⚠ LEO Ops Portal — Development Draft — Not Approved for Employee Use
§00 — Safety Briefing
Safety Briefing
🏽 Yellow Risk — Theory Lesson
This is a DC theory lesson. No hands-on energized work is performed in this lesson. However, the topics covered involve real energized equipment. Read this section before proceeding.
⚠ Battery and DC Supply Hazards
Batteries and DC power supplies are always energized. Even a 12V DC battery can deliver hundreds of amperes of fault current and cause severe arc burns, fire, and eye injury.
- Lead-acid battery areas: Explosion risk from hydrogen gas accumulation — eliminate all ignition sources (sparks, flames, hot surfaces). Ensure adequate ventilation.
- Never short-circuit battery terminals — the resulting arc can vaporize metal and cause severe burns.
- Always connect and disconnect battery cables with the circuit in the OFF state.
- Wear safety glasses and appropriate PPE when working near battery banks.
⚡ VFD DC Bus Hazard
Variable Frequency Drive (VFD) DC buses can reach 600–1,200VDC. Large filter capacitors retain lethal charge for minutes after the main disconnect is opened. Never work on VFD internals without verifying stored energy has dissipated per manufacturer procedure.
✓ This Lesson — Keep It Theory
Your task right now is to understand DC principles conceptually. Hands-on measurement practice occurs only in supervised lab exercises under direct instructor guidance with appropriate PPE and de-energized verification procedures in place.
§01 — Overview
Why DC Matters in Industrial Work
Direct Current (DC) is everywhere in industrial facilities. Before you can troubleshoot a control panel, interpret a PLC wiring diagram, or read an instrument transmitter, you need to understand how DC behaves.
Where You Will Encounter DC on the Job
Battery UPS Systems
48VDC or 120VDC banks keep critical systems alive during power outages
24VDC Control Circuits
The dominant voltage for PLC I/O, solenoids, and sensors throughout industry
VFD DC Bus
AC is rectified to DC internally before inversion to variable frequency AC for motor control
4–20 mA Loops
Process instrumentation standard — pressure, temperature, level, flow transmitters
Solar PV
Panels output variable DC before inversion — present at renewable-equipped facilities
Logic Supply Rails
5V, 12V, 15V rails power microcontrollers, displays, and communication modules
What Makes DC "Direct"
In DC circuits, current flows in one direction only — it does not reverse. The source (battery, rectifier, power supply) maintains a steady polarity: one terminal is always positive, one is always negative.
💧 The Water Pipe Analogy
| Electrical Quantity | Water Analogy | Unit |
|---|
| Voltage (V) | Water pressure (PSI) | Volts (V) |
| Current (I) | Flow rate (GPM) | Amperes (A) |
| Resistance (R) | Pipe restriction / narrow section | Ohms (Ω) |
| Power (P) | Hydraulic power (PSI x GPM) | Watts (W) |
A pump creates pressure (voltage). The pressure causes water to flow (current). A narrow pipe section restricts flow (resistance). Understanding this analogy makes Ohm's Law intuitive.
This lesson establishes the mathematical and conceptual foundation that every subsequent electrical lesson builds upon. Ohm's Law and the power formulas you learn here appear on every schematic, every panel label, and every instrument data sheet you will ever read.
§02 — Learning Objectives
Learning Objectives
Upon completing this lesson, you will be able to:
-
L5-02-01
Define voltage, current, resistance, and power in DC terms and identify their units and symbols.
-
L5-02-02
Apply Ohm's Law (V = IR) to solve for any unknown quantity in a simple DC circuit given the other two values.
-
L5-02-03
Calculate power dissipation using P = VI, P = I²R, and P = V²/R, selecting the correct form based on available data.
-
L5-02-04
Identify common DC sources in industrial applications and state their typical voltage ranges and associated hazards.
-
L5-02-05
Describe the correct procedure for using a multimeter to measure DC voltage and DC current safely, including lead placement and range selection.
-
L5-02-06
Explain the difference between conventional current flow and electron flow, and identify which convention is used in industrial wiring diagrams.
