Electrical Theory & Safety

Learning Objectives

Upon completing this chapter, you will be able to:

4.Apply Ohm’s Law and the power formula to calculate voltage, current, resistance, and power in DC and AC circuits.

5.Distinguish between series, parallel, and series-parallel circuits and calculate equivalent resistance.

6.Identify the requirements for electrical safety, including lockout/tagout (LOTO), arc-flash boundaries, and personal protective equipment (PPE) as referenced by the NEC.

7.Navigate the NEC to locate grounding and bonding requirements, overcurrent protection rules, and voltage-drop calculations.

8.Recognize common exam traps related to unit conversions, circuit calculations, and code terminology.

1.1 Fundamental Electrical Quantities

The electrician’s work is governed by four core quantities: voltage (E), current (I), resistance (R), and power (P).

Voltage (E) is the electrical pressure, measured in volts (V). It is the potential difference that drives current through a circuit.

Current (I) is the flow of electrons, measured in amperes (A). In the NEC, current is often referred to as "ampacity" when discussing conductor capacity.

Resistance (R) opposes current flow, measured in ohms (Ω). Conductors have low resistance; insulators have high resistance.

Power (P) is the rate of energy consumption, measured in watts (W). In AC circuits, power is also expressed as kilovolt-amperes (kVA) for apparent power.

Ohm’s Law states that voltage equals current times resistance: E = I × R. Rearranged: I = E ÷ R and R = E ÷ I.

Power Formula: P = E × I. Combining with Ohm’s Law gives P = I² × R and P = E² ÷ R.

Practical Field Point: When troubleshooting a circuit that trips a breaker, measure voltage first, then current. A high current reading with normal voltage indicates a short or overload; low voltage with normal current indicates high resistance (e.g., loose connection).

1.2 Series, Parallel, and Combination Circuits

Series Circuits

In a series circuit, components are connected end-to-end. The same current flows through all components. Total resistance is the sum: R_total = R1 + R2 + R3 + ... . Voltage drops across each resistor add up to the source voltage.

Key rule: If one component opens, the entire circuit stops working.

Parallel Circuits

In a parallel circuit, components are connected across the same two points. Voltage is the same across each branch. Total resistance is calculated as: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... . For two resistors, the shortcut is R_total = (R1 × R2) ÷ (R1 + R2) .

Key rule: Branch currents add up to the total current. If one branch opens, the others continue to operate.

Combination Circuits

These contain both series and parallel sections. Solve by reducing parallel groups to a single equivalent resistance, then add series resistances.

Common Exam Trap: Candidates often forget that in a parallel circuit, the total resistance is always less than the smallest branch resistance. If your calculation yields a value larger than the smallest resistor, you made an error.

NEC Connection: Article 210 addresses branch circuits. A multi-wire branch circuit (shared neutral) is a parallel application where the neutral carries only the unbalanced current. This is permitted under 210.4, provided all ungrounded conductors are disconnected simultaneously.

1.3 Alternating Current (AC) and Power Factor

Most commercial and industrial installations use AC. AC voltage alternates sinusoidally. Key values:

RMS (Root Mean Square) is the effective value (what meters read). For 120 V, the RMS is 120 V.

Peak value = RMS × 1.414. For 120 V, peak is approximately 170 V.

Peak-to-peak = 2 × peak.

In AC circuits with inductive loads (motors, transformers), current lags voltage. With capacitive loads, current leads voltage. The phase angle (θ) between voltage and current determines the power factor (PF) : PF = cos θ.

True power (W) = E × I × PF (measured by a wattmeter).

Apparent power (VA) = E × I.

Reactive power (VAR) = E × I × sin θ.

NEC Connection: Article 220 requires load calculations to include the larger of the actual load or 125% of continuous loads. For motors, Article 430 requires the branch-circuit conductor ampacity to be 125% of the motor’s full-load current (FLC), which accounts for the motor’s starting current and thermal characteristics.

Practical Field Point: When measuring a motor circuit, use a clamp meter to compare the actual running current to the nameplate FLC. If the current exceeds the nameplate rating, the motor is overloaded or the voltage is low.

