Commercial electricity is generated and transmitted as three phase electricity. Instead of a single emf, three separate wires carry currents for the emfs Ԑ₁ = Ԑ₀ cos ωt, Ԑ₂ = Ԑ₀ cos(ωt +120°), and Ԑ₃ = Ԑ₀ cos(ωt - 120°) over three parallel wires, each of which supplies one-third of the power. This is why the long distance transmission lines you see in the countryside have three wires. Suppose the transmission lines into a city supply a total of 450 MW of electric power, a realistic value.
a. What would be the current in each wire if the transmission voltage were Ԑ₀ = 120 V rms?
b. In fact, transformers are used to step the transmission line voltage up to 500 kV rms. What is the current in each wire?
c. Big transformers are expensive. Why does the electric company use step-up transformers?