Question

An electric cable contains a single copper wire of radius 9 mm. It’s resistance is $5\Omega$. This cable is replaced by six insulated copper wires connected in parallel, each of radius 3 mm. The resultant resistance of 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
$R_{eq}=\frac{R^{{}^{\prime }}}{6}=\frac{1}{6}\times \left(\rho \frac{l}{\pi \times (3\times {10}^{-3}{)}^2}\right)$ .......(ii)
On solving equation (i) and (ii) we get $R_{eq}=7.5\Omega$