5. If the length of a conductor is made double keeping its area of cross section constant, then find the change in its
i) resistance and
ii) resistivity
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Explanation:
Resistance = Resistivity * (Length/Area of Cross Section)
Let R be the original resistance
Let r be the resistivity
Let l be the original length
Let L be the changed length
So L = 2l
Let a be the area of cross section
Then original resistance R is given by
R= r*l/a
Let R¹ be the resistance after doubling the length keeping area constant
R¹ = r*L/a (Please note that resistivity remains constant)
So R¹ = r*2l/a
So R¹/R = (r*2l/a)/(r*l/a)
So R¹=2R
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