A 50 Hz balanced three-phase, Y-connected supply is connected

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A 50 Hz balanced three-phase, Y-connected supply is connected to a bal anced three-phase Y-connected load. If the instantaneous phase -a of the supply voltage is Vcos (ωt) and the phase-a of the load current is Icos (ωt – φ), the instantaueous three-phase power is

1. a constant with a magnitude of VI cos φ
2. a constant with a magnitude of (3/2)VI cos φ
3. time-varying with an aver age value of (3/2)VI cos φ and a frequency of 100 Hz.
4. time-varying with an average value of VIcos φ and a frequency of 50 Hz.

Correct Option: B

Total power transmitted = Sum of the individual powers in each phase
P = V_ai_a + V_bi_b + V_ci_c
= V cosωt · I cos (ωt – φ) + V cos (ωt – 120°) · I cos (ωt – 120° – φ) + V cos (ωt + 120°) cos (ωt + 120° – φ)

VI	[cos 2 ωt + cos φ + cos (2ωt – 240° – φ) + cos φ + cos (2ωt + 240° – φ) + cos φ]
2

VI	[cos (2ωt – φ) + 3cos φ + cos (2ωt – φ) + cos 240° – sin (ωt – φ) sin 240 + cos (2ωt – φ) cos 240° + sin (2ωt – φ) sin 240°]
2

VI	[cos (2ωt - φ) + 3 cos φ - cos (2ωt -φ)]
2

3	VI	cosφ .
	2