The Calculation of the New Resistance of a Doubled-up Resistance Wire

To determine the new resistance of a resistance wire when it is doubled up by folding, we need to consider the change in the wire's dimensions and its effect on resistance. The resistance of a wire depends on its length, cross-sectional area, and resistivity.

Resistance Calculation:
The resistance of a wire can be calculated using Ohm's Law, which states that the resistance (R) is equal to the ratio of voltage (V) across the wire to the current (I) passing through it: R = V/I.

When the wire is folded, its length remains the same, but its cross-sectional area doubles. Since resistance is directly proportional to the length and inversely proportional to the cross-sectional area, doubling the cross-sectional area will halve the resistance.

Step-by-Step Calculation:
1. Let's assume the original resistance of the wire is 6 ohms.
2. Folding the wire does not change its length, so the length remains the same.
3. The cross-sectional area of the wire doubles when it is folded.
4. Halving the resistance means that the new resistance will be half of the original resistance.
5. Therefore, the new resistance of the folded wire will be 6 ohms / 2 = 3 ohms.

Explanation:
- When a wire is folded, its length remains the same, as it is only the physical arrangement that changes.
- However, the cross-sectional area of the wire doubles because the wire is essentially folded onto itself.
- The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
- The formula for resistance is R = ρ * (L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.
- Since the length remains constant and the cross-sectional area doubles, the new resistance will be halved compared to the original resistance.
- Therefore, the new resistance of the folded wire is 3 ohms, which is half of the original resistance of 6 ohms.

In conclusion:
When a 6 ohm resistance wire is folded, the new resistance of the wire becomes 3 ohms. This is because folding the wire doubles its cross-sectional area, which in turn halves the resistance according to the relationship between resistance, length, and cross-sectional area.

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