Question

A wye connected source is connected to a wye connected load in a balanced three-phase circuit. The impedance of the load is Zᵧ = 100-j50 Ω while the impedance of the line is Zₗᵢₙₑ = 20+ j20 Ω. If the line-to-neutral voltage at the source is given by vₐₙt)= 80 cos(50t) V, what is the line-to-neutral voltage at the load, Vₐₙ(t), and the line current iₐₙ(t)?

Answer 1

To find the line-to-neutral voltage at the load, VAN(t), and the line current, iAN(t), we add the load and line impedances, calculate the line current using Ohm's law with the source voltage, and adjust the load voltage for the voltage drop across the line impedance.

Step-by-step explanation:

To calculate the line-to-neutral voltage at the load and the line current in a balanced three-phase circuit where a wye connected source is connected to a wye connected load, we can follow these steps:

• Firstly, determine the total impedance per phase by adding the load impedance, Z₇ = 100-j50 Ω, and the line impedance, Zline = 20+j20 Ω, which gives Ztotal = 120-j30 Ω.
• Calculate the phase current using Ohm's law:
  IAN = VAN/Ztotal, where VAN is the source line-to-neutral voltage.
• Since vAN(t) = 80 cos(50t) V, the phasor form is VAN = 80∠0°, thus the line current phasor is IAN = 80Ω0°/120-j30 Ω.
• Finally, adjust the line-to-neutral voltage at the load VAN(t) for the voltage drop due to line impedance.

To calculate these values accurately, we need to perform complex arithmetic involving phasors and, preferably, use a diagram to visualize the phase relationships.