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NEETS Module 1 — Chapter 3

Direct Current  ·  NAVEDTRA 14173

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Chapter 3: Direct Current

Ohm’s law, power, series and parallel circuits, Kirchhoff’s laws, voltage dividers, and electrical safety — the circuit math every technician uses.

Course Duration: 60–75 minutes

📚 Source: NEETS Module 1 (NAVEDTRA 14173)
🎯 Pass Score: 80% (16 of 20)
📝 Final Questions: 20

🎓 LEARNING OBJECTIVES

  • Identify circuit components from a schematic diagram
  • State Ohm’s Law and apply it to solve for E, I, and R
  • State and apply the three formulas for electrical power
  • Solve series circuits and apply Kirchhoff’s Voltage Law
  • Identify open and short circuits; explain source resistance and maximum power transfer
  • Solve parallel circuits with equivalent-resistance methods and Kirchhoff’s Current Law
  • Analyze combination (series-parallel) circuits
  • Compute voltage divider values
  • Describe electrical shock hazards and current first aid for shock victims

🛈 HOW THIS COURSE WORKS

  • Six sections, each ending with a knowledge check. You get two attempts, and a first miss gives you a hint rather than the answer. Answering unlocks the next section.
  • Then a 20-question final assessment, different from the knowledge checks.
  • When you submit, your results are emailed automatically to the training administrator and to you, whether or not you pass.
1

Basic Circuits, Ohm's Law & Power

A basic electric circuit contains three elements: a source (furnishes electrical energy), a load (device that converts electrical energy to another form), and a switch (controls current delivery). The schematic diagram is a "picture" of a circuit using standardized symbols — the technician's primary aid for troubleshooting.

Ohm's Law

Current in a circuit is DIRECTLY proportional to applied voltage and INVERSELY proportional to circuit resistance. Doubling the voltage doubles the current; doubling the resistance halves the current. (This holds for ordinary resistors at a steady temperature. Some devices, like lamp filaments and diodes, don’t follow it exactly.)

FIND CURRENT
I = E / R
Amps = Volts ÷ Ohms
FIND VOLTAGE
E = I × R
Volts = Amps × Ohms
FIND RESISTANCE
R = E / I
Ohms = Volts ÷ Amps

GRAPHICAL ANALYSIS

When resistance is held constant and voltage is varied, current changes linearly — a straight-line graph (volt-ampere characteristic). When voltage is held constant and resistance is varied, current varies inversely — a curved graph. Both relationships illustrate Ohm's Law visually.

Power (P)

The instantaneous RATE at which work is done. Basic unit: the WATT. Power in watts equals voltage times current. Three equivalent power formulas allow calculation from any two of the four quantities (E, I, R, P).

POWER — BASIC
P = E × I
Watts = Volts × Amps
POWER — VOLTAGE/R
P = E² / R
Power varies as square of voltage
POWER — CURRENT/R
P = I² × R
Power varies as square of current

POWER RATING & EFFICIENCY

  • Resistors have wattage ratings; NEETS applies a 50% safety factor (e.g., a resistor that normally dissipates 2W gets a 3W-rated part)
  • Carbon resistors: 1/8, 1/4, 1/2, 1, 2 W — larger physical size = higher wattage rating
  • Wirewound resistors: 5–200 W; special types handle more than 200 W
  • Efficiency = Power converted to useful energy ÷ Power consumed. Always less than 1.00 due to losses. Example: 0.95 efficiency = 95 W useful output per 100 W input
  • 1 horsepower = 746 watts

🧪 Section 1 Knowledge Check

A 12-volt circuit draws 2 amperes. How much power does it use?

Attempts: 0/2
2

Series Circuits & Kirchhoff's Voltage Law

A series circuit contains only ONE path for current flow. All components are connected end-to-end; current must pass through every component.

