The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then:
Correct answer: A. The resistance will be halved and the specific resistance will remain unchanged
- A. The resistance will be halved and the specific resistance will remain unchanged
- B. The resistance will be doubled and the specific resistance will be halved
- C. The resistance will be halved and the specific resistance will be doubled
- D. The resistance and the specific resistance will both remain unchanged
Explanation
When the length and radius of the wire are both doubled, we apply the formula for resistance: R=ρ×L/A. With the new values, we substitute:R'=ρ×(2L)/(2A)=ρ×L/A = R×1/2This shows that the resistance is halved. The specific resistance ρ, calculated as ρ'=R'×A/L, remains unchanged since it depends solely on the material properties of the wire. Therefore, option A is correct. Options B, C, and D are incorrect as they do not accurately reflect the relationships established by the calculations.
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