1.4 Grounding and Bonding

Grounding and bonding are critical for safety, ensuring that fault current has a low-impedance path to the source, which allows overcurrent devices to operate.

Grounded conductor (neutral) is the conductor intentionally connected to earth (Article 100). It is typically white or gray.

Grounding conductor (equipment grounding conductor, EGC) connects non-current-carrying metal parts to the grounded conductor or earth. It is green or bare.

Bonding is the permanent joining of metallic parts to form an electrically conductive path (Article 100).

Key NEC Sections:

Article 250 – Grounding and Bonding. This is the primary article.

250.4 – General requirements for grounding and bonding.

250.52 – Grounding electrodes (e.g., metal water pipe, concrete-encased electrode, ground rod).

250.66 – Sizing the grounding electrode conductor (GEC).

250.122 – Sizing the equipment grounding conductor based on the overcurrent device rating.

Critical Rule: The GEC is sized based on the largest ungrounded service conductor (Table 250.66), not on the load. The EGC is sized based on the overcurrent device rating (Table 250.122).

Common Exam Trap: Confusing the GEC and EGC sizing tables. The GEC uses Table 250.66; the EGC uses Table 250.122. They are not interchangeable.

Practical Field Point: When installing a subpanel, the neutral must be isolated from the enclosure (no bonding screw). The EGC and neutral are only bonded together at the first disconnecting means (service). This prevents parallel neutral paths and reduces shock hazards.

1.5 Overcurrent Protection

Overcurrent protection devices (fuses and circuit breakers) protect conductors and equipment from excessive current. The NEC defines three types:

Overload – excessive current within the normal path (e.g., motor overload).

Short circuit – unintended path with negligible impedance.

Ground fault – unintended path to ground.

Key NEC Sections:

Article 240 – Overcurrent Protection.

240.4 – Protection of conductors. This section limits the ampacity of conductors to the rating of the overcurrent device, with exceptions for motor circuits (430), transformer secondary conductors (450), and tap conductors.

240.6 – Standard ampere ratings (e.g., 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 110, 125, 150, 175, 200, 225, 250, 300, 350, 400, 450, 500, 600, 700, 800, 1000, 1200, 1600, 2000).

Conductor Protection Rule (240.4): The overcurrent device rating must not exceed the conductor’s ampacity, except for the "next size up" rule. If the ampacity does not correspond to a standard rating, you may use the next higher standard rating, provided it does not exceed 800 A and the conductor is not part of a multi-outlet branch circuit supplying receptacles.

Common Exam Trap: The "next size up" rule applies only to standard overcurrent device ratings. You cannot round up arbitrarily; you must use the next standard size.

1.6 Voltage Drop

Voltage drop is the reduction in voltage along a conductor due to resistance. Excessive voltage drop causes poor equipment performance and overheating.

NEC Reference: The NEC does not mandate a specific voltage drop for general circuits, but 210.19(A) Informational Note and 215.2(A)(1) Informational Note recommend a maximum of 3% for branch circuits and 5% total (feeders + branch circuits).

Formula for single-phase:

VD = (2 × K × I × L) ÷ Cmils

Where:

VD = voltage drop (volts)

K = resistivity of conductor (approximately 12.9 for copper, 21.2 for aluminum at 75°C)

I = current (amperes)

L = one-way length (feet)

Cmils = circular mil area of conductor (from Chapter 9, Table 8)

For three-phase, multiply by 1.732 instead of 2: VD = (1.732 × K × I × L) ÷ Cmils.

Practical Field Point: For a 120 V circuit, 3% drop equals 3.6 V. For a 240 V circuit, 3% equals 7.2 V. Use these thresholds to decide if you need to upsize the conductor.

Common Exam Trap: The length (L) in the formula is the one-way distance, not the total round-trip. The factor of 2 (or 1.732) already accounts for the return path.

