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# In an electrical cable there is a single wire of radius 9 mm of copper. Its resistance is 5Ω . The cable is replaced by 6 different insulated copper wires, the radius of each wire is 3 mm . Now the total resistance of the cable will be

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a
7.5 Ω
b
45Ω
c
90Ω
d
270Ω
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detailed solution

Correct option is A

Initially : Resistance of given cableR=ρlπ×9×10−32...(i)Finally : Resistance of each insulated copper wire isR′=ρlπ×3×10−32 . Hence equivalent resistance of cable Req=R′6=16×ρlπ×3×10−32....(ii)  On solving equation (i) and (ii) we get Req = 7.5 W

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