§03 — Prerequisites
Prerequisites
The following lesson must be completed before beginning this lesson:
✓
Lesson 5.1 — Electrical Safety Awareness | LEO-ACE-05-001 — Must be complete and recorded
⚠ Prerequisite Enforcement
Lesson 5.1 establishes the electrical safety framework that governs all hands-on electrical work at LEO Industrial Services. DC theory without safety context creates risk. Do not skip prerequisites.
§04 — Core Concepts
The Four Electrical Quantities
All electrical analysis in DC circuits involves four fundamental quantities. Master these and Ohm's Law becomes straightforward.
V
Voltage
Unit: Volts (V) | Symbol: V or E
The electromotive force (EMF) that pushes electrical charge through a circuit. Voltage can exist across an open circuit with no current flowing — like water pressure in a closed valve. Measured in parallel (across) a component.
I
Current
Unit: Amperes (A) | Symbol: I
The rate of electrical charge flow through a conductor. One ampere equals one coulomb of charge per second. Current requires a complete circuit path. Measured in series (meter is in the current path). Analogy: water flow rate in GPM.
R
Resistance
Unit: Ohms (Ω) | Symbol: R
The opposition to current flow through a material. All conductors have resistance. Resistance increases with temperature (for metals), smaller wire gauge, and longer wire runs. Analogy: a restriction in a pipe.
P
Power
Unit: Watts (W) | Symbol: P
The rate of energy conversion. In a resistor, electrical energy converts to heat. Power = Work / Time. A 100W load consumes 100 joules of energy every second. Analogy: hydraulic power = pressure x flow rate.
Voltage — Industrial Context
| Voltage | Typical Application | Notes |
|---|
5 VDC | Logic signals, microcontrollers, USB power | TTL and CMOS logic standard |
12 VDC | Sensors, transmitters, automotive | Common in mobile equipment |
24 VDC | PLC I/O, solenoids, control circuits | Most common industrial control voltage — SELV rated |
48 VDC | Telecom, modern UPS, PoE | Increasingly common in battery systems |
120–240 VDC | Battery banks, motor field supplies | Requires full electrical PPE for live work |
600–1,200 VDC | VFD DC bus, large drives | Extremely dangerous — capacitor stored energy hazard |
Resistance — Common Values
| Component / Material | Typical Resistance | Implication |
|---|
| Copper conductor (wire) | Very low (milliohms per meter) | Good current path; some voltage drop at high current |
| Resistor (fixed) | Designed value (Ω to MΩ) | Precisely controls current in signal circuits |
| Relay coil / solenoid | Typically 20–500 Ω | Limits operating current; determines coil power |
| Wire insulation / jacket | Very high (>100 MΩ when healthy) | Low insulation resistance indicates damage or moisture |
| Human body (skin to skin) | 1 kΩ – 100 kΩ (variable) | Lower when wet; determines severity of electric shock |
| Damaged / carbonized insulation | kΩ range | Leakage path — fire and shock hazard |
Current — Common Industrial Ranges
- Microamperes to milliamperes (μA – mA): Thermocouple signals (μV range), logic signals, sensor output currents
- 4–20 mA: Process instrumentation current loop standard — the most important current range for instrumentation technicians
- 1–30 A: Control panels, solenoids, small motor starters, 24VDC power supplies
- 100–6,000 A: Motor drives, welding equipment, large battery charge/discharge currents, busbar faults
§05 — Ohm's Law
Ohm's Law
Ohm's Law is the single most important equation in electrical theory. It defines the relationship between voltage, current, and resistance in a linear conductor. Every electrical calculation you perform in the field traces back to this equation.
The Ohm's Law Triangle
Cover the quantity you want to find. The remaining two show the calculation.
Cover V → I × R | Cover I → V ÷ R | Cover R → V ÷ I
Three Forms of Ohm's Law
Worked Examples
Example 1 — Find Current
A 24VDC control circuit supplies a proximity sensor with a coil resistance of 12 Ω. What current flows through the sensor?
Given: V = 24V, R = 12 Ω
Use: I = V ÷ R
I = 24 ÷ 12
I = 2.0 A
Example 2 — Find Resistance
A DC heater strip draws 5A from a 120VDC supply. What is the heater's resistance?
