Chapter 31, Problem 065 An ac generator provides emf to a resistive load in a re

Question

Chapter 31, Problem 065

An ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a step-down transformer reduces the voltage from its (rms) transmission value Vt to a much lower value that is safe and convenient for use in the factory. The transmission line resistance is 0.35 ?/cable, and the power of the generator is 273 kW. If Vt = 100 kV, what are (a) the voltage decrease ?V along the transmission line and (b) the rate Pd at which energy is dissipated in the line as thermal energy? If Vt = 9.3 kV, what are (c) ?V and (d)  Pd? If Vt = 1.1 kV, what are (e) ?V and(f)  Pd?

Explanation / Answer

a) current = P/V = 273 kW/100kV = 2.73 amps

voltage drop is V = IR = 2 x 2.73 x 0.35 = 1.911 volts

We have multiplied by 2 since there are 2 cables

b) P = VxI = 1.911 x 2.73 = 5.21 watts

Repeat the above for the other values of Vt

c) current = P/V = 273 kW/9.3kV = 27.57 amps

voltage drop is V = IR = 2 x 27.57 x 0.35 = 19.3 volts

We have multiplied by 2 since there are 2 cables

d) P = VxI = 19.3 x 27.57 = 532.18 watts

e) current = P/V = 273 kW/1.1kV = 248.18 amps

voltage drop is V = IR = 2 x 248.18 x 0.35 = 173.72 volts

We have multiplied by 2 since there are 2 cables

f) P = VxI = 173.72 x 248.18 = 43115.63 watts

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