Master Electrician Practice study guide with diagrams.
Calculations and Theory — Texas Master Electrician Exam Preparation
Learning Objectives
By the end of this chapter, you will be able to:
4.Perform voltage-drop calculations for feeders and branch circuits using the standard NEC-recognized formulas.
5.Calculate service and feeder loads for commercial and industrial occupancies, including continuous loads, demand factors, and neutral loads.
6.Apply the correct rules for sizing separately derived systems (transformers and generators), including primary and secondary protection.
7.Size conductors and overcurrent protection for motors and generators, applying the appropriate articles and tables.
8.Demonstrate an understanding of overcurrent protection coordination (selective coordination) for emergency and legally required systems.
9.Identify and apply the correct NEC tables and sections for conductor ampacity adjustments and corrections.
10.Recognize common exam traps and inspection pitfalls related to calculations.
1.1 Fundamentals of Voltage Drop
Voltage drop is not a mandatory calculation for all circuits, but it is a design requirement for the master electrician. The NEC recommends (Informational Note) that conductors be sized to limit voltage drop to 3% for branch circuits and 5% total for feeders and branch circuits combined. However, for fire pumps (Article 695) and critical operations (Article 708), voltage drop is a mandatory design criterion.
The Standard Formula (Single-Phase):
VD = 2 × K × I × D / CM
Where:
VD = Voltage drop (volts)
K = Resistance of conductor (approximately 12.9 for copper, 21.2 for aluminum at 75°C)
I = Load current (amperes)
D = One-way distance (feet)
CM = Circular mil area of the conductor (from Chapter 9, Table 8)
The Three-Phase Formula:
VD = 1.732 × K × I × D / CM
The 1.732 factor accounts for the phase-to-phase voltage relationship in a balanced three-phase system.
Master-Level Consideration: For exam purposes, you must know the difference between the one-way and round-trip distance. The formulas above use one-way distance. If you are given a round-trip distance, divide by 2 before plugging it in.
Inspection Point: On site, a master checks that the effective impedance (not just DC resistance) is considered for circuits with a power factor less than unity. For motor circuits, the power factor is typically 0.8 to 0.85 lagging. The NEC Chapter 9, Table 9 provides AC resistance and reactance values for this purpose. The formula using Table 9 data is:
VD = 1.732 × I × (R × cosθ + X × sinθ) × D (for three-phase)
Where R and X are in ohms per 1000 feet.
Exam Trap: Do not use the 12.9 K-factor for aluminum conductors. The K-factor for aluminum is 21.2. Also, remember that the K-factor changes with temperature; the 12.9 and 21.2 values are based on 75°C conductor temperature.
1.2 Services and Service Equipment (Article 230)
Service calculations are the foundation of the master's responsibility. The service must be sized for the calculated load per the optional or standard method, but the minimum service size is 100 amperes for a one-family dwelling (NEC 230.42 and 230.79). For commercial and industrial, there is no minimum, but the load calculation governs.
Standard Method (Article 220, Part III):
General lighting and receptacle loads: Table 220.12 (e.g., 3 VA/ft² for dwelling units, 3.5 VA/ft² for banks, 1.5 VA/ft² for warehouses).
Receptacle loads: 180 VA per receptacle strap (NEC 220.14(I)).
Continuous loads: Multiply by 125% (NEC 210.19(A)(1) and 215.2(A)(1)).
Demand factors: Table 220.42 for lighting, Table 220.44 for receptacles (the first 10 kVA at 100%, the remainder at 50%).
Optional Method (Article 220, Part IV):
This is only for dwelling units and some specific occupancies. The optional method allows a lower calculated load by applying a demand factor to the total connected load. The master must know when the optional method is permitted — it is not a general-purpose tool for all commercial buildings.
Neutral (Grounded Conductor) Sizing:
The neutral must be sized to carry the maximum unbalanced load. For a three-phase, four-wire system with line-to-neutral loads, the neutral current is the vector sum of the phase currents. In a perfectly balanced system, the neutral current is zero. However, for circuits with nonlinear loads (e.g., electronic ballasts, VFDs, computers), the neutral can carry triplen harmonics (3rd, 9th, 15th). Per NEC 310.15(E), the neutral must be counted as a current-carrying conductor for ampacity adjustment purposes when the load is nonlinear.
Service Disconnecting Means:
Maximum of six disconnects per service (NEC 230.71).
Each disconnect must be rated for the load it serves.
The service conductors must have an ampacity of at least the sum of the ratings of the disconnects connected to the load side (NEC 230.90(A) Exception No. 2 allows the next standard size if the calculated load is less).
