Find the new resistance of the cable:

Question

An electrical cable of copper has just one wire of radius 9mm. Its resistance is 10ohm. This single copper wire of the cable is replaced by 6 identical well insulated copper wires each of radius 3mm. What will be the new resistance of the cable?

Answer 1

We know that Resistance Formula :

R = resistance	Ω
ρ = specific resistance	Ω×m
l = length of the cable	m
A = cross section area	mm2

We know that resistance is inversely proportional to square of radius of the wire.

So if the radius of cross section is decreased by x then resistance will be increased by x^2.

So in the given question initial radius is 9mm and the radius is decreased by 3mm. 

Hence the resistance will be increased by 9 times the initial resistance of the single cable.

So the resistance of the new cable will be R= 9*10= 90 ohm