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 x2.

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= 910= 90 ohm**