How to Calculate New Resistance in a Stretched Wire with Uniform Cross Section?

[Steven7]

A wire has uniform cross sectional and resistance R. Then the wire is pulled so that the length increases by 10%. How to find the new resistance? Assumption: The wire thins uniformly.

 

[LowlyPion]

What equation would you think to apply to figure this?

 

[Steven7]

R=rho*l / A
I just don't get the part how the length of the wire affects the cross sectional area/radius.

 

[LowlyPion]

R=rho*l / A
I just don't get the part how the length of the wire affects the cross sectional area/radius.

Don't you figure that there is a conservation of mass?

What happens to the volume of wire when you stretch it?

Volume = L * A

if the volume is constant, then if L = 1.1*L then A must equal A/1.1

 

[Steven7]

I got it. I thought the increase of L decrease the r to r/1.1.
Can I ask another question about resistance?
A square carbon film of thickness 5x10^-7m, rho 4x10^-5 ohm m is formed on an insulator rod of diameter 3mm.What is the length of the rod so that the carbon film on its curve surface has a resistance of 100 ohm.

I tried:
RA/rho = L
100[3.142*(1.5mm+5x10^-7)^2]/4x10^-7 = L
But the answer is 1.18cm which is different from mine. Where did it gone wrong

 

[LowlyPion]

I got it. I thought the increase of L decrease the r to r/1.1.
Can I ask another question about resistance?
A square carbon film of thickness 5x10^-7m, rho 4x10^-5 ohm m is formed on an insulator rod of diameter 3mm.What is the length of the rod so that the carbon film on its curve surface has a resistance of 100 ohm.

I tried:
RA/rho = L
100[3.142*(1.5mm+5x10^-7)^2]/4x10^-7 = L
But the answer is 1.18cm which is different from mine. Where did it gone wrong

Consider that your cross sectional area is the cross section of a thin shelled tube.

A = L * T = π * d * 5*10^-7

So:

100Ω = 4*10^-5 * L / (3.14*.003*5*10^-7)

 

[Steven7]

I'm sorry but according to your equation, I don't get the answer which is 1.18cm. By the way, I also don't understand the statement "carbon film on its curve surface" means. Do you mind explaining it?

 

[LowlyPion]

I'm sorry but according to your equation, I don't get the answer which is 1.18cm. By the way, I also don't understand the statement "carbon film on its curve surface" means. Do you mind explaining it?

It's an insulating rod, so only the surface foil conducts.
If you unwrap the foil off the rod its cross sectional area is width (π * d) and its thickness is 5*10^-7

Area then is W*T = (π * d) *( 5*10^-7 ) = 3.14*.0003*5*10^-7

Substituting into

R = 100 = p*L/A

yields

100*3.14*.0003*5*10^-7 / 4*10^-5 = L = 1.1775*10^-2m

 

[Steven7]

I struggle with A = π r^2 and you cleared those. Thanks a lot.