How Does Stretching a Wire Affect Its Resistance?

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SUMMARY

When a wire with an initial resistance of 0.010 ohms is stretched to twice its original length while maintaining constant volume, its resistance increases to 0.040 ohms. This is due to the relationship defined by the equation R = ρL/A, where both the length (L) doubles and the cross-sectional area (A) is halved. The resistance effectively quadruples as a result of these changes. The correct calculation confirms that the resistance increases, not decreases, when the wire is stretched.

PREREQUISITES
  • Understanding of electrical resistance and Ohm's Law
  • Familiarity with the formula R = ρL/A
  • Knowledge of material properties affecting resistance
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the relationship between resistance, length, and cross-sectional area in conductors
  • Explore the effects of material resistivity on electrical resistance
  • Learn about the physical properties of materials that influence their electrical characteristics
  • Investigate practical applications of resistance changes in electrical engineering
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Students studying physics, electrical engineers, and anyone interested in understanding the principles of electrical resistance in conductive materials.

Mitchtwitchita
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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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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!
 

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