Given: V = 120V, I = 5A
Use: R = V ÷ I
R = 120 ÷ 5
R = 24 Ω
Example 3 — Find Voltage
A 4.7 kΩ pull-up resistor has a current of 0.005 A (5 mA) flowing through it. What is the voltage across the resistor?
Given: R = 4,700 Ω, I = 0.005 A
Use: V = I × R
V = 0.005 × 4,700
V = 23.5 V
✓ Unit Consistency
Always convert to base units before calculating: kilohms (kΩ) → ohms (Ω), milliamps (mA) → amperes (A). Mixing prefixes without converting is the most common source of calculation errors.
Quick conversions: 1 kΩ = 1,000 Ω | 1 mA = 0.001 A | 1 μA = 0.000001 A
§06 — Power Calculations
Power Calculations
Power tells you how much energy a component is consuming or dissipating per second. Undersized components that dissipate more power than rated will overheat, fail, and potentially start fires. Always verify power ratings when selecting or replacing components.
Three Power Formulas
All three are mathematically equivalent via Ohm's Law. Choose the one that matches the data you have.
ℹ Why Three Formulas?
You do not always have a direct voltage or current reading. If you know a resistor's value and either the voltage across it or the current through it, you can calculate power without measuring the other quantity. This is essential for panel design and component sizing.
Worked Examples
Example 1 — P = V x I
A 24VDC solenoid valve draws 0.5 A when energized. How much power does it dissipate?
Given: V = 24V, I = 0.5A
P = 24 × 0.5
P = 12 W
Example 2 — P = I² x R
A current-limiting resistor has 3A flowing through its 10 Ω resistance. What power does it dissipate?
Given: I = 3A, R = 10 Ω
P = 3² × 10 = 9 × 10
P = 90 W — This requires a 90W+ rated resistor. Always verify component rating!
Example 3 — P = V² / R
A panel heater connected to a 120VDC battery bank has a resistance of 480 Ω. What is its power rating?
Given: V = 120V, R = 480 Ω
P = 120² ÷ 480 = 14,400 ÷ 480
P = 30 W
Practical Power Ratings
| Component | Typical Power Rating | Notes |
|---|
| Signal resistor (PCB) | 1/8 W – 1/4 W | Low power — logic/signal circuits only |
| Through-hole resistor (industrial) | 1/2 W – 5 W | Common in control panels |
| Wire-wound power resistor | 10 W – 100 W | Requires heatsinking or open-air mounting |
| 24VDC solenoid | 5 W – 25 W | Check coil power on nameplate |
| 24VDC relay coil | 0.5 W – 3 W | Low power — many coils per power supply |
| PLC 24VDC power supply output | 25 W – 120 W | Size for sum of all 24V loads + 25% margin |
⚠ Derating Rule
Never run a component at 100% of its rated power continuously. Standard practice: derate to 50–70% of rated power for reliable long-term operation. A "100W" resistor in continuous industrial service should not dissipate more than 50–70W.
§07 — Interactive Tool
Ohm's Law & Power Calculator
✓ Practice Problems — Try These
- A 24VDC PLC relay coil with R = 240 Ω — what current and power? (Use V and R mode)
- A 48VDC alarm solenoid draws 0.2 A — what resistance and power? (Use V and I mode)
- A current-limiting resistor R = 10 Ω carries 3A — what voltage and power? (Use I and R mode)
§08 — DC Sources
DC Sources in Industrial Applications
Understanding the source characteristics of each DC supply type is essential for safe work and correct troubleshooting. Different DC sources carry very different hazard profiles.
