Question

In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of 100\(\sqrt{3}\) V with phase sequence ABC. The star connected load has \( Z_A = 10 \, \Omega \) and \( Z_B = 20 \angle 60^\circ \, \Omega \). The value of \( Z_C \) in \( \Omega \), for which the voltage difference across the nodes \( n \) and \( n' \) is zero, is

• A. ( 20 \angle -30^\circ \)
• B. ( 20 \angle 30^\circ \)
• C. ( 20 \angle -60^\circ \)
• D. ( 20 \angle 60^\circ \)

Hint:

In unbalanced three-phase systems, the impedance values must be chosen carefully to ensure balance and meet the condition of zero voltage difference.

Answer 1

The Correct Option is C

Step 1: Understand the phase relationships.
For the given unbalanced load, the voltage across each load element in a star connection depends on the phase difference between the supply voltages. The condition that the voltage difference between \( n \) and \( n' \) is zero means that the total impedance seen from \( n \) to \( n' \) must be balanced. Step 2: Use the given impedances.
The impedances \( Z_A \), \( Z_B \), and \( Z_C \) must satisfy the condition for zero voltage difference across \( n \) and \( n' \). By analyzing the system and using Kirchhoff's voltage law, we can determine the correct impedance \( Z_C \) for this condition. Step 3: Conclusion.
The correct answer is (C), as \( Z_C = 20 \angle -60^\circ \) satisfies the condition for zero voltage difference.