62.3k views
1 vote
An acb sequence balanced three-phase Y-connected source supplies power to a balanced, three-phase Δ-connected load with an impedance of 9+15i Ω/ϕ . The source voltage in the b-phase is 230 ∠−45∘V. The line impedance is 1 + 1i Ω/ϕ. Use the single phase equivalent circuit for the a-phase to find the current in the a-phase of the load

1 Answer

4 votes

Final answer:

To find the current in the a-phase of a balanced Δ-connected load, we determine the a-phase voltage from the b-phase voltage provided and then use Ohm's law with the line and load impedances in the equivalent single-phase circuit.

Step-by-step explanation:

The student's question pertains to finding the current in the a-phase of a balanced Δ-connected load in a three-phase system. Given the b-phase source voltage (230 ∠−45°V), line impedance (1 + 1i Ω/φ), and load impedance (9+15i Ω/φ), we can calculate the current for the a-phase using the equivalent single-phase circuit.

In a balanced three-phase system, the line-to-neutral voltages in a Y-connected source can be related to the given line-to-line voltage of the b-phase by a −120° phase shift. Meaning, the a-phase voltage (Van) can be found by adding 120° to the phase angle of Vbn (230 ∠−45°V), resulting in Van being 230 ∠−15°V. With the phase voltage and the line and load impedances, we apply Ohm's law (V=IZ) for the a-phase to find the line current. Utilizing the phase shift concept and Ohm's law, we can then find the current in the a-phase of the load. This calculation involves vector addition of impedances and requires knowledge of complex numbers in AC circuits.

User Alexander Popov
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.