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Power Distribution & Wiring Design

Class 2 Electrician 第二種電気工事士 (written exam) · 第二種電気工事士(学科試験) · Written by Tokutei Pass based on the official study texts; not copied verbatim.

Characteristics of Low-Voltage Distribution Systems (1-Phase 2-Wire, 1-Phase 3-Wire, 3-Phase 3-Wire)

There are three low-voltage distribution systems used to deliver electricity from pole transformers to residences and shops: "single-phase 2-wire", "single-phase 3-wire", and "three-phase 3-wire". Questions 6 through 10 of Part 1 on the exam come from this chapter.

The "single-phase 2-wire system (100 V)" is a small-scale method supplying only 100 V using two wires: an ungrounded live wire (black) and a grounded wire (white). Both the line-to-line voltage and the voltage to ground are 100 V.

The most widely used system in modern homes is the "single-phase 3-wire system (100 V / 200 V)". It uses three wires in total: a grounded neutral wire (white) tapped from the center of the transformer winding, and two outer voltage wires (black and red).

In a single-phase 3-wire system, connecting between either outer wire (black or red) and the center neutral wire (white) provides "100 V" for lighting and general outlets, while connecting between the two outer wires (black and red) simultaneously provides "200 V" for large air conditioners or IH cooktops.

A crucial point here is that "the voltage to ground in a single-phase 3-wire 100/200 V circuit is 100 V (150 V or less), even for 200 V appliances." Conversely, a "three-phase 3-wire 200 V" system used for factory motors grounds one phase wire, making its voltage to ground 200 V (exceeding 150 V).

Characteristics of Low-Voltage Distribution Systems (1-Phase 2-Wire, 1-Phase 3-Wire, 3-Phase 3-Wire)

Key points


  • Single-phase 3-wire provides 100 V between an outer voltage wire (black/red) and the center neutral wire (white), and 200 V between the two outer wires.

  • Because the center neutral wire of a single-phase 3-wire 100/200 V system is grounded, the voltage to ground is "100 V" even for 200 V loads.

  • A three-phase 3-wire 200 V system (delta with one corner grounded) has a voltage to ground of "200 V (exceeding 150 V)".
WordMeaning
single-phase 2-wire and single-phase 3-wire systems
three-phase 3-wire system
neutral wire (white) and voltage wires (black, red)
voltage to ground

Voltage Drop and Power Loss Calculations in 1-Phase 2-Wire and 1-Phase 3-Wire Systems

Questions 6 and 7 test calculations of "voltage drop ΔV (V)" and "line power loss Pl (W)" caused by the small resistance r (Ω) of each distribution wire (assuming load power factor cosφ = 1).

In a "single-phase 2-wire system", the same current I (A) flows through both the outgoing wire and the return wire (a total of 2 wires). Therefore, if the resistance of one wire is r (Ω), the round-trip voltage drop is "ΔV = 2 × r × I (V)", and the power loss is "Pl = 2 × r × I² (W)".

In a "single-phase 3-wire system", when the upper load current I1 and lower load current I2 are equal in a "balanced load (I1 = I2 = I)", the currents in the center neutral wire cancel each other out to become "0 A".

When neutral wire current is 0 A, the voltage drop along the neutral wire is also 0 V. Thus, the voltage drop for each load is just that of a single outer wire, "ΔV = r × I (V)", and total line power loss is the sum of the top and bottom outer wires: "Pl = 2 × r × I² (W)".

If the upper and lower currents differ (unbalanced, e.g., I1 > I2), the difference current "IN = I1 − I2" flows back toward the source through the neutral wire, and total power loss is the sum across all three wires: "Pl = r × I1² + r × IN² + r × I2²".

Key points


  • Single-phase 2-wire (2 wires round-trip): Voltage drop is "ΔV = 2rI (V)", and power loss is "Pl = 2rI² (W)".

