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.