Question

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 $3 \,mm$. 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
$R'=\rho \frac{l}{\pi \times\left(3 \times 10^{-3}\right)^{2}}$
Hence, equivalent resistance of cable
$R_{e q}=\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 $R_{ eq }=7.5\, \Omega$