If the resistivity of a material is halved, what happens to the resistance of a wire of fixed length and cross-sectional area?

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Q: If the resistivity of a material is halved, what happens to the resistance of a wire of fixed length and cross-sectional area?

Solution: Resistance is directly proportional to resistivity; halving resistivity halves the resistance.

Steps: 6

Step 1: Understand that resistance (R) is a property of a material that depends on its resistivity (ρ), length (L), and cross-sectional area (A). The formula is R = ρ * (L / A).
Step 2: Identify that resistivity (ρ) is a measure of how strongly a material opposes the flow of electric current.
Step 3: Note that if the resistivity is halved, it means the new resistivity (ρ') is ρ/2.
Step 4: Substitute the new resistivity into the resistance formula: R' = (ρ/2) * (L / A).
Step 5: Simplify the equation: R' = (1/2) * (ρ * (L / A)) = (1/2) * R.
Step 6: Conclude that if the resistivity is halved, the resistance of the wire is also halved.