Study Guide

Denken 3rd-Class Theory/Power/Machine/Law Guide

A focused, independent preview of the Third-Class Electric Chief Engineer examination. It teaches the calculation spine across Theory, Power, and Machinery, then connects Law and safety to practical facility reasoning. The 20 MCQs check supporting knowledge; they are not an official simulation or full syllabus cover.

Updated October 202611 min readStudy GuideDenken Exam
Claire Brooks

Claire Brooks

Denken Exam Editorial Team

This English-language knowledge preview covers the Japanese Third-Class Electric Chief Engineer examination (第三種電気主任技術者); the official subjects are Theory, Power, Machinery, and Law, and Power Systems and Electrical Machinery and Applications are study groupings rather than separate papers. The stated exam structure is 17/17/17/13 answers with 90/90/90/65 minutes, five-choice marking or CBT, subject exemptions, and a principle 60/100 subject pass with possible difficulty adjustment. Statutory supervision is described as facilities below 50,000 V, excluding generating stations of 5,000 kW or more. Application dates, fees, venue availability, completion-period eligibility, and current legal wording must be confirmed with current official sources; this preview does not cover the full syllabus and is not a simulation of the official paper. Use this package for diagnostic learning and mechanism-building. It does not replace the official five-choice paper, current legal text, or a complete syllabus review. The 20 MCQs check supporting knowledge; they are not an official simulation.

What the credential actually tests

The examination is a four-subject technical paper with distinct calculation and judgement demands; administrative details require current confirmation.

The credential is for safety supervision of commercial electrical facilities, and the official subject structure is Theory, Power, Machinery, and Law. Theory covers electrical/electronic theory and measurement; Power covers generating, transforming, transmitting, distributing, and electrical materials; Machinery covers machines, power electronics, applications, lighting, heating, control, mechatronics, and information handling; Law covers safety-related electrical laws and facility management. Topic labels such as Power Systems and Electrical Machinery and Applications are useful study buckets, but they do not replace the official subject descriptions.

The supplied R8 policy states that candidates answer 17 questions in Theory, 17 in Power, 17 in Machinery, and 13 in Law, with times of 90, 90, 90, and 65 minutes. It also states a principle subject pass at 60/100, with possible adjustment for difficulty. The overview describes five-choice marking or CBT and subject exemptions. Application windows, fees, venue availability, completion-period eligibility, and current legal text are administrative or legal details that require current confirmation.

Statutory supervision is described as facilities below 50,000 V, excluding generating stations of 5,000 kW or more. Treat that as a scope indicator, not a substitute for current legal text. For study, focus on calculating, interpreting equipment behaviour, and applying safety reasoning—not merely reciting a topic list.

A preparation priority that follows the paper

Build calculation fluency first, then machinery models, then law reasoning; use the official question counts as a planning constraint, not a weighting guarantee.

Start with Theory because it supplies the language for Power and Machinery: Ohm's and Kirchhoff's laws, impedance, phasors, three-phase relationships, and energy conversion. Then move to Power, where the same mathematics is applied to voltage drop, losses, reactive compensation, per-unit quantities, and fault estimation. Machinery should follow, because transformers, induction motors, and DC machines reuse circuit and magnetic reasoning.

Do not postpone Law until the end and then memorize isolated numbers. Law is shorter in answer count in the supplied policy, but each subject must be passed. Learn the safety logic: what the chief engineer supervises, why earthing and insulation matter, how inspection records support decisions, and how protection coordination limits damage. Verify current statutory wording rather than relying on slogans.

A useful weekly pattern is: diagnosis, worked examples, closed-book calculations, and a short error review. Keep a formula sheet with units and assumptions. When a result looks strange, check line-versus-phase, rms-versus-peak, per-unit base, and whether a loss is per phase or total. These checks are more valuable than collecting more formulas.

Electrical Theory: one calculation spine

Most Theory items reduce to network reduction, impedance triangles, resonance, three-phase relationships, and power-factor arithmetic.

For DC networks, reduce from the load backward. A 24 V source feeding 4 Ω in series with a 12 Ω and 6 Ω parallel pair gives a parallel value of 4 Ω, total 8 Ω, and source current 3 A. The parallel voltage is 12 V, so the 12 Ω branch carries 1 A and the 6 Ω branch carries 2 A. Always mark branch voltages before calculating branch currents.

For AC series circuits, combine resistance and reactance as a phasor triangle. If R = 3 Ω and X_L = 4 Ω, then Z = 5 Ω. At 100 V rms, current is 20 A, power factor is 0.6 lagging, and real power is 100 × 20 × 0.6 = 1,200 W. Do not add R and X arithmetically. For series resonance, f₀ = 1/(2π√(LC)); check units before substituting.

