How Does Stretching a Wire Affect Its Resistance?

Click For Summary

Homework Help Overview

The discussion revolves around the effect of stretching a wire on its electrical resistance, specifically when the wire's length is doubled while maintaining its volume. The original poster presents a calculation based on the resistance formula, R = pL/A, and seeks clarification on their approach.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between length, cross-sectional area, and resistance, questioning how each factor changes when the wire is stretched. There is a focus on the implications of maintaining constant volume and how that affects the area.

Discussion Status

Some participants have provided guidance on the original poster's calculations, pointing out errors related to the changes in area and resistance. There is an ongoing exploration of how to correctly apply the resistance formula under the given conditions.

Contextual Notes

Participants are discussing the implications of the problem's constraints, particularly the requirement to keep the volume constant while altering the wire's dimensions. This leads to questions about the relationship between length and area in the context of resistance.

Mitchtwitchita
Messages
187
Reaction score
0

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?
 
Physics news on Phys.org
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.
 
Mitchtwitchita said:

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

R = p(2L)/(1/2)A?
 
Mitchtwitchita said:
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?
 
R = (0.010) x 4 = 0.040?
 
Mitchtwitchita said:
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!
 
Thanks for the for the help!
 

Similar threads

Electric current and resistance question
  • · Replies 2 ·
Replies
2
Views
2K
Long distance electrical transmission efficiency
  • · Replies 2 ·
Replies
2
Views
2K
Current in a circuit without external resistance
  • · Replies 8 ·
Replies
8
Views
2K
Incandescent Bulb - suitable approximation for voltage-current curve
  • · Replies 2 ·
Replies
2
Views
1K
Potential Gradient of potentiometer wire
  • · Replies 2 ·
Replies
2
Views
4K
Why do the headlights on the car become dim when the car is starting?
  • · Replies 4 ·
Replies
4
Views
2K
Lab: Plot graph of resistance, R (in Ohms) versus 1/d^2
  • · Replies 21 ·
Replies
21
Views
12K
Question for the resistance of the wire
  • · Replies 4 ·
Replies
4
Views
4K
Length of Wire Effect on Current and Inner Electric Field.
  • · Replies 4 ·
Replies
4
Views
4K
How does the rise in temperature of fuse wire depend upon its radius?
  • · Replies 12 ·
Replies
12
Views
2K