How Does Stretching a Wire Affect Its Resistance?

[Mitchtwitchita]

Homework Statement

A wire has a resistance of 0.010 ohms. What will the wire's resistance be if it is stretched to twice its original length without changing the volume?

Homework Equations

R = pL/A

The Attempt at a Solution

R = p(2L)/A
pL/A = R/2
=0.010/2
=0.0050 ohms

I think I this is wrong. Can anybody let me know? And, if so, can you please steer me in the right direction?

 

[Doc Al]

It's wrong for two reasons:
- You only considered the change in length. How does the area change?
- You didn't calculate the change in resistance due to the doubled length correctly. Assuming everything else remains the same, what happens to the resistance if the length doubles?

You must account for both the changing length and cross sectional area.

 

[berkeman]

Homework Statement

A wire has a resistance of 0.010 ohms. What will the wire's resistance be if it is stretched to twice its original length without changing the volume?

Homework Equations

R = pL/A

The Attempt at a Solution

R = p(2L)/A
pL/A = R/2
=0.010/2
=0.0050 ohms

I think I this is wrong. Can anybody let me know? And, if so, can you please steer me in the right direction?

You started with the correct equation, but there are two things wrong with your work. First, if you stretch the wire and the volume stays constant, what else changes in addition to its length?

Second, the resistance has to be going up, not down. Your algebra gets a bit off in your calculation. Remember, you are solving for R, not pL/A.

 

[Mitchtwitchita]

So, if the length doubles, the area would have to be halved?

R = p(2L)/(1/2)A?

 

[berkeman]

So, if the length doubles, the area would have to be halved?

R = p(2L)/(1/2)A?

Correct-a-mundo. So by inspection, what happens to the resistance?

 

[Mitchtwitchita]

R = (0.010) x 4 = 0.040?

 

[berkeman]

R = (0.010) x 4 = 0.040?

Correct. The resistance doubles because the length doubles, and it doubles again because the area is halved. Good job!

 

[Mitchtwitchita]

Thanks for the for the help!