FIVE RULES FOR SERIES DC CIRCUITS

  • The same current flows through EACH PART of a series circuit.
  • Total resistance = SUM of individual resistances: RT = R₁ + R₂ + R₃ + … Rₙ
  • Total voltage = SUM of individual voltage drops: ET = E₁ + E₂ + E₃ + … Eₙ
  • Voltage drop across a resistor is PROPORTIONAL to its ohmic value (larger resistance → larger drop).
  • Total power = SUM of individual powers: PT = P₁ + P₂ + P₃ + … Pₙ
Kirchhoff's Voltage Law (KVL)

"The algebraic sum of the voltage drops in any closed path in a circuit and the electromotive forces in that path is equal to zero." In practice: the sum of all voltage sources equals the sum of all voltage drops. Use assumed current direction to assign polarities; a negative result means the assumed direction was wrong (not that the answer is wrong).

APPLYING KVL — PROCEDURE

  • Assume a direction of current through the circuit
  • Assign polarities to all resistors based on assumed current direction
  • Place correct polarities on all voltage sources
  • Trace the closed loop; record voltage and polarity of each component in succession
  • Set the sum equal to zero and solve for the unknown
  • A negative result for current means the assumed direction was opposite to actual flow

SERIES AIDING vs. OPPOSING SOURCES

Series aiding: Sources driving current in the same direction — voltages ADD. Series opposing: Sources driving current in opposite directions — effective voltage is the DIFFERENCE; current flows in the direction of the larger source.

🧪 Section 2 Knowledge Check

A 12-volt and a 9-volt source are connected series OPPOSING. What is the effective voltage, and which way does current flow?

Attempts: 0/2
3

Reference Points, Open & Short Circuits, Source Resistance

Reference Point (Ground)

An arbitrarily chosen point to which all other circuit points are compared. The reference point is always considered to be at ZERO potential. By convention, earth ground is treated as zero potential. In electronics, the common chassis or circuit “ground” serves as the reference even when it isn’t connected to earth. Moving the reference point changes the apparent polarity of other points but does NOT change actual circuit voltages or currents. Provides both positive AND negative voltages from a single source.

🔓
Open Circuit

A BREAK in the conducting path. No current flows. RT = ∞. The full source voltage appears across the open. Can be caused by blown fuses, broken wires, or burned-out resistors.

⚡
Short Circuit

An accidental path of near-ZERO resistance. Current increases drastically. Usually caused by improper wiring or broken insulation. Can destroy components and cause fires.

Source Resistance (Internal Resistance, Ri)

All voltage sources have some internal resistance that causes the terminal voltage to DROP when current flows. The battery voltage measured with no load is higher than when supplying current. Internal resistance can’t be measured directly with an ohmmeter, but you can calculate it: Ri = (no-load voltage − loaded voltage) ÷ load current. A rising internal resistance is a sign of a worn-out battery. It is represented in a schematic as a small resistor in series with an ideal battery.

MAXIMUM POWER TRANSFER & EFFICIENCY

  • Maximum power transfer occurs when the load resistance EQUALS the internal (source) resistance
  • At maximum power transfer, efficiency is exactly 50% — half the power is lost in the source
  • High efficiency is achieved when load resistance is MUCH LARGER than source resistance (most power goes to the load, less is wasted internally)
  • Practical compromise: communications circuits favor max power transfer; power systems favor high efficiency

🧪 Section 3 Knowledge Check

A battery reads 12.6 V with no load and 12.0 V while supplying 2 A. What is its internal resistance?

Attempts: 0/2
4

Parallel Circuits & Kirchhoff's Current Law

A parallel circuit has MORE THAN ONE current path connected to a common voltage source. Each separate current path is called a branch. Two or more branches form a network.

FIVE RULES FOR PARALLEL DC CIRCUITS

  • The SAME VOLTAGE appears across each branch — equal to source voltage.
  • Branch current is INVERSELY PROPORTIONAL to branch resistance (more resistance → less current).
  • Total current = SUM of individual branch currents: IT = I₁ + I₂ + … Iₙ
  • Equivalent resistance is always LESS than the smallest individual branch resistance.
  • Total power = SUM of individual branch power consumptions.
Kirchhoff's Current Law (KCL)

"The algebraic sum of the currents entering and leaving any junction is equal to zero." Currents ENTERING a junction are POSITIVE; currents LEAVING are NEGATIVE. The total of all currents at any junction must sum to zero.

