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+2 votes
asked in Physics by (8k points)
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?

1 Answer

+4 votes
answered by (21.3k points)

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= 9*10= 90 ohm

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