A piece of wire of resistance 20Ω is drawn

A piece of wire of resistance 20Ω is drawn out so that its length increases to twice its original length. Calculate the resistance of the wire in the new situation.

Given: R= 20Ω

l′​ = 2l

To find : R′

Solution : By the definition of resistance,

R=ρl​/A

when length of wire is doubled i.e. 2l

R = ρl²/V ( We know that Area = Volume/length, i.e. A = V/l because volume remains same on changing dimensions but area varies )

Now new resistance will be according to the question,

R′= ρl′​/A’

R’=ρ(2l)²/V ( according to question given l′​ = 2l )

R’ = 4ρl²/V

R’ = 4R ( We know that R = ρl²/V )

R’ = 4 Χ 20 ( R = 20Ω )

R’ = 80Ω

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