If the cross-sectional area of a piece of wire is doubled what happens to the resistance in the wire?
Question
If the cross-sectional area of a piece of wire is doubled what happens to the resistance in the wire?
Solution
The resistance of a wire is inversely proportional to its cross-sectional area. This relationship is described by the formula:
R = ρL/A
where:
- R is the resistance,
- ρ (rho) is the resistivity of the material,
- L is the length of the wire, and
- A is the cross-sectional area of the wire.
If the cross-sectional area (A) is doubled, the resistance (R) will be halved, assuming the resistivity and length of the wire remain constant. This is because the larger cross-sectional area allows more paths for the current to flow through, reducing the resistance.
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