  • Single-phase 3-wire (balanced I1 = I2 = I): Neutral current is 0 A, single-phase voltage drop is "ΔV = rI", and power loss is "Pl = 2rI²".

  • When one switch is opened in a single-phase 3-wire circuit, the remaining side acts like a single-phase 2-wire circuit (2 wires), so loss is "2rI²".

  • Example: In a single-phase 2-wire circuit with wire resistance r = 0.15Ω and current I = 20A → Voltage drop ΔV = 2 × 0.15 × 20 = 6V, power loss Pl = 2 × 0.15 × 20 × 20 = 120W

  • Example: In a balanced single-phase 3-wire circuit with wire resistance r = 0.2Ω and current I = 15A → Neutral current is 0A, single-phase voltage drop ΔV = 0.2 × 15 = 3V, total loss Pl = 2 × 0.2 × 15 × 15 = 90W
WordMeaning
voltage drop (ΔV)
line power loss (Pl)
balanced load
neutral wire current

3-Phase 3-Wire Voltage Drop/Loss and Neutral Wire Disconnection in 1-Phase 3-Wire

In a "three-phase 3-wire system", line current I (A) flows through all three wires with a 120-degree phase shift between each wire. Consequently, the line-to-line voltage drop is multiplied by √3 rather than 2: "ΔV = √3 × r × I (V) (where √3 = 1.73)".

Meanwhile, the line power loss Pl (W) in a three-phase 3-wire system is simply the sum of the heat loss "r × I²" generated in each of the three wires of resistance r (Ω), giving "Pl = 3 × r × I² (W)".

Another frequent topic in Question 7 is calculating abnormal voltage when the center "neutral wire breaks (disconnects)" in a single-phase 3-wire 100/200 V circuit. If the neutral wire breaks, the upper load resistance R1 and lower load resistance R2 become "connected in series across the outer 200 V source".

As a result, the 200 V voltage divides in proportion to resistance, applying "V1 = 200 × R1 ÷ (R1 + R2) (V)" across upper load R1. For example, if R1 = 100 Ω and R2 = 50 Ω, an overvoltage of "200 × 100 ÷ 150 ≈ 133 V" is applied to R1, burning out the appliance.

Because a broken neutral wire subjects 100 V appliances on the higher-resistance (lower-power) side to dangerous overvoltage above 100 V, electrical regulations strictly stipulate that "fuses or single-pole switches must never be installed in the neutral wire" of a multi-wire circuit.

Key points


  • In a three-phase 3-wire system, voltage drop is "ΔV = √3 × r × I (V)" and power loss across all 3 wires is "Pl = 3 × r × I² (W)".

  • If the neutral wire breaks in a single-phase 3-wire circuit, loads R1 and R2 are in series across 200 V, dividing voltage as "V1 = 200 × R1 ÷ (R1 + R2)".

  • To prevent overvoltage burnout from neutral disconnection, installing a fuse (overcurrent breaker) on the neutral wire is strictly prohibited.

  • Example: In a three-phase 3-wire system with wire resistance r = 0.1Ω and line current I = 20A → Voltage drop ΔV = 1.73 × 0.1 × 20 = 3.46V, power loss Pl = 3 × 0.1 × 20 × 20 = 120W

  • Example: If the neutral breaks in a single-phase 3-wire circuit (200V line-to-line) with upper load R1 = 60Ω and lower load R2 = 40Ω → Voltage across R1 is V1 = 200 × 60 ÷ (60 + 40) = 120V
WordMeaning
three-phase 3-wire voltage drop (√3rI)
neutral wire disconnection (break)
overvoltage
neutral wire of a multi-wire circuit

Standard Allowable Current of Insulated Wires (Solid Wires and Stranded Wires)

When current flows through a wire, Joule heat raises its temperature. The maximum current that can flow without exceeding the maximum allowable temperature of the insulation (60°C for vinyl-insulated IV wire) is called the "allowable current (ampacity, unit: A)".

