If the resistivity of a material is halved, what will happen 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 will happen 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 related to resistivity (ρ) by the formula R = ρ * (L/A), where L is the length and A is the cross-sectional area of the wire.
Step 2: Note that in this scenario, the length (L) and cross-sectional area (A) of the wire are fixed and do not change.
Step 3: Recognize that if the resistivity (ρ) is halved, it means ρ becomes ρ/2.
Step 4: Substitute the new resistivity into the formula: R = (ρ/2) * (L/A).
Step 5: Simplify the equation: R = (1/2) * (ρ * (L/A)) = (1/2) * R_initial, where R_initial is the original resistance.
Step 6: Conclude that halving the resistivity results in halving the resistance of the wire.