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# A wire of resistance 10 ohm is stretched 20% determinant its new resistance

Arun
25763 Points
one year ago
resistance is given by, R = ρl/A

R = ρl²/(Al) = ρl²/V.....(1), where V is volume of wire.

at constant volume, V resistance of wire depends on only length of wire.

as it is clear in expression (1), resistance is directly proportional to square of its length.

now, according to question,

length is increased by 20%

so, new length of wire = l + 20% of l

= l + 0.2l = 1.2l

now, new resistance , R' = ρ(1.2l)²/V....(2)

from equations (1) and (2),

R'/R = 1.44 => R' = 1.44R

it is given initial resistance, R = 10ohm

so, R' = 1.44R = 14.4ohm

Vikas TU
14149 Points
one year ago
Dear student
resistance is given by, R = ρl/A
R = ρl²/(Al) = ρl²/V.....(1), where V is volume of wire.
at constant volume, V resistance of wire depends on only length of wire.
as it is clear in expression (1), resistance is directly proportional to square of its length.
now, according to question,
length is increased by 20%
so, new length of wire = l + 20% of l
= l + 0.2l = 1.2l
now, new resistance , R' = ρ(1.2l)²/V....(2)
from equations (1) and (2),
R'/R = 1.44 => R' = 1.44R
Good Luck