For a balanced star load, line current equals phase current, while phase voltage is line voltage divided by √3. A 400 V line-to-line star load with 10 Ω per phase has phase voltage about 231 V, phase current about 23.1 A, and line current about 23.1 A. In delta, line current is √3 times phase current and phase voltage equals line voltage. Draw the connection before choosing a formula.

Power Systems: losses, reactive power, and bases

Power questions reward consistent three-phase bookkeeping: current from power, loss from current squared, reactive power from tangent, and per-unit from a declared base.

For a balanced three-phase load, I = P/(√3 V_LL cosφ). A 100 kW load at 400 V and 0.8 power factor draws about 180.4 A. If each line has 0.03 Ω resistance, total copper loss is 3 I²R ≈ 3 × 180.4² × 0.03 ≈ 2.93 kW. A common error is to use the line-to-line voltage in a per-phase I²R expression without converting the circuit correctly; the 3 I²R form is convenient when I is line current and R is per-phase resistance.

Reactive compensation is calculated from the change in reactive power: Q = P tanφ. For 100 kW at 0.8 lagging, Q₁ = 75 kvar. At 0.95 lagging, Q₂ ≈ 32.9 kvar. The capacitor rating is about 42.1 kvar, not the whole original 75 kvar. Capacitors reduce current and losses upstream, but they do not remove the load's real power.

Per-unit calculations require a voltage and power base. With 10 MVA and 66 kV, Z_base = V²/S = 66²/10 = 435.6 Ω. A 20 Ω impedance is therefore about 0.046 pu. For a simple three-phase fault estimate, use per-phase voltage divided by per-phase source impedance: at 11 kV line-to-line and 2 Ω per phase, I ≈ (11,000/√3)/2 ≈ 3.18 kA. These are planning estimates, not a substitute for full fault study.

Machinery: transformer, induction, and DC models

Machine questions are usually equivalent-circuit or ratio questions in disguise; keep power, speed, and loss terms separate.

For an ideal transformer, power is conserved. A 6,600/400 V transformer supplying 20 A at 400 V delivers about 8 kVA, so the primary current is about 8,000/6,600 ≈ 1.21 A. For efficiency, use output divided by input, where input is output plus losses. An output of 50 kW with 2 kW total losses gives 50/52 ≈ 96.2%. Do not divide output by output plus only copper loss if core loss is also stated.

For an induction motor, synchronous speed is N_s = 120f/p. A 4-pole, 50 Hz motor has N_s = 1,500 rpm. At 1,440 rpm, slip is (1,500 − 1,440)/1,500 = 4%. At a given slip, torque is approximately proportional to voltage squared, so 90% voltage gives about 0.81 times torque. Slip and rotor frequency are linked: rotor frequency equals slip times stator frequency.

For a DC generator, the generated EMF balances terminal voltage plus armature drop: E = V + I_aR_a. With 220 V, 20 A, and 0.5 Ω, E = 220 + 10 = 230 V. For a motor, the sign reverses in the speed equation. Always identify whether the machine is generating or motoring before choosing the sign. Field-circuit details matter, but only use the data given.

Law and safety: reason from protection, not slogans

Safety questions should be answered by tracing the fault path, the protective response, and the evidence needed to show the facility remains safe.

The third-class chief engineer's role is described as safety supervision over construction, maintenance, and operation of commercial electrical facilities, in coordination with other engineers. The scope statement—below 50,000 V and excluding generating stations of 5,000 kW or more—is a starting point. Because legal wording can change, treat exact classifications, notification duties, and inspection frequencies as subject review requiring current official text.

Protective earthing is not a power-factor measure. It gives fault current a low-impedance path so protective devices operate quickly and touch voltage is limited. Insulation resistance testing is likewise a safety activity: confirm isolation, prove dead, discharge stored energy, and follow the applicable procedure. A measurement is meaningful only when the equipment state and test conditions are known.

Maintenance records are engineering evidence. They reveal trends, support decisions about replacement or adjustment, and demonstrate that inspection and repair were considered. They do not eliminate future faults or replace protection. In Law preparation, practise explaining why a measure exists and what could go wrong if it is omitted; that reasoning transfers better than memorizing isolated phrases.

Common errors and how to catch them

Most lost marks come from unit, connection, and assumption errors rather than from obscure theory.

Check these repeatedly: using line voltage where phase voltage is needed; treating a star phase current as √3 times line current; adding resistance and reactance directly; forgetting that power factor is cosφ, not φ; using output power as input power in efficiency; and reporting slip as rpm rather than a fraction or percentage. In three-phase loss, decide whether resistance is per phase and whether the current is line current.

