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NCERT Class XII Chapter
Current Electricity
Questions With Solutions

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Question : 16
Total: 24
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 = 2.63 × 10–8 Ω m, ρCu = 1.72 × 10–8 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, RCu = ρCu = ρCu
l
ACu
For aluminium wire, RAl = ρAl
l
AAl
So , ρCu
l
ACu
 = ρAl
l
aAl
AAl
ACu
 =
ρAl
ρCu
 =
2.63×10−8
1.72×10−8
 =
263
172
Ratio of masses ,
MAl
MCu
 =
dAllAAl
dCulACu
 =
2.7×263
8.9×172
 = 0.46
MAl < MCu
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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