Question

A wire of resistance R is compressed in such a way that its length becomes half . What would be the new resistance ?​

Answer 1

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/Density and 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.

Thanks.