The impedances of motors, transformers, and electromagnets have inductive reactance. Suppose that the phase angle of the total impedance of a large industrial plant is 25^o when the plant is under full operation and using 2.3 MW of power. The power is supplied to the plant from a substation 4.5 km from the plant; the 60 Hz rms line voltage at the plant is 40,000 V. The resistance of the transmission line from the substation to the plant is 5.2 Ω. The cost per kilowatt-hour is 0.07 dollars. The plant pays only for the actual energy used.

(a) What are the resistance and inductive reactance of the plant's total load?

(b) What is the current in the power lines and what must be the rms voltage at the substation to maintain the voltage at the plant at 40,000 V?

(c) How much power is lost in transmission?

(d) Suppose that the phase angle of the plant's impedance were reduced to 18^o by adding a bank of capacitors in series with the load. How much money would be saved by the electric utility during one month of operation, assuming the plant operates at full capacity for 16 h each day?

(e) What must be the capacitance of this bank of capacitors?