1.7 Electrical Safety: Lockout/Tagout and Arc Flash

Safety is the foundation of the trade. The NEC works in conjunction with OSHA standards (29 CFR 1910.147 for LOTO, 1910.269 for electric power).

Lockout/Tagout (LOTO) : Before working on any circuit, you must:

89.Notify all affected employees.

90.Shut down the equipment using normal procedures.

91.Isolate the energy source (open the disconnecting means).

92.Apply a lock and tag to the disconnecting means.

93.Verify the circuit is de-energized using a tested voltmeter.

Arc Flash: An arc flash is a dangerous release of energy caused by an electric arc. The NEC requires equipment to be marked with warning labels (Article 110.16) indicating the arc-flash hazard.

Approach Boundaries (per NFPA 70E, not NEC, but essential knowledge):

Limited Approach Boundary – distance from exposed live parts where a shock hazard exists.

Restricted Approach Boundary – distance from exposed live parts where only qualified persons with appropriate PPE may enter.

Prohibited Approach Boundary – distance considered the same as direct contact with live parts.

PPE Categories range from 1 (low risk) to 4 (high risk). Category 4 requires an arc-rated suit with a minimum rating of 40 cal/cm².

Practical Field Point: Always verify the absence of voltage at the point of work, not just at the panel. Use a voltage tester that you have tested on a known live source immediately before and after checking the de-energized circuit.

1.8 Code Navigation: Where to Find Key Concepts

Concept	NEC Location
Definitions (grounded, bonding, etc.)	Article 100
Branch circuits	Article 210
Feeders	Article 215
Overcurrent protection	Article 240
Grounding and bonding	Article 250
Wiring methods	Articles 300–398
Conductors for general wiring	Article 310
Motors	Article 430
Transformers	Article 450
Services	Article 230
Load calculations	Article 220
Conductor properties (cmils, resistance)	Chapter 9, Table 8
Ampacity tables	Table 310.16 (copper/aluminum)
EGC sizing	Table 250.122
GEC sizing	Table 250.66
Standard overcurrent ratings	240.6(A)
Arc-flash labeling	110.16
Voltage drop (informational)	210.19(A) Note, 215.2(A)(1) Note

Exam Strategy: In the open-book exam, do not memorize tables. Instead, memorize the article numbers and table numbers. When you see a question about "sizing an equipment grounding conductor," your first action is to flip to Table 250.122, not to search the index.

1.9 Common Exam Traps and How to Avoid Them

107.Unit Confusion: The NEC uses kcmil (thousand circular mils) for large conductors. 500 kcmil is not 500,000 cmils in the same way you might think—it is 500 × 1000 cmils. Always convert correctly.

108.Temperature Ratings: Conductor ampacity is based on the insulation temperature rating (60°C, 75°C, 90°C). The 90°C column can only be used for derating, not for the final ampacity if the terminals are rated 75°C.

109.Continuous vs. Non-continuous Loads: A continuous load is one where the maximum current is expected to continue for 3 hours or more. Branch circuits must be sized at 125% of the continuous load (210.20).

110.Neutral as Current-Carrying Conductor: In a multi-wire branch circuit, the neutral is not counted as a current-carrying conductor for derating purposes if it only carries the unbalanced current (310.15(C)(1)).

111.Rounding Up: You may only round up to the next standard overcurrent device size, and only if the conductor ampacity is less than 800 A (240.4(B)).

112.Grounding Electrode vs. Equipment Ground: A ground rod (electrode) does not clear faults; it is for lightning and static dissipation. The EGC clears faults by providing a low-impedance path back to the source.

Summary

This chapter covered the essential theory and safety concepts that underpin the Texas Journeyman exam. Master the calculations for Ohm’s Law, power, and voltage drop. Understand the difference between grounding and bonding, and know exactly where to find the sizing tables in the NEC. Finally, always prioritize safety: LOTO procedures, arc-flash awareness, and verifying a zero-energy state are non-negotiable habits for a professional journeyman.

This chapter is for study purposes only and does not replace the official NEC text. Always consult the current edition of NFPA 70 for code requirements.

Electrical Theory & Safety