Exam Trap: For a service with multiple disconnects, the service conductors are sized for the calculated load, not the sum of the disconnect ratings, provided the calculated load is less than the disconnect ratings. This is a common point of confusion.
1.3 Separately Derived Systems (Article 250.30)
A separately derived system (SDS) is a source of power with no direct electrical connection to the supply conductors from another system. Examples: a transformer secondary, a generator with a transfer switch, or a UPS.
Grounding Requirements:
The SDS must have a grounding electrode conductor (GEC) connected to a grounding electrode (NEC 250.30(A)(4)).
The GEC must be sized per Table 250.66 based on the largest ungrounded conductor of the SDS.
The system must be bonded to the equipment grounding conductor (EGC) at the source or at the first disconnecting means.
The grounded conductor (neutral) must be bonded to the equipment grounding conductor at only one point — the source or the first disconnecting means.
Transformer Sizing (Article 450):
Transformer primary and secondary conductors must be protected per Article 240.
Primary protection: If the primary overcurrent device is rated at 125% of the primary full-load current (FLC), secondary protection may not be required (NEC 450.3(B) Exception 1).
Secondary protection: If the secondary is protected at 125% of the secondary FLC, the primary protection can be up to 250% of the primary FLC (Exception 2).
Generator Sizing (Article 445):
Generators must have a nameplate rating. The ampacity of the conductors must be at least 115% of the generator's nameplate current rating (NEC 445.13).
Overcurrent protection must be provided per Article 240, and the generator's short-circuit current rating must be coordinated with the overcurrent devices.
Master-Level Consideration: For a generator used as a legally required standby system (Article 701), the transfer switch must be listed for the purpose, and the generator must be able to start and carry the connected load within 60 seconds of a power failure.
Inspection Point: On site, the master verifies that the neutral of the SDS is not bonded to the EGC at more than one location. A second bond creates a parallel path for neutral current, which is a violation of NEC 250.6 and a safety hazard.
1.4 Feeder Sizing and Conductor Ampacity (Article 310)
Feeder conductors must have an ampacity of not less than the calculated load, with continuous loads at 125% (NEC 215.2(A)(1)). However, the ampacity of a conductor is not simply the value from Table 310.16.
Adjustment and Correction Factors:
Ambient Temperature Correction (Table 310.16, Correction Factors): If the ambient temperature exceeds 30°C (86°F), the ampacity must be multiplied by the correction factor.
Conductor Bundling Adjustment (Table 310.15(B)(3)(a)): If more than three current-carrying conductors are in a raceway or cable, the ampacity must be reduced by the appropriate percentage.
Master-Level Consideration: The termination temperature rating (usually 60°C or 75°C) limits the final ampacity. You cannot use the 90°C ampacity for terminations unless the equipment is rated for 90°C terminations. However, you can use the 90°C ampacity for the adjustment and correction calculations, as long as the final value does not exceed the termination rating.
Example:
A 4/0 AWG THHN conductor (90°C) has a base ampacity of 260 A. If four current-carrying conductors are in a raceway (adjustment factor 0.80) and the ambient temperature is 40°C (correction factor 0.91), the adjusted ampacity is:
260 × 0.80 × 0.91 = 189.3 A.
However, if the terminations are rated at 75°C, the maximum ampacity is 230 A (the 75°C column). The adjusted value of 189.3 A is the governing ampacity.
Exam Trap: Do not forget to apply the adjustment factor for neutral conductors carrying nonlinear loads. A 4-wire circuit with a nonlinear load has four current-carrying conductors, not three.
1.5 Motor and Generator Applications (Article 430)
Motor calculations are a critical portion of the master exam. The key is to use the tables in Article 430, not the nameplate, for conductor sizing and overcurrent protection.
Conductor Sizing (NEC 430.22):
Single motor: Conductors must have an ampacity of at least 125% of the motor's full-load current (FLC) as listed in Tables 430.247 through 430.250.
Multiple motors: The feeder must be sized for 125% of the largest motor FLC plus the sum of the FLCs of all other motors.
Overcurrent Protection (NEC 430.52):
The motor branch-circuit short-circuit and ground-fault protective device (SCGFP) must be sized per Table 430.52.
For a standard inverse-time circuit breaker, the maximum is 250% of the FLC.
For a non-time-delay fuse, the maximum is 300% of the FLC.
If the maximum rating does not allow the motor to start, the next higher standard size is permitted (NEC 430.52(C)(1) Exception 1).
Motor Overload Protection (NEC 430.32):
The overload device must be sized at not more than 115% of the motor nameplate current rating for motors with a service factor of 1.15 or more, or a temperature rise of 40°C or less.
For all other motors, the maximum is 125% of the nameplate current rating.
