The resistance of a wire is R ohm . The wire is stretched to double its length . then the resistance in ohms is

a) R/2

b) 4R

c) 2R

d) R/4

Resistance ‘R = 6ohm’ is related to length ‘L’, area of cross-section ‘A’ and resistivity ‘ρ’ as,

R = ρL/A

When L is doubled ,

As we know that the volume of the wire remains same.

old volume = new volume

AL = A'L' ....(i) ( as volume = area x length )

L' = 2L

So, from (i)

A' = A/2

So the new resistance is ,

R' = ρL'/A'


R' = ρ(2L)/(A/2) = 4 (ρL/A)

=> R' = 4R

thus, correct answer is option (b).

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