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. The total resistance of the cable will now be equal to

Let the resistance of single copper wire be .R1. If p is the specific resistance of copper wire, thenR1=ρ×lA1=ρ×lπr12………………(1)When the wire is replaced by six wires, let the resistance of each wire be R2. ThenR2=ρ×lA2=ρ×lπr22………………(2)From eqs. (1) and (2), we getR1R2=r22r12  or  5R2=3×10−329×10−32R2=45ΩThese six wires are in parallel. Hence the resistance of the combination would be R=456=7⋅5Ω