In reactive-power problems, calculate the initial and final Q separately. A capacitor does not supply the load's real power. In per-unit problems, write the bases before substituting. In transformer problems, identify which side is primary and whether the current is given on the secondary. In DC machine problems, choose generator or motor sign convention before solving.

For Law and safety, avoid absolute statements such as “earthing removes all danger” or “records prevent faults.” Prefer causal statements: earthing limits touch voltage and supports disconnection; records support trend detection and accountability. When a question asks for the best action, look for isolation, verification, protection, and documentation—not shortcuts.

Integrated practice task and self-check

A good practice task combines power calculation, reactive compensation, and safety evidence in one facility scenario.

Scenario: a 400 V three-phase feeder supplies 120 kW at 0.85 lagging. Each line has 0.03 Ω resistance; reactance is ignored. (a) Find line current. (b) Estimate total copper loss. (c) Find the capacitor kvar needed to raise the load power factor to 0.95. (d) Outline the safety and inspection evidence you would expect before and after the change.

Self-check: (a) I = 120,000/(√3 × 400 × 0.85) ≈ 203.8 A. (b) Loss = 3 × 203.8² × 0.03 ≈ 3.74 kW. (c) Q₁ = 120 tan(acos 0.85) ≈ 74.4 kvar; Q₂ = 120 tan(acos 0.95) ≈ 39.4 kvar; capacitor ≈ 35.0 kvar. (d) A strong answer mentions isolation and proving dead, discharge, earthing/bonding, insulation and protection checks, updated records, and verification against current technical requirements. It should not invent a legal inspection interval.

Rubric: 1 point for correct formulas and units; 1 point for correct numerical results within rounding; 1 point for explaining capacitor effects on current and losses; 1 point for safe, evidence-based reasoning without unsupported legal claims. This open task is representative practice; the 20 MCQs are supporting-knowledge checks, not a simulation of the official written paper.

A practical study sequence

Use a ten-week cycle that moves from fundamentals to integrated timed practice, with weekly error review.

Weeks 1–2: Theory fundamentals—DC networks, AC impedance, phasors, resonance, three-phase relationships, and measurement concepts. Weeks 3–4: Power—voltage drop, line loss, reactive compensation, per-unit, fault estimation, and protective coordination basics. Weeks 5–6: Machinery—transformer ratios and efficiency, induction-motor slip and torque, DC machine EMF, and power-electronics concepts. Week 7: Law and safety—scope, chief-engineer duties, earthing, insulation, and maintenance records, using current official text.

Week 8: integrated tasks such as the calculation above. Week 9: mixed timed sets drawn from all four subjects, followed by error classification. Week 10: review only the highest-frequency errors, rebuild the formula sheet, and practise explaining safety decisions aloud or in writing. Keep a log with three columns: error, cause, and corrective rule.

Before registering or relying on any administrative detail, check the current official test-centre information. This preview gives a general assessment structure, but it is not a complete syllabus, not a current fee schedule, and not a guarantee that the exam will be available in any particular format or location.

References and further reading

Use these references to explore the concepts and check the latest information from the relevant organizations.

Continue your preparation

FAQ

Frequently Asked Questions

Practical answers to help you apply the guidance for Third-Class Electric Chief Engineer 電験三種 (Theory/Power/Machine/Law).

Is this a full mock examination?
No. The 20 questions check supporting knowledge across four domains and are not a simulation of the official paper. The integrated task in the guide provides representative open practice, but neither component covers the full syllabus.
Can I ignore Law because it has fewer answers?
No. The supplied policy indicates 13 Law answers, but each subject must be passed. Fewer questions can mean less margin for error, so practise safety reasoning, scope, earthing, insulation, and records alongside calculations.
Should I memorize formulas or derive them?
Memorize a compact set—Ohm/Kirchhoff, impedance, three-phase power, per-unit, speed/slip, transformer ratio, and DC EMF—but practise deriving relationships and checking units. Derived understanding prevents sign and line/phase mistakes.
How should I study legal and safety material?
Learn the purpose of each safeguard and verify current wording from official sources. Treat exact classifications, notification duties, and inspection intervals as subject review rather than relying on old notes or isolated slogans. This guide is educational, not legal advice.
Why does this guide treat administrative rules as subject review?
The subject-exemption and overall pass routes involve separate conditions, and application dates, fees, venue availability, and current legal text can change. Confirm them with current official information rather than inferring them from a study guide or older notes.

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