If the cross-sectional area of a wire is doubled, how does its resistance change
Practice Questions
Q1
If the cross-sectional area of a wire is doubled, how does its resistance change?
Doubles
Halves
Remains the same
Increases four times
Questions & Step-by-Step Solutions
If the cross-sectional area of a wire is doubled, how does its resistance change?
Correct Answer: Resistance halves.
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.
Ohm's Law and Resistance – Resistance is determined by the material's resistivity, length, and cross-sectional area, with resistance being inversely proportional to the area.
