Circuit Theory-2 #11 | Y-Y Connection and Line-Phase Relations

Instructor: Dr. Süleyman Burak ÇELİK

In this lesson, we connect the balanced three-phase set from #10 to a real Y-Y circuit and derive the line versus phase relations from scratch. Topics covered: - Y-Y topology: source neutral n, load neutral N, three lines plus optional neutral wire - positive-sequence phase voltages V_a, V_b, V_c at 0, -120, +120 degrees - line voltage definition: V_ab = V_a - V_b by Kirchhoff's voltage law - geometric construction of V_ab on the phasor plane (parallelogram / cosine rule) - the headline result: |V_line| = sqrt(3) * |V_phase|, leading the phase by 30 degrees - in a Y connection, line current equals phase current (no sqrt(3) on the current side) - total three-phase power in two languages: 3 V_phase I_phase cos(theta) = sqrt(3) V_line I_line cos(theta) - worked example with 120 V_phase and Z_Y = 10 + j5 ohm: I_phase = 10.73 A rms, V_line = 207.85 V rms, P_total ≈ 3.45 kW - in a balanced Y-Y system the neutral current is zero Timestamps: 00:00 Cover 00:03 From phasor symmetry to a real Y-Y circuit 00:36 The Y-Y connection (full topology) 01:17 Positive-sequence phase voltages 01:53 Line voltage = subtraction of phase voltages 02:23 Geometric construction of V_ab 03:16 Line voltage result: sqrt(3) factor and +30 degrees 03:54 In Y, line current equals phase current 04:25 Three-phase total average power 05:11 Worked example (120 V_phase, 10 + j5 ohm) 06:35 Balanced Y-Y: neutral current is zero 07:07 Wrap and what is next Next lesson: #12 - Delta connections and three-phase power. Part of the AcEdumy Circuit Theory 2 course.