GATE EE 2022 Set 1 — Question 21
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Electric Circuits → AC Power & Three-Phase → Unbalanced Circuits
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Question
In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of with phase sequence . The star connected load has and . The value of in , for which the voltage difference across the nodes and is zero, is
Correct answer
(C) 20 -60^
Solution
For the voltage difference across nodes and to be zero (), the neutral point of the load must be at the same potential as the neutral point of the supply. Using Millman's theorem:This implies:Given a balanced supply of (line-to-line), the phase voltage magnitude is .
Let , , and .
Substituting the values:Since :
Let , , and .
Substituting the values:Since :
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