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Question
How does the resistance of a wire change when:
its diameter is tripled?
Solution
Resistance,
`R=l/A`
where l = length of wire
A= area of cross-section of the wire
When the diameter is tripled, d' = 3d Radius, r' = 3r
Area of cross-section, `A=Api^2=A(3pi)^2=9Api^2=9A`
Thus, the area of cross-section will become nine times.
Then the new resistance,
`R'=l/A`
`R'=l/9A`
`R'=R/9`
Thus, the resistance will be reduced by nine times.
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