Q. An electric cable of copper has just one wire of radius 9 mm. Its resistance is $5\Omega$. This single copper wire of 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) $7.5\ \Omega$
B) $45\ \Omega$
C) $90\ \Omega$
D) $270\ \Omega$
Explanation
(a) For one wire cable,
Resistance, $R^{'} = \rho l/\pi\left( 9 \times 10^{- 3} \right)^{2} = 5\Omega$
For other wire of cable,
Resistance, $R^{'} = \rho l/\pi\left( 3 \times 10^{- 3} \right)^{2}$
$= 9^{2} \times 5/3^{2} = 45\Omega$
When six wires each of resistance $R’$ are connected in parallel, their effective resistance will be
$R_{p} = \frac{R'}{6} = \frac{45}{6} = 7.5\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.