Denken Exam · Free practical tool

Series RLC impedance calculator

Keep inductive and capacitive reactance signs visible in a series circuit. Read the impedance phasor before interpreting its magnitude and phase angle.

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The method

XL = 2πfL; XC = 1/(2πfC); Z = R + j(XL−XC); φ = atan2(XL−XC, R).

Before using the result

  • Series ideal RLC network with positive capacitance and frequency. No component losses beyond supplied R.

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

Keep inductive and capacitive reactance signs visible in a series circuit. Read the impedance phasor before interpreting its magnitude and phase angle.

Resistance (Ω)
20
Inductance (H)
0.1
Capacitance (F)
0.0001
Frequency (Hz)
50
  1. XL = 31.415926535897935 Ω; XC = 31.830988618379067 Ω.
  2. Z = 20 + j(-0.41506208248113197) Ω; |Z| = 20.004306449670118 Ω.
  • Inductive reactance: 31.41593 Ω
  • Capacitive reactance: 31.83099 Ω
  • Impedance magnitude: 20.00431 Ω
  • Phase angle: -0.02075013 rad

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.

Resistance (Ω)
20
Inductance (H)
0.1
Capacitance (F)
0.0001
Frequency (Hz)
60
  1. XL = 37.69911184307752 Ω; XC = 26.525823848649225 Ω.
  2. Z = 20 + j(11.173287994428293) Ω; |Z| = 22.90943833022616 Ω.
  • Inductive reactance: 37.69911 Ω
  • Capacitive reactance: 26.52582 Ω
  • Impedance magnitude: 22.90944 Ω
  • Phase angle: 0.509471 rad

Check your understanding

1. Which relationship is used?

XL = 2πfL; XC = 1/(2πfC); Z = R + j(XL−XC); φ = atan2(XL−XC, R).

2. Which assumption should you check first?

Series ideal RLC network with positive capacitance and frequency. No component losses beyond supplied R.

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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