Problem Statement:
A piece of wire has an initial resistance of 20 ohms. The wire is then drawn out to twice its original length. We need to calculate the resistance of the wire in this new situation and provide a detailed explanation.

Solution:

Given:
- Initial resistance of the wire = 20 ohms.
- The wire is drawn out to twice its original length.

Explanation:
To find the resistance of the wire in the new situation, we need to consider the relationship between resistance, length, and resistivity.

1. Relationship between Resistance, Length, and Resistivity:
The resistance of a wire is directly proportional to its length and resistivity, and inversely proportional to its cross-sectional area. Mathematically, we can express this relationship using the formula:

R = (ρ * L) / A

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

2. Change in Length:
In the given problem, the wire is drawn out to twice its original length. Let's assume the original length of the wire is L0. After being drawn out, the new length of the wire becomes 2 * L0.

3. Relationship between Resistance and Length:
From the formula mentioned earlier, we can see that resistance is directly proportional to length. Therefore, if the length of the wire is doubled, the resistance will also double.

4. Calculation of Resistance in the New Situation:
Since the length of the wire is doubled, the resistance in the new situation will be twice the initial resistance. Therefore, the resistance of the wire in the new situation is:

R_new = 2 * R_initial
= 2 * 20 ohms
= 40 ohms

Conclusion:
The resistance of the wire in the new situation, where its length is increased to twice its original length, is 40 ohms. This is because resistance is directly proportional to length, and doubling the length of the wire results in doubling its resistance.

80 ohm