the sum of the individual powers in each phase
The correct answer is that the total power delivered by a balanced three-phase system is the sum of the individual powers in each phase.
In a balanced three-phase system, the three phases have equal voltage magnitudes and equal current magnitudes, and the phase angles are 120 degrees apart. The power in each phase is given by \(P_{phase} = V_{phase}I_{phase}\cos(\theta)\), where \(V_{phase}\) is the phase voltage, \(I_{phase}\) is the phase current, and \(\theta\) is the phase angle between the voltage and current. Because the system is balanced, the power in each phase is the same.
The total power \(P_{total}\) is simply the sum of the power in each phase:
\(P_{total} = P_a + P_b + P_c = 3P_{phase}\)
Therefore, the total power is three times the power in any one phase. While options 2 and 3 might seem plausible at first glance, they are incorrect. Option 2 only considers two phases, neglecting the power contribution of the third. Option 3 averages the power across the phases, ignoring the fact that total power is a sum, not an average. Option 4 only calculates the power in a single phase, not the total power of the three-phase system.
Similar Questions
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