To solve Question 8, you must memorize the "base allowable current" values for 600 V vinyl-insulated wire (IV) in open air. First, memorize the four standard sizes of "solid wire (single copper conductor, specified by diameter in mm)".

The allowable currents for solid wires (by diameter) are: "1.6 mm diameter = 27 A", "2.0 mm diameter = 35 A", "2.6 mm diameter = 48 A", and "3.2 mm diameter = 62 A". In particular, "1.6 mm = 27 A" and "2.0 mm = 35 A" appear on almost every exam.

Next, the allowable currents for "stranded wires (multiple thin copper wires twisted together, specified by nominal cross-sectional area in mm²)" are: "2.0 mm² area = 27 A", "3.5 mm² = 37 A", "5.5 mm² = 49 A", "8.0 mm² = 61 A", and "14 mm² = 88 A".

The biggest exam trap here is that "2.0 mm diameter (solid wire) is 35 A", whereas "2.0 mm² cross-sectional area (stranded wire) is 27 A (the same as 1.6 mm solid wire)." Always double-check whether the unit in the question is "mm (diameter)" or "mm² (area)".

Key points


  • Allowable current of solid wires (diameter mm): 1.6 mm = 27 A, 2.0 mm = 35 A, 2.6 mm = 48 A, 3.2 mm = 62 A.

  • Allowable current of stranded wires (area mm²): 2.0 mm² = 27 A, 3.5 mm² = 37 A, 5.5 mm² = 49 A, 8.0 mm² = 61 A.

  • Confusing "2.0 mm diameter (35 A)" with "2.0 mm² cross-sectional area (27 A)" is the most common trap on the exam.
WordMeaning
allowable current (ampacity)
solid wire (diameter in mm)
stranded wire (nominal cross-sectional area in mm²)
600 V vinyl-insulated wire (IV)

Current Reduction Factor for Wires in Conduit and Allowable Current Calculation

When multiple insulated wires are bundled inside a conduit (metal or synthetic resin pipe), heat is trapped and dissipates poorly. Therefore, you must multiply the base allowable current from the previous section by a "current reduction factor (a number less than 1)".

The current reduction factors according to the number of wires placed inside the same conduit (usually given in the exam question) are: "3 wires or fewer = 0.70", "4 wires = 0.63", "5 to 6 wires = 0.56", and "7 to 15 wires = 0.49".

The formula for allowable current inside a conduit is: "Allowable current per wire = Base allowable current × Current reduction factor". Even when the reduction factor is stated in the problem, the base allowable current (27 A, 35 A, 48 A, 49 A, etc.) is never given and must be memorized.

For example, when "3 solid IV wires of 1.6 mm are placed in a conduit (reduction factor 0.70)", the allowable current is "27 A × 0.70 = 18.9 A (19 A in answer choices)". For 4 wires (0.63), it is "27 A × 0.63 = 17.01 A (17 A)".

Similarly, "3 solid 2.0 mm wires (35 A) in a conduit (0.70)" gives "35 A × 0.70 = 24.5 A (24 A)", and "4 stranded 5.5 mm² wires (49 A) in a conduit (0.63)" gives "49 A × 0.63 = 30.87 A (30 A)". Being familiar with these common products ensures fast, accurate answers.

Key points


  • Allowable current inside a conduit is calculated as "Base allowable current × Current reduction factor".

  • Standard current reduction factors: ≤ 3 wires = 0.70, 4 wires = 0.63, 5–6 wires = 0.56 (memorize as multiples of 7: 70, 63, 56).

  • Frequent calculations: 1.6 mm × 3 wires = 27 × 0.70 ≈ 19 A / 2.0 mm × 3 wires = 35 × 0.70 ≈ 24 A / 1.6 mm × 4 wires = 27 × 0.63 ≈ 17 A.

