In Fig. 31-37, a three-phase generator G produces

Chapter 31, Problem 77

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In Fig. 31-37, a three-phase generator G produces electrical power that is transmitted by means of three wires. The electric potentials (each relative to a common reference level) are Vj = A sin Wdt for wire 1, V2 = A sin( wdt - 120) for wire 2, and V3 = A sin( wdt - 240) for wire 3. Some types of industrial equipment (for example, motors) have three terminals and are designed to be connected directly to these three wires. To use a more conventional two-terminal device (for example, a lightbulb), one connects it to any two of the three wires. Show that the potential difference between any two of the wires (a) Three-wire transmission line oscillates sinusoidally with angular Fig.31-37 77. frequency w" and (b) has an amplitude ofAV3.