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Question
A cylindrical conductor of length l and uniform area of cross section A has resistance R. Another conductor of length 2l and resistance R of the same material has area of cross section
Options
A/2
3A/2
2A
3A
Solution
2A
Explanation -
Let the resistivity of the material be ρ
Resistance (R) of the first cylindrical conductor = `(rho"l")/"A"`
where, l = length of conductor
A = area of cross section
Now, another cylindrical conductor has double length but same resistance.
Let its area of cross section be A'
Its resistance (R') will be = `(rho xx 2"l")/"A"^"'"`
Since resistance is same
R = R'
`(rho xx "l")/"A" = (rho xx 2"l")/"A"^"'"`
Solving it, we get A' = 2A
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