Question

An electric cable contains a single copper wire of radius 9mm. Its resistance is $5\Omega$. This cable is replaced by six insulated copper wires, 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

Answer: (A)

$7.5\Omega$

Resistance of the wire is

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

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

$R=\frac{\rho L}{\pi (9{)}^2}$

$R=\frac{\rho L}{81\pi }$ .........................(1)

The copper cable is replaced by six insulated copper wires, hence length of

wires and $\rho$ will be same as for cable.

Resistance of each of six insulated copper wires is

$R^{\prime }=\frac{\rho L}{9\pi }$ .............................(2)

From (1) and (2)

$\frac{R^{\prime }}{R}=\frac{81}{9}$

$R^{\prime }=9\times 5=45\Omega$

Since wires are parallel to each other hence the equivalent resistance of combination will be

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