If a wire is stretched 3 times its original length then its strain in the wire will be
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If a wire is stretched to double its length, what will its new resistance be?
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Pankaj Kumar Jha, M. tech Electrical and Electronics Engineering & Electrical Power Systems (2010)
Answered Jun 18
We know that,
R = (rho)*length/Cross Sectional Area
Since, the length of the wire has doubled, hence there will definitely be some change in cross sectional area.
Now we know that, volume = Mass/Densityand since neither mass nor density has changed due to change in length, thus volume must remain constant.
We further know that,
Volume = Length * Cross Sectional Area
This implies that, due to doubling the length of wire, the cross sectional area will become half for volume to remain constant.
Thus we get, new cross sectional area = (1/2) of old cross sectional area
New length = 2 * old length of wire.
Putting these value into t
R = (rho)*length/Cross Sectional Area
We easily can conclude that Resistance will increase four times due to doubling the length of wire.
Interpretation can be drawn qualitatively as follows:
Due to increase in the length of wire it will become thinner and longer. If it is thinner it will be harder for the charge to move through, so the resistance will increase. If it is longer, the charge has further to travel, so its resistance has increased.
Hope you get your answer.
Answer
6667
Follow
Request
More
81 ANSWERS

Pankaj Kumar Jha, M. tech Electrical and Electronics Engineering & Electrical Power Systems (2010)
Answered Jun 18
We know that,
R = (rho)*length/Cross Sectional Area
Since, the length of the wire has doubled, hence there will definitely be some change in cross sectional area.
Now we know that, volume = Mass/Densityand since neither mass nor density has changed due to change in length, thus volume must remain constant.
We further know that,
Volume = Length * Cross Sectional Area
This implies that, due to doubling the length of wire, the cross sectional area will become half for volume to remain constant.
Thus we get, new cross sectional area = (1/2) of old cross sectional area
New length = 2 * old length of wire.
Putting these value into t
R = (rho)*length/Cross Sectional Area
We easily can conclude that Resistance will increase four times due to doubling the length of wire.
Interpretation can be drawn qualitatively as follows:
Due to increase in the length of wire it will become thinner and longer. If it is thinner it will be harder for the charge to move through, so the resistance will increase. If it is longer, the charge has further to travel, so its resistance has increased.
Hope you get your answer.
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