Question

a given wire is streched to n times in lenght what will be its new resistance if original resistance is r​

Answer 1

Answer:

If a copper wire of resistance R ohm is stretched till its length is increased n times of its original length, what will the resistance be now? ... For n=3 : length will change to 3* l and diameter will change to approx 0.677*d thereby making R as 6.54 times and so on.

Answer 2

As per actual calculations :

For copper and n=2 ; length will change to 2* l and diameter will change to approx 0.781*d thereby making R as 3.27 times.

For n=3 : length will change to 3* l and diameter will change to approx 0.677*d thereby making R as 6.54 times and so on.

Some answers have suggested n^2.

In simpler words it would have been n^2 but practically it is not and depends on material being stretched.

Practically, Change in Diameter = - original diameter* (1-(1+ change in length/original length))^-poission ratio) (Source : Wikipedia.com) and the calculation given at the top is based on this.

The amount of reduction in cross section is determined according to Poisson's ratio (signed ratio of transverse strain to axial strain). Without considering Poisson's ratio, one would expect the area of the cross section to be halved, and the final volume to remain constant, but this would be wrong.

Resistance is defined as : R = pl/A,

where R is resistance, p is the material's resistance in ohms, l is the length, and A is the cross sectional area in m^2.

As a wire gets longer its resistance increases, and while it is being stretched, its resistance increases further because its cross sectional area also decreases.

One might assume that decrease in cross section will be same for all materials and it is linearly proportional to the increased length. However, this is not true and depends on material.

Most materials resist change in volume (based on bulk modulus) more than they resist a change in shape (Shear Modulus) , and because of that, they lose less volume than otherwise would be expected when stress is applied and therefore, calculation of new cross section requires consideration of wire material.

In this particular question, copper wire is stretched and copper has a Poisson's ratio of about 0.355 and therefore results in a increase in resistance by a factor other than n^2

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