Generator Applications:
The generator's FLC is based on the nameplate kVA rating, not the kW rating. For a three-phase generator:
FLC = (kVA × 1000) / (1.732 × Voltage)
Conductors must be sized at 115% of the generator's FLC (NEC 445.13).
Exam Trap: The motor nameplate current is used for overload protection, but the table FLC is used for conductor sizing and short-circuit protection. Mixing these up is a classic error.
Selective coordination is the process of ensuring that the overcurrent device closest to the fault opens first, isolating the fault without de-energizing the entire system.
Mandatory Selective Coordination:
Emergency Systems (Article 700): All overcurrent devices must be selectively coordinated.
Legally Required Standby Systems (Article 701): All overcurrent devices must be selectively coordinated.
Critical Operations Power Systems (Article 708): Selective coordination is required.
Master-Level Consideration: For non-mandatory systems, the NEC recommends selective coordination (Informational Note to 240.12), but it is not a code requirement. However, a master electrician should design for it as a best practice.
How to Achieve Coordination:
Use the time-current curves (TCCs) of the overcurrent devices.
The upstream device must have a longer clearing time at the available fault current than the downstream device.
Fuses are inherently easier to coordinate because they are current-limiting.
Circuit breakers may require adjustment of the short-time and instantaneous trip settings.
Inspection Point: On site, the master verifies that the short-circuit current rating (SCCR) of the equipment is not less than the available fault current at the point of installation. This is a common deficiency found during inspections.
1.7 Commercial and Industrial Load Calculations (Article 220)
For commercial occupancies, the standard method is used. The master must know how to apply the demand factors correctly.
Key Loads:
Sign and Outline Lighting (NEC 220.14(F)): A minimum of 1,200 VA for each required sign circuit.
Show Windows (NEC 220.14(G)): 200 VA per linear foot of show window.
Receptacles (NEC 220.14(I)): 180 VA per receptacle strap. For general-purpose receptacles in a commercial occupancy, the first 10 kVA at 100% and the remainder at 50% (Table 220.44).
Fixed Electric Space Heating (NEC 220.51): 100% of the connected load.
Kitchen Equipment (NEC 220.56): Demand factors are permitted for commercial kitchen equipment, but the master must verify that the equipment is not all used simultaneously.
Neutral Loads:
The neutral must be sized for the maximum unbalanced load.
For a three-phase, four-wire system, the neutral is not required to be larger than the largest ungrounded conductor (NEC 220.61(C)).
Exam Trap: Do not apply the 125% continuous load factor to the neutral unless the neutral is carrying nonlinear loads. The neutral is not a continuous load in the same sense as the phase conductors.
Article 220, Part III (Standard), Part IV (Optional)
Service Disconnects
Article 230, Part VI
Grounding of SDS
250.30
Transformer Protection
Article 450, Part I
Generator Sizing
Article 445
Motor Conductors
430.22
Motor Overload
430.32
Motor SCGFP
430.52, Table 430.52
Motor FLC Tables
Tables 430.247–430.250
Selective Coordination
700.32, 701.27, 708.54
Receptacle Loads
220.14(I)
Lighting Loads
Table 220.12
Neutral Sizing
220.61
1.9 Common Exam Traps and Supervision Points
Exam Traps:
131.Using nameplate current for conductor sizing — always use the table FLC.
132.Forgetting the 125% factor for continuous loads or the largest motor.
133.Applying adjustment factors to the 90°C column and then exceeding the 75°C termination rating.
134.Sizing the neutral for the full phase current in a balanced three-phase system without considering nonlinear loads.
135.Using the single-phase voltage drop formula for a three-phase circuit.
136.Forgetting that the GEC for an SDS is sized from Table 250.66, not from the primary overcurrent device.
Supervision Points (What a Master Checks On Site):
Verify that the neutral is bonded to the EGC at the service or SDS source only.
Check that all terminations are torqued to the manufacturer's specifications.
Confirm that the available fault current is marked on the equipment and does not exceed the SCCR.
Ensure that the grounding electrode conductor is continuous and properly connected to the electrode.
Verify that the motor overloads are sized per the nameplate, not the table.
Confirm that the feeder conductors are not derated due to bundling without proper adjustment.
Summary
This chapter has covered the core calculation and theory topics required for the Texas Master Electrician exam. The master electrician is not just a technician; they are the person responsible for the design and safety of the installation. Mastery of these calculations — voltage drop, service sizing, SDS grounding, motor applications, and coordination — is what separates the master from the journeyman. Always navigate to the specific NEC article and table during the exam, and always verify your work against the code's minimum requirements.
Preparing for the Texas Master Electrician license?
See the full licensing path, exam format, eligibility and application steps.
