If a wire's length is doubled while keeping its cross-sectional area constant, how does its resistance change?

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Q: If a wire's length is doubled while keeping its cross-sectional area constant, how does its resistance change?

Solution: Resistance is directly proportional to length; doubling the length doubles the resistance.

Steps: 6

Step 1: Understand that resistance is a property of a wire that affects how easily electricity can flow through it.
Step 2: Know that resistance (R) is affected by the length (L) of the wire and its cross-sectional area (A).
Step 3: Remember the formula for resistance: R = ρ * (L / A), where ρ is the resistivity of the material.
Step 4: If the length of the wire is doubled, we replace L with 2L in the formula: R = ρ * (2L / A).
Step 5: This shows that the new resistance is R' = 2 * (ρ * (L / A)), which means the resistance has doubled.
Step 6: Conclude that if the length of the wire is doubled while keeping the cross-sectional area constant, the resistance also doubles.