Final answer:
The magnitude of line current and line voltage at the source can be calculated using complex impedances and Ohm's law. The total impedance is found by adding the load and line impedances. The phase voltage is derived from the line voltage, which is then used to calculate the line current and source voltage.
Step-by-step explanation:
The question involves complex number calculations to determine electrical quantities in a balanced Y connected load, and thus falls under the category of electrical engineering. Line voltage, line current, and load impedance are key concepts required to solve the problem.
To find the line current (I), we first calculate the total impedance (Ztotal) by adding the load impedance (Zload) to the line impedance (Zline):
Ztotal = Zload + Zline
Ztotal = (216 + j63) + (0.25 + j2) = 216.25 + j65 (Ω/ φ)
Now, using Ohm's law:
I = V / Ztotal
Where V is the phase voltage (Vph), which is the line voltage (VL) divided by √3 since it's a Y-connected system:
Vph = VL / √3
Vph = 12800V / √3
The magnitude of I (Imag) can then be found by dividing the magnitude of Vph by the magnitude of Ztotal.
For part b, the voltage at the source (VS), can be found using the line current and the line impedance:
VS = I ⋅ (Zload + Zline) + VL
We calculate I (calculated in part a) and then calculate VS.a