A small town with a demand of \(900\text{ kW}\) of electric power at \(220\text{ V}\) is situated \(20\text{ km}\) away from an electric power generating station. Each wire of the two-wire transmission line has a resistance per unit length of \(5 \times 10^{-4} \, \Omega\text{ m}^{-1}\). The town gets power from the line through a \(45000\text{ V}\) to \(220\text{ V}\) step-down transformer at a substation in the town. The line power loss in the form of heat is:

The total length of the two-wire transmission line is:
\(L = 2 \times 20 \text{ km} = 40 \text{ km} = 40000 \text{ m}\)

The total resistance of the transmission line is:
\(R = L \times \text{resistance per unit length}\)
\(R = 40000 \text{ m} \times 5 \times 10^{-4} \, \Omega\text{ m}^{-1} = 20 \, \Omega\)

The power demanded by the town is \(P = 900 \text{ kW} = 9 \times 10^5 \text{ W}\).
The voltage at the primary of the step-down transformer is \(V = 45000 \text{ V}\).

Assuming an ideal transformer, the current in the transmission line is:
\(I = \dfrac{P}{V} = \dfrac{9 \times 10^5 \text{ W}}{45000 \text{ V}} = 20 \text{ A}\)

The line power loss in the form of heat is given by:
\(P_{\text{loss}} = I^2 R\)
\(P_{\text{loss}} = (20 \text{ A})^2 \times 20 \, \Omega = 400 \times 20 \text{ W} = 8000 \text{ W} = 8 \text{ kW}\)

Answer: \(8\) kW