Question

The length of a wire is increased to twice while keeping its volume constant. The resistivity of wire become​

Answer 1

Answer:

Assuming ideal conditions with no distortions in the process that would alter the resistivity of the wire being stretched, this becomes a relatively simple arithmetic calculation for sixth grade algebra students. Realizing that the amount of wire does not change and assuming the shape of the wire still takes on the shape of a right circular cylinder, then the volume of the wire can be determined by V = A x L where V is the volume, A is the cross sectional area, and L is the length of the wire. This relationship tells us that the volume of a right circular is directly proportional to both the area of the cylinder and the length of the cylinder. This means that if we double the length and not change the cross sectional area the volume doubles, and if we double the length and halve the area the volume will remain the same.

The resistance of any conductor is determined by the simple arithmetic relationship R = rL/A , where R is the resistance, r is a constant number representative of the type of material being stretched, L is the wire length, and A is the cross sectional area of the wire. In this relationship R is directly proportional to r and L but inversely proportional A. This is a simplistic way of saying that if we double L the resistance doubles assuming nothing else changes, but if we double the area simultaneously the resistance of the wire would not change. R = r2L/2A. The 2’s cancel thereful we revert back to R = rL/A Meaning we are back where we started the resistance is the same as it was before we made any changes in the dimensions of the wire.

Now back to solving the problem. If the wirelength is doubled, what is the affect on the wires resistance. Simply, if the volume of the wire remains constant using V = A x L then V =A x 2L meaning that the area of the wire must be A/2 in order for the V to remain the same. V = A/2 x 2L. The 2’s cancel and V= A x L. Telling us that doubling the length has the effect of halving the area.

Keeping this in mind the wires resistance will now be using R =rL/A or simply R = r2L / 1/2A simplifies to

R = r4L/A meaning the resistance will be four times greater.

Answer 2

Given:

The length of a wire is increased to twice while keeping its volume constant.

To find:

Resistivity of wire becomes ?

Solution:

First of all , let's define resistivity :

• Resistivity of a wire is defined as numerically equal to the resistance of a wire with unit dimensions (i.e. unit length and unit area of cross-section).

• Resistivity is a materialistic property, i.e. its value doesn't depend upon the dimensions of the conductor.

• The only parameter upon which resistivity depends is the temperature of the ambience.

So, even when length of wire is doubled, keeping the volume constant , the resistivity of the wire will remain constant (provided we are assuming that ambient temperature is constant).

$\star$ Hope It Helps.