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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 =R

The radius of the wire =r

The new radius of the wire r=2r

Step 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 is

Volumeofthewire=Al=constant

Thus,

The volume of the wire in the original case= The volume of the wire in the new case

Now,

Resistance of a conducting wire is given by

R=ρlA×AA

Since,Al=Volume(V)

R=ρVA2

Step 3: Calculation of new resistance of the wire:

According to the question, Originally

R=ρVA2

R=ρV(πr2)2

R=ρVπ2r4

In new case if the resistance of the wire is R' then

R=ρVA2

R=ρV(πr2)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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