A wire of resistence 10ohm is drawn out so that its length is thriceits original length. Calculate its new resistence.
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We have, initial resistance, R = 10 Ω
Original length be L and area of cross-section be A and the resistivity be ρ.
When the length is stretched to make it thrice, i.e. L/ = 3L, the area of cross-section A/ is such that,
AL = A/L/ [volume of the wire remains constant]
=> AL = A/(3L)
=> A/ = A/3
Now, the new resistance is,
R/ = ρL//A/ = ρ(3L)/(A/3)
=> R/ = 9ρL/A = (9)(10) = 90 Ω
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