PE Integrated Concepts (a) An aluminum power transmission line has a resistance of 0.0580 ? / km . What is its mass per kilometer? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.
Step-by-step solution Given : 1) Resistance of (Al) wire = 0.0580 / km 2) Resistivity of the Al wire = 2.65 x 10 .m-8 3 3 3) Density of the Al wire= 2.70 x 10 kg /m 3 3 4) Density of copper wire = 8.90 x 10 kg /m 5) Resistivity of the Cu wire = 1.72 x 10 .m -8 Calculate; 1)Mass per km of the Al wire= 2) Mass per Km of Cu wire (with same resistance)= 3) Comment on practical limits of lowering the resistance and heat. Step 1 o f 6 We know that, The resistance R of a uniform cylindrical wire of length L, cross-section area A, and made of a material of material with resistivityis given by equation (1) as below. R = L/A R= L/r ……………………..(1) Here, r is the radius of the wire.