Question

An electrical cable of copper has just one wire of radius 9 mm. Its resistance is 5 ohm. This single copper wire of the cable is replaced by 6 different well insulated copper wires each of radius 3 mm. If now the resistances are connected in parallel, the total resistance of the cable will now be equal to:

• A. 7.5 ohm
• B. 45 ohm
• C. 90 ohm
• D. 270 ohm

Answer 1

The correct option is A 7.5 ohm

Resistance of a wire is given by,

$R=\frac{\rho l}{A}$

$R=\frac{\rho l}{\pi r^2}$

$\frac{R_2}{R_1}=\frac{(r_1{)}^2}{(r_2{)}^2}$

$R_2=\frac{(r_1{)}^2{R}_1}{(r_2{)}^2}$

As per the example

$R_2=\frac{5\times 9^2}{3^2}$

$R_2=\frac{5\times 81}{9}$

$R_2=45\Omega$

If such six wires each of $45\Omega$ is connected in parallel, then

$R_P=\frac{45}{6}=7.5\Omega$