}})}^{2}}}\]. Hence equivalent resistance of cable \[{{R}_{eq}}=\frac{R\,'}{6}=\frac{1}{6}\times \left( \rho \frac{l}{\pi \times {{(3\times {{10}^{-3}})}^{2}}} \right)\]?.(ii) On solving equation (i) and (ii) we get Req = 7.5 W