Finding New Resistance of a Length of Wire

[B3NR4Y]

Homework Statement

A length of wire, length l, is clamped at its midpoint. It is then stretched on the right side, with the left side unchanged, to a length of l (the right side has a length l). The original Resistance of the wire was R, what is the new resistance of the wire?

Homework Equations

R is proportional to length

The Attempt at a Solution

Using the fact that R is proportional to length (it wants R' in terms of R, so I am ignoring resistivity and such), I conclude that R' = 1.5*R, which is wrong. I got 1.5 by saying the left side is length l/2 and the rightside is length l so l+l/2 = 1.5l. So R'=1.5*R

 

[Dick]

Homework Statement

A length of wire, length l, is clamped at its midpoint. It is then stretched on the right side, with the left side unchanged, to a length of l (the right side has a length l). The original Resistance of the wire was R, what is the new resistance of the wire?

Homework Equations

R is proportional to length

The Attempt at a Solution

Using the fact that R is proportional to length (it wants R' in terms of R, so I am ignoring resistivity and such), I conclude that R' = 1.5*R, which is wrong. I got 1.5 by saying the left side is length l/2 and the rightside is length l so l+l/2 = 1.5l. So R'=1.5*R

The resistance of the wire is proportional to length if the wire has the same diameter along it's length. When you stretch the wire the stretched part will get thinner. You need to take that into account.

 

[B3NR4Y]

How would I do that? Should I set up a ratio of diameter to length that should remain constant?

 

[BvU]

Yes. Not a simple ratio like d/l or so. Think of what does remain constant.

 

[B3NR4Y]

Ah, is it cross sectional area that changes? So a ratio of length to cross sectional area, since resistivity remains constant?

 

[BvU]

Yep