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

Step-by-step solution

The total length of the two-wire transmission line is: L = 2 20 km = 40 km = 40000 m The total resistance of the transmission line is: R = L resistance per unit length R = 40000 m 5 10⁻⁴ , m ⁻¹ = 20 , The power demanded by the town is P = 900 kW = 9 10^5 W . The voltage at the primary of the step-down transformer is V = 45000 V . Assuming an ideal transformer, the current in the transmission line is: I = P V = 9 10^5 W 45000 V = 20 A The line power loss in the form of heat is given by: P_ loss = I^2 R P_ loss = (20