Explanation:

When a copper wire is stretched to make its cross-sectional area radius 0.1% thinner, the following steps can be used to calculate the percentage increase in its resistance:

Step 1: Determine the initial radius of the copper wire
Let the initial radius of the copper wire be denoted by r.

Step 2: Determine the new radius of the copper wire
Since the copper wire is stretched to make its cross-sectional area radius 0.1% thinner, the new radius of the copper wire can be determined as follows:

New radius = r – 0.001r = 0.999r

Step 3: Calculate the initial resistance of the copper wire
The initial resistance of the copper wire can be calculated using the formula:

Initial resistance = (ρL)/A

where ρ is the resistivity of copper, L is the length of the wire, and A is the initial cross-sectional area of the wire.

Step 4: Calculate the new resistance of the copper wire
The new resistance of the copper wire can be calculated using the formula:

New resistance = (ρL)/A'

where A' is the new cross-sectional area of the wire, which can be determined as follows:

A' = π(0.999r)^2 = 0.998r^2π

Step 5: Calculate the percentage increase in resistance
The percentage increase in resistance can be determined using the formula:

Percentage increase = ((New resistance – Initial resistance)/Initial resistance) x 100%

Substituting the values obtained in Steps 3 and 4 into the formula above, we get:

Percentage increase = ((ρL/0.998r^2π) – (ρL/r^2π))/(ρL/r^2π) x 100%
Percentage increase = (1/0.998 – 1) x 100%
Percentage increase = 0.2004%

Therefore, the percentage increase in resistance of the copper wire when it is stretched to make its cross-sectional area radius 0.1% thinner is 0.2004%.