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The resistance of a wire is expressed as R = rℓ/a. If the wire's length is increased by 10%, determine the updated cross-sectional area.

1. The new area remains the same as the original area.
2. The new area is equal to the original area multiplied by 10/9.
3. The new area is equal to the original area multiplied by 9/10.
4. The new area is equal to the original area multiplied by 11/10.

Correct answer: The new area is equal to the original area multiplied by 9/10.

Solution

When the length of the wire increases by 10%, its volume remains constant. Since volume V = A × ℓ, if ℓ becomes 1.1ℓ, the area A must decrease proportionally to maintain constant volume. Thus, A' = A × (ℓ / 1.1ℓ) = A × 10/11 ≈ A × 9/10.

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