What happens to the length of a coductor when its cross sectional area is doubled?

Question

What happens to the length of a coductor when its cross sectional area is doubled?

Answer 1

Wire resistance is volume dependent.  That is, both its length and its area make a difference.

For a given cross sectional area A, resistance R = rho L; where rho is the linear resistivity in ohms per length L (e.g., meter or foot).  Thus, for a given voltage E = IR, where I is the current, we have I = E/R = E/rho L.  That is, the current, for a given voltage, will go up as the length of wire between the voltage terminals goes down.  When L ~ 0, the current is very high and we call that, ta da, a "short circuit."  The very high current through that very short wire is why short circuits often burn out.

Current I is a measure of charge flow over time.  So many charges n per sec is defined as an ampere.  (I've forgotten what the value of n is, but its not important to answer your question.)  n depends on the volume V of the wire because n is the number of free electrons in that volume.  

Thus n = RhoV = Rho AL; where A is the cross sectional area of the wire, L is some length, and Rho is the charge density which depends on what kind of wire it is.  The better conductors are those with the higher numbers of n in a volume of wire.

To answer your question, assume n = Rho a L; where a < A is some cross sectional area.  Assume N = Rho A L; where A = 2a.  Then N/n = Rho A L/Rho a L = 2a/a = 2, so that N = 2n, which means the number of free electrons in a given length of wire will double when the cross sectional area is doubled.

As i ~ n and I ~ N, which means the current is proportional to the number of free charges, we have I/i = N/n = 2n/n = 2.  Thus, I = 2i, which means, for a given voltage E and length of wire L, the current will double if you double the cross sectional area of a wire of the same material.

Answer 2

Nothing, but its resistance to electricity is lowered.

Answer 3

nothing.

I think you left out part of the question!

do you want the resistance to be constant? doubling the area reduces the resistance by 2, so you have to double the length.

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Answer 4

To answer your question: Nothing.  Length has nothing to do with cross sectional area.

But if your question was:

what happens to the resistance of a conductor when it's cross sectional area is doubled?

R_1 = ρ L/A_1

A_2 = 2 * A_1.

R_2 = ρ L/A_2 = ρ L/[2*A_1] = 1/2 * ρ L/A_1 = 1/2 * R_1,

If Area is doubled, resistance is halved.

Answer 5

You have not asked a right question.The question should have been what happens to the resistance of a conductor when its cross sectional area is doubled.

As resistance of a conductor is inversely proportional to its cross sectional area,when  the area is doubled the resistance is halved.

Answer 6

if we use the same material then ,

and also, volume is not changed then its length will be halved.

the material will  conduct more current or in other words,their resistivity will decrease.

Answer 7

Tohave a constantvolume the length should be halved.

Answer 8

To have a constant volume the length should be halved.