In Fig. 31-38, a three-phase generator G produces

Chapter , Problem 77

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In Fig. 31-38, 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 V1 ! A sin vdt for wire 1, V2 ! A sin(vdt ' 120) for wire 2, and V3 ! A sin(vdt ' 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) oscillates sinusoidally with angular frequency vd and (b) has an amplitude of .

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