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NCERT Class XII Chapter
Current Electricity
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Question : 16 of 24
Marks: +1, -0
Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables.
(ρAl\rho_{Al} = 2.63 × 10−810^{-8} Ω m, ρCu\rho_{Cu} = 1.72 × 10−810^{-8} Ω m, Relative density of Al = 2.7, andof Cu = 8.9).
Solution:  
Two wires have same length, and resistance. As the specific resistances are unequal, the areas are different.
For copper wire, RCuR_{Cu} = ρCu\rho_{Cu} = ρCulACu\frac{\rho_{Cu} l}{A_{Cu}}
For aluminium wire, RAlR_{Al} = ρAl\rho_{Al} lAAl\frac{l}{A_{Al}}
So , ρCu\rho_{Cu} lACu\frac{l}{A_{Cu}} = ρAllaAl\frac{\rho_{Al} l}{a_{Al}}
AAlACu\frac{A_{Al}}{A_{Cu}} = ρAlρCu\frac{\rho_{Al}}{\rho_{Cu}} = 2.63×10−81.72×10−8\frac{2.63 \times 10^{-8}}{1.72 \times 10^{-8}} = 263172\frac{263}{172}
Ratio of masses , MAlMCu\frac{M_{Al}}{M_{Cu}} = dAllAAldCulACu\frac{d_{Al} l A_{Al}}{d_{Cu} l A_{Cu}} = 2.7×2638.9×172\frac{2.7 \times 263}{8.9 \times 172} = 0.46
MAlM_{Al} < MCuM_{Cu}
Thus, the aluminium wire for the same resistance is very light than copper and that is why aluminium wires are preferred for overhead power cables
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