Test: Balanced Three Phase Circuits

As the line voltage V_RY = V∠0⁰ is taken as a reference phasor. Then the source voltage V_YB is V∠-120⁰.

In a delta-connected load, the relation between line voltage and the phase voltage is line voltage = phase voltage.

As the load impedance is Z∠Ø, the current flows in the three load impedances and the current flowing in the Y impedance is I_Y = V_YB∠120⁰/Z∠Ø = (V/Z)∠-120-Ø.

Taking the line voltage V_RY = V∠0⁰ as a reference V_RY = 400∠0⁰V, V_YB = 400 ∠ -120 ⁰V and V_BR = 400∠-240⁰V. Impedance per phase = (4 + j8) Ω = 8.94∠63.4⁰Ω. Phase current I_R = (400∠0o)/(8.94∠63.4o )= 44.74 ∠ -63.4⁰A.

Power is defined as the product of voltage and current. So the power drawn by the load is P = 3V_PhI_PhcosØ = 24kW.

As the line voltage V_RY = V∠0⁰ is taken as a reference phasor. Then the source voltage V_BR is V∠-240⁰.

As the load impedance is Z∠Ø, the current flows in the three load impedances and the current flowing in the R impedance is I_R = V_BR∠0⁰/Z∠Ø = (V/Z)∠-Ø.

As the load impedance is Z∠Ø, the current flows in the three load impedances and the current flowing in the B impedance is I_B = V_BR∠240⁰/Z∠Ø = (V/Z)∠-240-Ø.

In wye or star connection, similar ends of the three phases are joined together within the alternator. The common terminal so formed is referred to as the neutral point or neutral terminal.

The voltage between line and line is called line voltage. And the voltage between line and neutral point is called phase voltage. The currents flowing through the phases are called the phase currents, while those flowing in the lines are called the line currents.