| Source | Typical Voltage | Application | Key Hazards / Notes |
|---|
| Lead-Acid Battery Bank |
12V, 24V, 48V |
UPS systems, emergency lighting, switchgear trip power |
High fault current (>500A possible). Hydrogen gas explosion hazard. Check electrolyte levels (flooded type). Wear face shield and acid-rated gloves. |
| Lithium Battery Bank |
48V – 400V |
Modern UPS, EV support, large-scale energy storage |
Do NOT open, puncture, or short. Thermal runaway risk. High voltage even when "discharged." Requires BMS monitoring. Call a specialist if damaged. |
| PLC 24VDC Power Supply |
24 VDC ± 10% |
Control circuit logic, PLC I/O, solenoids, sensors |
SELV (Safe Extra-Low Voltage) rated. Low shock risk at 24V. However, high fault current from some supplies can cause arc burns — treat as energized. |
| Rectified DC (VFD Internal Bus) |
600 – 1,200 VDC |
Variable Frequency Drive intermediate DC link |
EXTREMELY DANGEROUS. Large filter capacitors store lethal charge. Voltage persists for minutes after main breaker opens. Never open VFD panels until verified discharged per manufacturer procedure. |
| Solar PV Array Output |
24 – 600 VDC |
Renewable energy generation, fed to inverters |
Cannot be switched off while panels are illuminated. Requires DC-rated disconnects. Check string voltage before touching combiner box. |
| Thermocouple Output |
0 – 50 mV |
Temperature sensing at heat exchangers, furnaces, reactors |
Very low voltage — use mV range on multimeter. Easily corrupted by ground loops. Reversed TC leads show wrong temperature reading. |
| 4–20 mA Transmitter Loop |
24VDC loop supply (typical) |
Process instruments: pressure, flow, level, temperature transmitters |
Current (not voltage) is the measured quantity. Loop must be unbroken for transmitter to operate. Current loops are noise-immune over long cable runs. |
⚡ VFD Capacitor Energy Storage — Never Assume De-Energized
A 30 kW VFD with a 1,000VDC bus and 2,000 μF of capacitance stores approximately 1,000 joules of energy. Manufacturers require a minimum discharge wait time (typically 5–15 minutes) plus verification below 50V before opening the enclosure. Always follow the specific drive manufacturer's lockout procedure — never rely on waiting alone.
§09 — Multimeter Use
Multimeter Use for DC Measurements
The digital multimeter (DMM) is the technician's primary tool for DC circuit verification. Using it incorrectly can damage the meter, trip breakers, or create a fault. Follow these procedures exactly.
Measuring DC Voltage
ℹ Voltage Measurement — Parallel Connection
The voltmeter connects IN PARALLEL with the component being measured. It does NOT break the circuit. The meter has very high internal resistance (typically >1 MΩ) so it draws negligible current.
1
Set meter function to DCV (DC Volts). If the meter has manual ranges, select a range higher than the expected voltage. For 24VDC circuits, select the 200V or 600V range first. Auto-ranging meters select automatically.
2
Inspect test leads for damage — cracked insulation, bent tips, damaged banana plugs. Do not use damaged leads.
3
Insert the BLACK lead into the COM terminal. Insert the RED lead into the V / Ω terminal.
4
Touch the BLACK lead to the negative terminal or circuit ground. Touch the RED lead to the positive terminal or test point.
5
Read the display. A positive reading confirms correct polarity (RED is more positive than BLACK). A negative reading means RED is more negative — note the reversed polarity; the magnitude is still correct.
6
If on a manual range meter and the display shows OL or 1 (overload), the voltage exceeds the range. Switch to the next higher range.
Measuring DC Current
⚠ Current Measurement — Series Connection Required
Measuring current requires BREAKING the circuit and inserting the meter IN SERIES so all current flows through the meter. This is more involved than voltage measurement — plan the break point before starting.
1
Estimate the expected current. If unknown, use Ohm's Law (I = V/R) to calculate before connecting.
2
Set meter to DC Amperes. Select A for currents above ~200 mA, or mA for smaller currents. Start high and work down.
3
Move the RED lead to the A or mA terminal (NOT the voltage terminal). The COM terminal remains with the BLACK lead.
4
De-energize the circuit (or plan a live-circuit break point with appropriate PPE per your job hazard analysis).
5
BREAK the circuit at a convenient series point (e.g., open a terminal block connection). Connect the meter across this break so current flows: source → meter → load.
6
Re-energize. Read the current. After reading, de-energize before removing the meter — do not break a live current-carrying conductor while the meter is in series.
