How Does Stretching a Wire Affect Its Resistance?

In summary: I understand it now.In summary, the resistance of a wire will double if it is stretched to twice its original length without changing the volume, as both the length and the cross sectional area will change. The correct equation to use is R = p(2L)/(1/2)A.
  • #1
Mitchtwitchita
190
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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
So, if the length doubles, the area would have to be halved?

R = p(2L)/(1/2)A?
 
  • #5
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?
 
  • #6
R = (0.010) x 4 = 0.040?
 
  • #7
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!
 
  • #8
Thanks for the for the help!
 

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Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. It is measured in volts (V).

2. How is electric potential different from electric potential energy?

Electric potential is a scalar quantity that describes the potential energy of a unit charge at a specific point in an electric field. Electric potential energy, on the other hand, is the energy that a charged particle possesses due to its position in an electric field.

3. What is the relationship between electric potential and electric field?

Electric potential is directly proportional to electric field strength. This means that as the electric field increases, the electric potential also increases, and vice versa.

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