How Does Stretching a Wire Affect Its Resistance?

[logearav]

Homework Statement

Resistance of a metal wire of length 10 cm is 2 ohm. If the wire is stretched uniformly to 50 cm, the resistance is-----

Homework Equations

R = (Specific resistance * length)/ Area
R1= (specific resistance * length1^2)/ Volume
similarly for R2
so R1/R2 = length1^2 / length2^2
so the resistance is 50 ohm.
Am i correct? some of my friends say that i should go for R1/R2 = length1 / length2, when applied i get the answer 10 ohm.
Which is correct?
could u help?

The Attempt at a Solution

 

[tiny-tim]

hi logearav!

(try using the X² and X₂ icons just above the Reply box )

R1 = specific resistance * length1^2 / volume
R2 = specific resistance * length2^2 / volume
when simplified R1/R2 = length1^2 / length2^2 which gives 50 ohm
some friends say i should use the formula R1 / R2 = length1 / length 2 which gives the answer 10 ohm
which is correct? could u help

your formula is correct

length₁/length₂ only applies if the cross-section area stays the same …

resistance is proportional to length, and inversely proportional to area, so altogether it's proportional to length/area, = length²/volume

 

[vela]

You're correct. The volume remains constant, so the cross-sectional area must change, which will affect the resistance of the wire.