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If the cross-sectional area of a wire is doubled, how does its resistance change
If the cross-sectional area of a wire is doubled, how does its resistance change?
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Practice Questions
1 question
Q1
If the cross-sectional area of a wire is doubled, how does its resistance change?
Doubles
Halves
Remains the same
Increases four times
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Resistance is inversely proportional to cross-sectional area; doubling the area halves the resistance.
Questions & Step-by-step Solutions
1 item
Q
Q: If the cross-sectional area of a wire is doubled, how does its resistance change?
Solution:
Resistance is inversely proportional to cross-sectional area; doubling the area halves the resistance.
Steps: 6
Show Steps
Step 1: Understand that resistance is a property of a wire that affects how easily electricity can flow through it.
Step 2: Know that the formula for resistance (R) is R = ρ * (L/A), where ρ is resistivity, L is length, and A is cross-sectional area.
Step 3: Recognize that if the cross-sectional area (A) is doubled, the new area becomes 2A.
Step 4: Substitute the new area into the formula: R = ρ * (L/(2A)).
Step 5: Notice that this means the resistance is now half of what it was before, because R is inversely proportional to A.
Step 6: Conclude that if the cross-sectional area of the wire is doubled, the resistance is halved.
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