  • Example: Placing four 2.0mm wires (base allowable current 35A, reduction factor 0.63) in a conduit → Allowable current = 35 × 0.63 = 22.05A → 22A (for 5–6 wires with factor 0.56, 35 × 0.56 = 19.6A → 19A)
WordMeaning
current reduction factor
inside the same conduit
heat dissipation
maximum allowable temperature

Low-Voltage Indoor Feeder Size (IW), Breaker Rating (IB) and Tap Distance Rules

The main heavy wiring that carries power from the service entrance to distribution boards or control panels is called a "feeder (trunk line)". Question 9 asks you to find the feeder allowable current IW and feeder breaker rating IB from the total motor rated current IM and total heater/lighting current IH.

First is the minimum allowable current IW of the feeder wires. When motor load is small, "IM ≤ IH (or no motors)", simply add them: "IW ≥ IM + IH". Conversely, when "IM > IH", you must account for starting current: if IM ≤ 50 A, then "IW ≥ 1.25 × IM + IH" (if IM > 50 A, "IW ≥ 1.1 × IM + IH").

Next is the maximum rated current IB of the overcurrent breaker protecting the feeder. With no motors, "IB ≤ IW"; when motors are present, to prevent nuisance tripping during startup, the upper limit is the "smaller value satisfying both IB ≤ 3 × IM + IH and IB ≤ 2.5 × IW".

Furthermore, when tapping a smaller branch wire (allowable current Iw) from a feeder, as a general rule an overcurrent breaker must be installed "within 3 m from the tap point".

As exceptions, if the branch wire's allowable current Iw is "at least 35% (Iw ≥ 0.35 × IB)" of the feeder breaker rating IB, the distance may extend to "8 m or less"; if it is "at least 55% (Iw ≥ 0.55 × IB)", there is "no length limit (a breaker may be omitted at any distance)".

Key points


  • Feeder wire allowable current IW: If IM ≤ IH then "IW ≥ IM + IH"; if IM > IH (and IM ≤ 50 A) then "IW ≥ 1.25 × IM + IH".

  • Feeder breaker rating IB (with motors): Must not exceed the smaller of "3 × IM + IH" and "2.5 × IW".

  • Distance from feeder tap point to breaker: Principle ≤ 3 m; ≤ 8 m if Iw ≥ 0.35 IB; unlimited if Iw ≥ 0.55 IB.

  • Example: A feeder with total motor current IM = 20A and heater current IH = 10A (IM > IH) → Required allowable current IW = 1.25 × 20 + 10 = 35A or more; using a wire with IW = 35A gives max breaker rating IB = 3 × 20 + 10 = 70A (smaller than 2.5 × 35 = 87.5A)

  • Example: When feeder breaker rating IB = 60A → Branch wire allowable current for up to 8m is Iw = 0.35 × 60 = 21A or more; for unlimited distance, Iw = 0.55 × 60 = 33A or more
WordMeaning
low-voltage indoor feeder (trunk line)
overcurrent circuit breaker
starting current
tap distance limits (3 m, 8 m)

Branch Circuit Design (Combinations of Breaker Rating, Wire Size and Receptacles)

Question 10 always tests "branch circuits" running from branch breakers in the distribution board to receptacles, asking for the "correct (or incorrect) combination of breaker rating, wire thickness, and receptacle rated current" under Article 149 of the Interpretation of Technical Standards.

The overarching rule is that "the rated current of a receptacle must never exceed the branch circuit rating; use a receptacle with the same rating or one step smaller" (a 15 A branch circuit allows only 15 A receptacles).

① For a "15 A branch circuit" and a "20 A molded-case circuit breaker (MCCB) branch circuit": wires must be "1.6 mm diameter or larger", and receptacles can be "15 A (or 15 A / 20 A for the 20 A MCCB circuit)". ② For a general "20 A branch circuit" using fuses: wires must be "2.0 mm diameter or larger" and receptacles "20 A only".

③ For a "30 A branch circuit": wires must be "2.6 mm diameter or larger (or 5.5 mm² cross-section or larger)", and receptacles must be "20 A or 30 A". Wrong choices pairing a 30 A circuit with 2.0 mm wire or a 15 A receptacle are extremely common exam traps.

