Copper and aluminum are being considered for the cables in a highvoltage transmission line where each must carry a current of 50 A. The resistance of each cable is to be 0.15 Ω per kilometer. 

(a) If this line carries power from Niagara Falls to New York City (approximately 500 km), how much power is lost along the way in the cable? Compute for each choice of cable material 

(b) The necessary cable diameter and 

(c) the mass per meter of the cable. The electrical resistivities for copper and aluminum are given in Table 18.1; the mass density of copper is 8920 kg/m³ and that of aluminum is 2702 kg/m³.

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Table 18.1 Resistivities and Temperature Coefficients at 20°C p (Q-) a(C-1) P (Q.) a (°C-1) Conductors Semiconductors (pure) 1.59 x 3.8 x 10-3 Carbon 3.5 x -0.5 x Silver 10-8 10-5 10-3 1.67 x 4.05 x 0.6 -50 x Copper Germanium 10-8 10-3 10-3 2.35 x 3.4 x 10-3 Silicon 2300 -70 x Gold 10-8 10-3 2.65 x 3.9 x 10-3 Aluminum 10-8 5.40 x 10-8 4.50 x 10-3 Tungsten 9.71 x 5.0 x 10-3 Insulators Iron 10-8 10.6 x 3.64 x 108 - Platinum Wood 10-8 10-3 1011 21 x 10-8 3.9 x 10-3 Glass 1010 – Lead 1014 44 x 10-8 0.002 x 1013 – Manganin Rubber 10-3 1016 (hard) Constantan 49 × 10-8 0.002 x > 1013 Lucite 10-3 96 x 10-8 0.89 x > 1013 Mercury Teflon 10-3 108 x 0.4 x 10-3 > 1016 Nichrome Quartz 10-8 (fused)