Question

In an electrical cable there is a single wire of radius $9mm$ 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. $270\Omega$

Answer 1

Answer: (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
$R^{\prime }=\rho \frac{l}{\pi \times {\left(3\times 10^{-3}\right)}^2}$
Hence, equivalent resistance of cable
$R_{eq}=\frac{R^{\prime }}{6}=\frac{1}{6}\times \left(\rho \frac{l}{\pi \times {\left(3\times 10^{-3}\right)}^2}\right)........(ii)$

On solving equation (i) and (ii) we get $R_{eq}=7.5\Omega$