Q. 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 $3mm.$ Now the total resistance of the cable will be
A) $7.5\ \Omega$
B) $45\ \Omega$
C) $90\ \Omega$
D) $270\ \Omega$
Explanation
(a) Initially : Resistance of given cable
$R = \rho\frac{l}{\pi \times \left( 9 \times 10^{- 3} \right)^{2}}$ …(i)
Finally : Resistance of each insulated copper wire is
$R^{'} = \rho\frac{l}{\pi \times \left( 3 \times 10^{- 3} \right)^{2}}.$ Hence equivalent resistance of
cable $R_{eq} = \frac{R^{'}}{6} = \frac{1}{6} \times \left( \rho\frac{l}{\pi \times \left( 3 \times 10^{- 3} \right)^{2}} \right)$ …(ii)
on solving equation (i) and (ii), we get $R_{eq} = 7.5\ \Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.