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

The correct option is A $7.5\Omega$

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

$R^{\prime }=\rho \frac{l}{\pi \times (3\times {10}^{-3}{)}^2}$. Hence equivalent resistance of cable

$R_{eq}=\frac{R^{\prime }}{6}$ ...(ii)

On solving equation (i) and (ii) we get $R=7.5\Omega$