⚡ Critical Safety Rule — Never Measure Current on Voltage Mode
If the meter is set to Amperes and connected in parallel across a voltage source, the meter's low internal resistance creates a SHORT CIRCUIT through the meter. This can:
- Blow the meter's internal fuse (best case)
- Destroy the meter (common case)
- Create a dangerous arc, injure the technician, and damage equipment (worst case)
After measuring current, IMMEDIATELY move the RED lead back to the V/Ω terminal.
Multimeter Safety Rules
| Rule | Reason |
|---|
| Inspect leads before every use | Cracked insulation creates electrocution and arc flash risk |
| Start on highest range, work down | Prevents overload damage and unexpected readings |
| Never use voltage terminal for current measurement | Short circuit through meter — see danger callout above |
| Verify meter CAT rating for the circuit | CAT III 600V for most panel work; CAT IV for service entrance |
| Check meter fuse before current measurements | A blown fuse gives a zero reading — misleading open-circuit result |
| One-hand policy when possible | Prevents current path across the chest if accidental contact occurs |
§10 — Polarity
Polarity and Current Flow Conventions
Two conventions exist for describing the direction of current flow. Understanding both — and knowing which is used on your drawings — prevents wiring errors and confusion when reading different references.
Conventional Current Flow
➕ → ➖
Flows from positive terminal to negative terminal through the external circuit (outside the source). Established before electrons were discovered. Used on virtually all industrial wiring diagrams, schematics, and engineering references. The arrow on a diode symbol shows conventional current direction.
Electron Flow
➖ → ➕
Electrons (negative charge carriers) physically move from the negative terminal to the positive terminal. This is what actually happens physically. Used in semiconductor physics and some physics texts. Electrons flow toward the anode (positive terminal) inside the source.
ℹ Which Convention to Use
At LEO Industrial Services: Use conventional current flow (positive to negative). All NEC wiring diagrams, PLC schematics, relay logic diagrams, and instrument drawings use conventional current. Unless a text explicitly states otherwise, assume conventional current.
Why Polarity Matters — Practical Consequences
| Component | Reversed Polarity Result | Consequence |
|---|
| Diode (rectifier) | Blocks current instead of conducting | Circuit does not work; no damage if within PIV rating |
| Polarized capacitor (electrolytic) | Operates in reverse bias | Rapid heating, failure, possible explosion — catastrophic |
| 24VDC PLC I/O module | Reverse polarity on power input | May destroy module — some have reverse polarity protection, many do not |
| Thermocouple leads | Wrong polarity at termination | Temperature reading inverts below ambient — wrong direction |
| 4–20 mA transmitter | Reversed loop power polarity | Transmitter fails to operate; may damage output stage |
| Battery charger cables | Reversed connection to battery | High fault current, severe arc, possible battery damage or explosion |
✓ Verify Before Connecting
Always verify polarity with a multimeter before connecting DC devices. Meter convention: RED lead = positive reference. A positive reading with RED on a terminal confirms it is positive relative to your BLACK reference point.
§11 — Industrial Context
DC in Control Circuits — Industrial Context
This section shows how the DC principles in this lesson translate directly to the circuits you will encounter on the job at LEO Industrial Services.
How 24VDC Appears in PLC Systems
🔚
PLC Input Cards (Digital Input)
Field devices — pushbuttons, limit switches, proximity sensors, float switches — supply 24VDC to PLC input terminals. When the device closes (or its output transistor conducts), 24V appears on the input terminal. The PLC reads this as logic "1" (TRUE). The input card has an internal load resistor (~2–5 kΩ) that limits current to ~5–10 mA per input. Input voltage: typically 18–30VDC for a "high" state on 24V cards.
🔛
PLC Output Cards (Digital Output)
When the PLC program turns on an output, the output card applies 24VDC to the field device — relay coil, solenoid valve, indicator light, motor contactor coil. Total output current per card is limited (commonly 0.5A per point, 4–8A per card). Overloading a PLC output destroys the output transistor — always verify load current vs. output card rating.
📡
4–20 mA Current Loop
The most important analog signal standard in industrial instrumentation. A transmitter (pressure, temperature, flow, level) outputs a DC current between 4 mA and 20 mA proportional to the measured process variable. 4 mA = 0% of range, 20 mA = 100% of range. The loop supply is typically 24VDC. A 250 Ω precision resistor at the receiver converts current to a 1–5VDC voltage signal for analog input cards.
