Explanation:

To calculate the new resistance of the wire after it is stretched, we need to consider the effect of the change in length on the wire's resistance. The resistance of a wire is directly proportional to its length. This means that when the length of the wire increases, the resistance also increases.

The resistance of a wire can be calculated using the formula:

R = ρ * (L/A)

Where:
R is the resistance of the wire
ρ is the resistivity of the material of the wire
L is the length of the wire
A is the cross-sectional area of the wire

In this case, the resistivity and the cross-sectional area of the wire remain constant. So, we can focus on the change in length of the wire.

Step 1: Calculate the new length of the wire:

Since the wire is stretched by 2%, the new length of the wire can be calculated by adding 2% of the original length to the original length.

Let's assume the original length of the wire is 'L'. The new length of the wire, 'L_new', can be calculated as:

L_new = L + 0.02 * L

Step 2: Calculate the new resistance:

Now, we can substitute the new length into the resistance formula to calculate the new resistance of the wire.

R_new = ρ * (L_new/A)

Since the resistivity and the cross-sectional area remain constant, we can simplify the equation as:

R_new = R * (L_new/L)

Substituting the value of L_new from Step 1, we get:

R_new = R * ((L + 0.02 * L)/L)

Simplifying further:

R_new = R * (1 + 0.02)

R_new = R * 1.02

Therefore, the new resistance of the wire is 1.02 times the original resistance. In this case, the new resistance would be:

New resistance = 20 ohm * 1.02 = 20.4 ohm