A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire.Part AHow does the resistance of this new combination compare to the resistance of the original wire?
Question
A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire.Part AHow does the resistance of this new combination compare to the resistance of the original wire?
Solution
The resistance of a wire is given by the formula R = ρL/A, where R is the resistance, ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.
Part A: When the wire is cut in half and wrapped side by side, the length (L) of the wire is halved, but the cross-sectional area (A) is doubled.
- Halving the length of the wire would halve the resistance, according to the formula.
- Doubling the cross-sectional area would also halve the resistance.
Therefore, the resistance of the new combination would be a quarter (1/4) of the resistance of the original wire.
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