🔢
4–20 mA Percentage Calculation
To convert a measured milliamp reading to a percentage of process range:
% = (I_measured − 4 mA) ÷ (20 mA − 4 mA) × 100
Example: 12 mA reading → (12 − 4) ÷ 16 × 100 = 8 ÷ 16 × 100 = 50%
This is the exact calculation used in Assessment Question 4.
🔔
HART Signal (Highway Addressable Remote Transducer)
HART superimposes a digital communication signal (1.2 mA peak-to-peak FSK at 1200 Hz) on top of the standard 4–20 mA DC loop. The DC current level carries the primary process value; the HART signal carries device configuration, diagnostics, secondary variables, and calibration data. The average DC current is not disturbed by the HART signal, so both systems operate simultaneously. Most modern field instruments support HART.
🔋
UPS Battery Systems and Emergency Power
Uninterruptible Power Supply (UPS) systems use DC battery banks to maintain power during grid outages. The battery bank is maintained at float voltage by a rectifier. During an outage, the inverter converts battery DC to regulated AC. For critical facilities, DC battery systems also directly supply 125VDC to switchgear trip coils — allowing circuit breakers to open even when all AC power is lost.
4–20 mA Range Visualization
Interactive: slide to see current vs. percentage of process range
§12 — Assessment
Knowledge Check — 5 Questions
Select your answer and click Check. All five questions must be answered before your score is displayed.
Assessment Score
0/5
Complete all questions above to see your score.
§13 — Summary & Next Steps
Summary & Next Steps
You have completed the foundational DC principles lesson. Everything you learn in subsequent electrical lessons builds directly on these relationships.
Key Formulas — Quick Reference
V = I × R
Ohm's Law — voltage equals current times resistance. The fundamental relationship in all DC circuits.
I = V ÷ R
Current equals voltage divided by resistance. Use when troubleshooting why a device draws unexpected current.
R = V ÷ I
Resistance equals voltage divided by current. Use to identify component value from measured V and I.
P = V × I
Power from voltage and current. Most direct formula when both are available from meter readings.
P = I² × R
Power from current and resistance. Useful for I²R heating calculations in cable sizing and derating.
P = V² ÷ R
Power from voltage and resistance. Use when current is not available but voltage and resistance are known.
Key Concepts Covered
- Voltage (V) — electromotive force in Volts; exists across components; measured in parallel
- Current (I) — rate of charge flow in Amperes; requires complete circuit; measured in series
- Resistance (R) — opposition to flow in Ohms; all real conductors have resistance
- Power (P) — energy conversion rate in Watts; resistors convert electrical energy to heat
- Ohm's Law — V = IR; solve for any unknown given the other two values
- Power formulas — P = VI = I²R = V²/R; three equivalent forms for different available data
- DC sources — battery banks, 24VDC control supplies, VFD DC bus, solar PV, instrument loops
- Multimeter procedure — voltage in parallel (V/Ω terminal), current in series (A terminal, break circuit)
- Conventional vs. electron flow — conventional (+ to −) used on all industrial drawings
- 4–20 mA loops — standard industrial current signal; % = (I − 4) ÷ 16 × 100
✓ Building on This Lesson
DC principles are the gateway to understanding AC circuits, where the same quantities exist but voltage and current continuously reverse direction. The next lesson introduces sinusoidal waveforms, RMS values, frequency, and phase — all described using the same V, I, R, and P framework you have just learned.
📋 Next: Lesson 5.3 — Principles of Alternating Current (AC)
Building directly on DC foundations: sinusoidal waveforms, peak vs. RMS values, frequency and period, capacitive and inductive reactance, power factor, and three-phase power fundamentals. Estimated time: 55 minutes.
Proceed to Lesson 5.3 →
Lesson Information
Code: LEO-ACE-05-002 | Version: 1.0 | Issued: 2026-06-14 | Discipline: Electrical | Level: L1 Awareness | Module: 5 — Electrical Systems