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Circuit Analysis: AC, Linear Circuits and Transients

A Δ-connected load with a 20 Ω resistor in each phase, as in figure (b), is connected to a balanced three-phase source with a line voltage of 200 V RMS. Which of the following is closest to the RMS line current?

Y (star) and Δ (delta) connections of a three-phase load (a) Y a Z b Z c Z N Ia Vp = VL/√3 (b) Δ a b c Z Z Z Ia Iab IL = √3 × Ip
Y (star) and Δ (delta) connections of a three-phase load · View in diagrams
  1. AAbout 5.8 A
  2. B10 A
  3. CAbout 17 A
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Answer: C. About 17 A

Method 1 (Δ relations): in a Δ connection the line voltage appears directly across each phase resistor, so the phase current is 200/20 = 10 A. A line current is the phasor difference of two phase currents, and its magnitude is √3 times the phase current: 10√3 ≈ 17.3 A. Method 2 (convert to Y): the equivalent Y has 20/3 Ω per phase, and dividing the phase voltage 200/√3 ≈ 115.5 V by 6.67 Ω gives a line current of about 17.3 A. Method 3 (check with power): the total power of the load is 3 × 10² × 20 = 6 kW, and P = √3 VL IL gives IL = 6000/(√3 × 200) ≈ 17.3 A.

  • A. 10/√3 ≈ 5.8 A divides by √3 where you should multiply. In a Δ connection the line current is larger than the phase current.
  • B. 10 A is the phase current (the current in each phase resistor).
  • C. Correct. The line current is √3 times the phase current, about 17 A.
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