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Three-phase systems: board exam questions with solutions

On the REE exam under Electrical Engineering Professional Subjects and the RME exam under Technical Subjects. Try each question before you open its solution, then practise with fresh numbers below: 3 computed question types on this topic.

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Build it in the lab

Three-phase star (Y) · Three-phase delta (Δ): the same circuits on a live bench, with meters you can move.

Questions

1. A balanced wye-connected source has a phase (line-to-neutral) voltage of 230 V. What is the line-to-line voltage?

  1. 398 V
  2. 230 V
  3. 690 V
  4. 133 V
Show the answer and solution

Answer: A. 398 V

In a wye system V_L = √3 × V_ph = 1.732 × 230 = 398.4 ≈ 398 V.

2. A balanced three-phase load draws 25 A per line from a 400 V (line-to-line) supply at 0.8 power factor lagging. What is the real power?

  1. 8.00 kW
  2. 13.86 kW
  3. 17.32 kW
  4. 24.00 kW
Show the answer and solution

Answer: B. 13.86 kW

P = √3 × V_L × I_L × pf = 1.732 × 400 × 25 × 0.8 = 13856 W ≈ 13.86 kW.

3. Three identical 20 Ω resistors are connected in delta across a 400 V three-phase supply. What is the line current?

  1. 20.0 A
  2. 11.5 A
  3. 34.6 A
  4. 60.0 A
Show the answer and solution

Answer: C. 34.6 A

Each delta phase sees the full line voltage: I_ph = 400/20 = 20 A. Line current I_L = √3 × I_ph = 34.6 A.

4. In the two-wattmeter method on a balanced three-phase load, the meters read 6 kW and 2 kW (both positive). What is the load power factor?

  1. 0.866
  2. 0.500
  3. 0.894
  4. 0.756
Show the answer and solution

Answer: D. 0.756

tan φ = √3 (W1 − W2)/(W1 + W2) = 1.732 × 4/8 = 0.866, so φ = 40.89° and pf = cos φ = 0.756.

5. In a balanced three-phase system, by how many electrical degrees are the phase voltages displaced from one another?

  1. 120°
  2. 90°
  3. 60°
  4. 180°
Show the answer and solution

Answer: A. 120°

The three phase voltages are equal in magnitude and displaced 120° apart (360°/3).

6. A balanced wye load has an impedance of 8 + j6 Ω per phase and is supplied from a 400 V, 60 Hz three-phase system. What total real power does it absorb?

  1. 38.4 kW
  2. 12.8 kW
  3. 16.0 kW
  4. 4.27 kW
Show the answer and solution

Answer: B. 12.8 kW

V_ph = 400/√3 = 230.9 V, |Z| = 10 Ω, so I = 23.09 A. P = 3 I² R = 3 × 23.09² × 8 = 12800 W = 12.8 kW.

7. A 50 kW three-phase load operates at 0.75 power factor lagging. How much capacitive kvar is needed to raise the power factor to 0.95 lagging?

  1. 44.1 kvar
  2. 16.4 kvar
  3. 27.7 kvar
  4. 14.0 kvar
Show the answer and solution

Answer: C. 27.7 kvar

Q_c = P (tan φ1 − tan φ2) = 50 × (tan(cos⁻¹0.75) − tan(cos⁻¹0.95)) = 50 × (0.8819 − 0.3287) = 27.7 kvar.

8. A 30 kvar, 400 V, 60 Hz three-phase capacitor bank is connected in delta. What capacitance is required in each phase?

  1. 497 µF
  2. 55.3 µF
  3. 287 µF
  4. 166 µF
Show the answer and solution

Answer: D. 166 µF

Each delta phase supplies 10 kvar at 400 V. C = Q/(ωV²) = 10 000/(2π × 60 × 400²) = 165.8 µF ≈ 166 µF.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. A balanced three-phase load takes 75 kW at 380 V line-to-line and 1 power factor. What is the line current?

  1. 65.8 A
  2. 197 A
  3. 114 A
  4. 171 A
Show the answer and solution

Answer: C. 114 A

IL = P/(√3·VL·pf) = 75000/(1.732 × 380 × 1) = 114 A.

10. A wye-connected supply has 480 V between lines. What is the line-to-neutral voltage?

  1. 831.4 V
  2. 277.1 V
  3. 160 V
  4. 240 V
Show the answer and solution

Answer: B. 277.1 V

In wye VL = √3·Vph, so Vph = 480/√3 = 277.1 V.

11. A balanced delta load draws 30 A per line. What current flows in each phase winding?

  1. 10 A
  2. 30 A
  3. 52 A
  4. 17.3 A
Show the answer and solution

Answer: D. 17.3 A

In delta IL = √3·Iph, so Iph = 30/√3 = 17.3 A.

Other topics in the same subjects

DC circuits · AC circuits · Transients (RC, RL, RLC) · Semiconductors and diodes · Power electronics · Instrumentation and measurement · Control systems · Transformers · DC machines · Induction motors · Synchronous machines · Power systems and transmission · Protection: fuses, breakers, relays · Illumination · Power plant engineering · PEC: branch circuits, ampacity and protection · Tools and test equipment · Motors, starters and control circuits · RA 7920 and ethics (electrical)

An independent, free reviewer: not affiliated with the PRC or the Boards. Subject weights and passing rules are from the PRC examination programs and the laws (RA 9292, RA 7920); check the current PRC program before you file. Code questions follow the Philippine Electrical Code 2017 Part 1; check them against your own copy of the Code.