# 3.16 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. ($\rho_{Al} = 2.63\times 10^{-8} \Omega m$. $\rho_{Cul} = 1.73\times 10^{-8} \Omega m$ Relative density of Al = 2.7, of Cu = 8.9.)

We know,

R = $\dpi{100} \rho$l / A

The wires have the same resistance and also are of the same length.

Hence,

$\dpi{100} \frac{\rho_{Al}}{A_{Al}} = \frac{\rho_{Cu}}{A_{Cu}}$

$\dpi{100} \implies \frac{A_{Al}}{A_{Cu}} = \frac{\rho_{Al}}{\rho_{Cu}} = \frac{2.63}{1.73}$

Now, mass = Density x Volume = Density x Area x length

Taking the ratio of their masses for the same length

$\dpi{100} \implies \frac{m_{Al}}{m_{Cu}} = \frac{d_{AL}A_{Al}}{d_{Cu}A_{Cu}} = \frac{2.7\times2.63}{8.9\times1.73} < 1$

Hence, $\dpi{100} m_{Al} < m_{Cu}$

Therefore, for the same resistance and length, the aluminium wire is lighter.

Since aluminium wire is lighter, it is used as power cables.

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