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Question
Two copper wires are of the same length, but one is thicker than the other. Which wire will have more resistance?
Solution 1
We know that,
R = `ρl/A`
Where, ρ = specific resistance
L = length of wire
A = area of cross-section
let the area of the cross-section of the wires be A1 & A2. It is said that one is thicker than the other.
So A1 > A2
When the length of the wire is given to be the same then we can see that `R prop 1/A`.
So, the wire with less area of the cross-section will have more resistance.
Solution 2
The area of the cross-section has an inverse relationship to resistance, so a thinner wire will have more resistance.
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