THREE METHODS FOR EQUIVALENT RESISTANCE

  • Equal resistors: Req = R ÷ N (resistance value divided by the number of equal resistors)
  • Reciprocal method (general formula): 1/Req = 1/R₁ + 1/R₂ + 1/R₃ + … (find common denominator; take the reciprocal of the result)
  • Product-over-sum (two resistors only): Req = (R₁ × R₂) ÷ (R₁ + R₂)

EQUIVALENT CIRCUIT

Any complex resistor network can be reduced to a single equivalent resistor representing total resistance. This process — called reduction to an equivalent circuit — simplifies analysis. The equivalent circuit contains the voltage source and a single resistor (Req).

🧪 Section 4 Knowledge Check

Two resistors, 20 Ω and 30 Ω, are connected in parallel. Using the product-over-sum method, what is the equivalent resistance?

Attempts: 0/2
5

Combination Circuits, Opens & Shorts in Parallel Networks

A combination (series-parallel) circuit contains both series and parallel elements. Solving it uses equivalent circuits: reduce parallel sections to a single equivalent resistor, redraw as a series circuit, then apply series-circuit rules.

SOLVING COMBINATION CIRCUITS — PROCEDURE

  • Identify all parallel branches and calculate their equivalent resistance
  • Redraw the circuit — replace each parallel network with its equivalent resistor
  • Calculate total resistance of the resulting series circuit
  • Find total current using Ohm's Law (IT = ES / RT)
  • Find voltage drops across each element using the series-circuit rules
  • Use branch voltages to find individual branch currents and power

REDRAWING CIRCUITS FOR CLARITY

Complex schematics are rarely drawn in neat box form. To simplify: trace current paths; label junctions (A, B, C…); recognize that wires have NO resistance and any unbroken wire is at the same potential; "stretch" or "shrink" wires as needed; redraw in stages into a standard box form.

🔓
Open in a Parallel Branch

That branch is disabled. Current still flows through remaining branches. RT INCREASES. IT DECREASES.

🔓
Open in a Series Portion

No current flows anywhere. The entire circuit is disabled. RT = ∞.

⚡
Short in a Parallel Branch

The shorted branch routes all current around the other parallel resistors — entire parallel network is disabled. RT DECREASES. IT INCREASES dramatically.

⚡
Short in a Series Portion

That resistance drops to zero. Total resistance decreases. Current increases. Remaining components carry the higher current and may be damaged.

CIRCUIT PROTECTION

Fuses and circuit breakers are connected in SERIES to protect circuits. When current exceeds a set value, the device opens and stops all current flow. Replace a fuse only with one of the same type and rating, and find the cause before resetting a breaker. Covers for fuse boxes and junction boxes must be kept closed. Only authorized personnel should service electrical equipment.

🧪 Section 5 Knowledge Check

In a series-parallel circuit, one branch of the parallel network shorts. What happens to that parallel network?

Attempts: 0/2
6

Voltage Dividers & Electrical Safety

Voltage Divider

Two or more resistors in series across a source voltage, used to supply multiple voltage levels from a single source. Any desired portion of the source voltage can be "tapped off." Source voltage must be as high or higher than any voltage required by the divider.

VOLTAGE DIVIDER DESIGN STEPS

  • Determine load voltage and current requirements and available source voltage
  • Select bleeder current using the 10% rule-of-thumb: bleeder current ≈ 10% of TOTAL load current (the current that flows through the divider resistors without going to any load)
  • Calculate bleeder resistor value: R₁ = Eload1 / Ibleeder
  • Calculate total current = load current + bleeder current
  • Calculate remaining divider resistors from the current through them and the voltage across them

POSITIVE AND NEGATIVE VOLTAGES FROM ONE SOURCE

By placing the ground (reference point) between two of the divider resistors, a single voltage source can supply both positive and negative voltages. Points above ground are positive; points below ground are negative. The exact placement of ground depends on the voltage requirements of the loads.

