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Two wires of equal length , one of alumi...

Two wires of equal length , one of aluminimum and the other of copper have the same resistance.Which of the two wires is lighter? Hence explain why aluminium when are preferred for over head power cables .
`[rho_(Al)=2.63times10^-8Omega.m,rho_(Ca)=1.72times10^-8Omega.m` relative density of Al=2.7 of Cu=8.9].

Text Solution

Verified by Experts

Mass of wire ,M=A.t.d
[where A= area of cross section of the wire ,l=length of the wire, d= density of the material of the wire]
`therefore A=M/(ld)`
Resistance of the wire, `R=rho.l/A=rho.l^2/Md`
`because R_(Al)=R_(Cu)` and l is same for both the wires
`(rho_(Al).d_(Al))/M_(Al)=(rho_(Cu).d_(Cu))/M_(Al)`
`therefore M_(Cu)/M_(Al)=rho_(Cu)/rho_(Al)timesd_(Cu)/d_(Al)=(1.72times10^-8)/(2.63times10^-8)=8.9/2.7=2.16`
`therefore` The copper wire is 2.16 times heavier than the aluminium wire i.e., aluminium wire is higher. This is the reason for using aluminium wire in overhead power cables.
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