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

Solution: Resistance R is directly proportional to resistivity; if resistivity doubles, resistance also doubles.

Steps: 7

Step 1: Understand that resistivity is a property of a material that affects how easily electricity can flow through it.
Step 2: Know that resistance (R) of a wire depends on its resistivity (ρ), length (L), and cross-sectional area (A) using the formula R = ρ * (L / A).
Step 3: Recognize that if the resistivity (ρ) of the material is doubled, it means the new resistivity is 2ρ.
Step 4: Since the length (L) and cross-sectional area (A) of the wire remain fixed, the only change in the resistance formula is the resistivity.
Step 5: Substitute the new resistivity into the formula: R' = 2ρ * (L / A).
Step 6: Compare the new resistance (R') with the original resistance (R = ρ * (L / A)).
Step 7: Notice that R' = 2 * R, which means the new resistance is double the original resistance.