A wire P has resistance R. If the wire is stretched and its length is increased by 10%, what would be the percentage change in its resistance? (Assume the density of the wire remains constant)

A) - 10%
B) 0 %
C) 10%
D) 20%

My thoughts:
Since resistance is R = resistivity x length / cross-sectional area of wire, when the length increases by 10%, R should increase by 10%. Cross sectional area doesn't change as the wire is stretched, as the atoms are horizontally pulled apart in the direction of the stretch and have a wider spacing between each other.

However, the answer given is D.

Since the density stays the same, the volume (area*length) must stay the same and the cross sectional area must decrease.

Resistance = Resisitivity*Length/Area
(new resistance)/(old resistance)
= [(new length)/(old length)]*(old area)/(new area)]
= 1.1/(1/1.1) = 1.21

The increase is acually 21%, not 20%

To find the correct answer, we need to use the concept of resistivity and how it relates to the resistance of a wire.

The resistance of a wire is given by the formula R = resistivity × length / cross-sectional area, where R is the resistance, resistivity is a material property, length is the length of the wire, and the cross-sectional area is the area perpendicular to the direction of the current flow.

In this scenario, the wire is stretched and its length is increased by 10%. Let's assume the initial length of the wire is L. After stretching, the new length will be L + 0.1L = 1.1L.

To calculate the percentage change in resistance, we need to compare the initial resistance (R1) with the final resistance (R2).

Using the resistance formula, R = resistivity × length / cross-sectional area, we can rewrite it as R = R0 × length / cross-sectional area, where R0 is the initial resistance.

So, the initial resistance is R1 = R0 × L / A, where A is the initial cross-sectional area.

The final resistance is R2 = R0 × 1.1L / A, where 1.1L is the new length of the wire.

To find the percentage change in resistance, we can use the formula:

Percentage change = (R2 - R1) / R1 × 100%

Substituting the values we found earlier:

Percentage change = (R0 × 1.1L / A - R0 × L / A) / (R0 × L / A) × 100%

Now, let's simplify the equation:

Percentage change = (R0 × 0.1L / A) / (R0 × L / A) × 100%
Percentage change = (0.1L / L) × 100%
Percentage change = 0.1 × 100%
Percentage change = 10%

Hence, the correct answer is C) 10%, which means the resistance of the wire increases by 10% when its length is increased by 10%.