Question

# a wire of resistance R and of radius r is drawn into another wire of radius 2r, the new resistance of the wire will be-

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Solution

## Step 1: Given that:The resistance of the wire =RThe radius of the wire =rThe new radius of the wire r′=2rStep 2: Formula used:As the same wire of radius r is converted into the wire of radius 2r.Therefore the volume of the wire in both cases will be equal. That isVolumeofthewire=Al=constant Thus,The volume of the wire in the original case= The volume of the wire in the new caseNow, Resistance of a conducting wire is given byR=ρlA×AASince,Al=Volume(V)R=ρVA2Step 3: Calculation of new resistance of the wire:According to the question, OriginallyR=ρVA2R=ρV(πr2)2R=ρVπ2r4In new case if the resistance of the wire is R' thenR′=ρVA′2 R′=ρV(πr′2)2 R′=ρV(π(2r)2)2 R′=ρV16π2r4 But,R=ρVπ2r4 Therefore,R′=R16 Thus, the new resistance of the wire will be R16 .

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