Two wires A and B of same material have their lengths in the ratio 1:5 and diameters in the ratio 3:2. If the resistance of the wire B is 180Ω, find the resistance of wire A.
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Answer:
La:Lb=1:5
Da:Db=3:2
2Ra:2Rb=3:2
Ra:Rb=3:2
( here R is radius)
Ra²:Rb²=9:4 = Aa: Ab
Ra/Rb = (La/Aa)×(Ab/Lb) [ here R is resitance and A is area]
Ra / 180 = (La/Lb)×(Ab/Aa)
Ra/180 = (1/5) ( 4/9)
Ra/180= (4/ 5×9)
Ra=(4/5×9)×180
Ra=4×4
Ra=16
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