Denken Exam · Free practical tool

Balanced three phase calculator

Separate line and phase quantities for star and delta connections in electrical theory practice. Use RMS line measurements when calculating total balanced power.

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The method

Star: Vphase = VL/√3, Iphase = IL. Delta: Vphase = VL, Iphase = IL/√3. S = √3 VLIL.

Before using the result

  • Balanced sinusoidal three-phase RMS quantities. Inputs are line voltage and line current.

Worked examples

These original training examples illustrate the method for Third-Class Electric Chief Engineer 電験三種 (Theory/Power/Machine/Law). Use the matching “Load example” button above to explore a variation; example values are not equipment settings or prescribed criteria.

1. Worked example

Separate line and phase quantities for star and delta connections in electrical theory practice. Use RMS line measurements when calculating total balanced power.

Connection
Star
Voltage (V)
230
Current (A)
10
Power factor (lagging)
90 %
  1. Star connection; VL = 230 V; IL = 10 A.
  2. S = √3 × 230 × 10 = 3983.7168574084176 VA.
  3. P = S × 0.9; Q = S × √(1 − 0.9²).
  • Phase voltage: 132.7906 V
  • Phase current: 10 A
  • Apparent power: 3,983.717 VA
  • Real power: 3,585.345 W
  • Reactive power: 1,736.462 var

2. Comparison example

Compare a different supplied condition using the same method. For Denken Exam, the important check is that the input meaning, units and method assumptions still match the problem.

Connection
Delta
Voltage (V)
400
Current (A)
10
Power factor (lagging)
90 %
  1. Delta connection; VL = 400 V; IL = 10 A.
  2. S = √3 × 400 × 10 = 6928.203230275509 VA.
  3. P = S × 0.9; Q = S × √(1 − 0.9²).
  • Phase voltage: 400 V
  • Phase current: 5.773503 A
  • Apparent power: 6,928.203 VA
  • Real power: 6,235.383 W
  • Reactive power: 3,019.934 var

Check your understanding

1. Which relationship is used?

Star: Vphase = VL/√3, Iphase = IL. Delta: Vphase = VL, Iphase = IL/√3. S = √3 VLIL.

2. Which assumption should you check first?

Balanced sinusoidal three-phase RMS quantities. Inputs are line voltage and line current.

3. How should you verify a different unit system?

Convert every input to the displayed calculation units first. Equivalent physical inputs must give equivalent results; a unit label alone does not convert a number.

Continue with the matching exam topic

This tool connects to Third-Class Electric Chief Engineer 電験三種 (Theory/Power/Machine/Law) free practice. Work through a question independently, then use the calculation steps to identify where your method differs. The tool stays free whether or not you choose paid preparation.

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