④ A "40 A branch circuit" requires "8.0 mm² or larger" wire and "30 A or 40 A" receptacles; ⑤ a "50 A branch circuit" requires "14 mm² or larger" wire and "40 A or 50 A" receptacles. Note that regulations place no upper limit on the number of receptacles connected to a 15 A or 20 A branch circuit.

Branch Circuit Design (Combinations of Breaker Rating, Wire Size and Receptacles)

Key points


  • 15 A circuit: wire ≥ 1.6 mm, 15 A outlet only / 20 A MCCB circuit: wire ≥ 1.6 mm, 15 A or 20 A outlets allowed.

  • 30 A branch circuit: wire "≥ 2.6 mm diameter or ≥ 5.5 mm² area", outlets "20 A or 30 A" (15 A outlets and 2.0 mm wire are prohibited).

  • 40 A branch circuit: wire "≥ 8 mm²", outlets "30 A or 40 A" / 50 A branch circuit: wire "≥ 14 mm²", outlets "40 A or 50 A".
WordMeaning
branch circuit
20 A molded-case circuit breaker branch circuit
rated current of a receptacle
Article 149 of the Interpretation of Technical Standards

Frequently Tested Points & Memory Aids

For Questions 6 and 7 on voltage drop and power loss, organize by the number of active wires: "1-phase 2-wire = ΔV is 2rI, loss is 2rI²"; "balanced 1-phase 3-wire = neutral is 0 A so ΔV is 1 wire rI, loss is 2 outer wires 2rI²"; "3-phase 3-wire = ΔV is √3rI, loss is 3 wires 3rI²".

For Question 8 on allowable current, memorize solid wires "1.6 mm = 27 A, 2.0 mm = 35 A, 2.6 mm = 48 A" and multiply by the 7-times-table reduction factors: "≤ 3 wires = 0.70, 4 wires = 0.63, 5–6 wires = 0.56". Watch out for 2.0 mm diameter (35 A) versus 2.0 mm² area (27 A).

For Question 9 feeder tap distance: remember "Principle 3 m – 35% gives 8 m – 55% gives unlimited". For Question 10 branch circuits: the #1 trap is "a 30 A circuit cannot use 2.0 mm wire or 15 A outlets (requires ≥ 2.6 mm or 5.5 mm² wire and 20 A/30 A outlets)".

Key points


  • Voltage Drop & Loss: 1-phase 2-wire (ΔV = 2rI, Pl = 2rI²) / Balanced 1-phase 3-wire (ΔV = rI, Pl = 2rI²) / 3-phase 3-wire (ΔV = √3rI, Pl = 3rI²).

  • Solid wire ampacity: 1.6 mm = 27 A, 2.0 mm = 35 A, 2.6 mm = 48 A / Stranded wire: 2.0 mm² = 27 A, 3.5 mm² = 37 A, 5.5 mm² = 49 A, 8 mm² = 61 A.

  • Conduit reduction factors: ≤ 3 wires = 0.70, 4 wires = 0.63, 5–6 wires = 0.56 (multiply by base allowable current).

  • Feeder design: If IM > IH then "IW ≥ 1.25 IM + IH", breaker "IB ≤ 3 IM + IH and ≤ 2.5 IW" / Tap distance: 3 m, 8 m at ≥ 35%, unlimited at ≥ 55%.

  • Branch circuit table: 20 A MCCB allows 1.6 mm wire & 15 A/20 A outlets / 30 A circuit requires ≥ 2.6 mm (5.5 mm²) wire & 20 A/30 A outlets only.
WordMeaning
balanced load in 1-phase 3-wire system
base allowable current (27 A, 35 A, 48 A)
current reduction factor (0.70, 0.63, 0.56)
feeder tap distance (3 m, 8 m, unlimited)

Power Distribution & Wiring Design

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