PRACTICAL NOTE

Calculated divider resistor values often don't come out to standard values. The bleeder resistor can be rounded to the nearest standard value; the actual bleeder current must then be recalculated. Series, parallel, or series-parallel resistor networks can be used to construct non-standard values.

Electrical Safety — Shock Hazard: Current, not voltage, is the measure of shock intensity. Even very small currents through vital body parts can cause death.

Current (60 Hz AC, 1 second, hand to foot)Effect on Human Body (OSHA)
1 mAPerception level — slight tingling. Still dangerous under some conditions.
5 mASlight shock; not painful but disturbing. Average person can let go.
6–16 mAPainful; loss of muscle control begins — the “let-go” range
17–99 mAExtreme pain, respiratory arrest, severe muscle contractions; can’t let go. Death is possible.
100–2,000 mAVentricular fibrillation — death is likely
Over 2,000 mACardiac arrest, internal organ damage, severe burns — death is probable

NEETS summarizes these as about 1 mA felt, 10 mA can’t let go, and 100 mA for one second fatal. The OSHA ranges above show the same pattern in more detail.

⚠ CRITICAL SAFETY FACTS

  • NEETS notes fatalities from voltages as LOW as 30 volts — it’s the current through the body that kills
  • Body resistance drops sharply when skin is wet: OSHA cites about 100,000 Ω dry but about 1,000 Ω wet. At 120V, that’s 120 mA — enough to cause ventricular fibrillation. Broken skin lowers it further.
  • ALL live electric circuits must be treated as potential hazards at ALL times
  • On the job: contact with grounded metal (conduit, racks, ceiling grid, ladders), wet locations, and perspiration all lower body resistance — extra caution required (NEETS gives the shipboard example)
  • For electrical fires, de-energize the circuit if you can, then use a CO₂ (or other Class C-rated) extinguisher — nonconductive, least equipment damage. Never use water on energized equipment.
  • Do NOT attempt repairs if not qualified; report suspected malfunctions immediately

FIRST AID FOR ELECTRIC SHOCK

  • First, protect yourself: Shut off the power if you can. If you can’t, free the victim using dry, nonconductive material (a dry board, belt, or rope). DO NOT touch the victim until they’re clear of the source.
  • Call for help: Call 911 (or your site’s emergency number) and have someone bring an AED.
  • Check: Tap and shout. Look at the chest for normal breathing for no more than about 10 seconds. (NEETS’s older method was to feel the lower ribs.)
  • If not breathing normally: Start CPR immediately — hard, fast chest compressions in the center of the chest. Use the AED as soon as it arrives and follow its prompts.
  • Time is critical: For every minute without CPR and defibrillation, the chance of surviving cardiac arrest drops by roughly 7–10%. (NEETS cited 7 of 10 shock victims revived when artificial respiration began within 3 minutes.) Get CPR/AED training from the Red Cross or American Heart Association.

🧪 Section 6 Knowledge Check

A coworker is still in contact with an energized conductor. What do you do before touching them?

Attempts: 0/2

📋 Final Assessment

Answer all 20 questions, then submit. A score of 80% (16/20) or higher is required to pass. These questions are different from the section knowledge checks.

1. A schematic diagram uses symbols to represent circuit components primarily to:

2. According to Ohm's Law, if the voltage across a resistor is doubled and the resistance stays the same, the current will:

3. A 24-volt source is connected across an unknown resistor and 3 amperes flows. What is the resistance?

4. Which of the following is NOT one of the three basic power formulas?

5. A resistor dissipates 2 watts in normal operation. Applying the NEETS 50% safety factor, what is the minimum power rating to use?

6. In a series circuit with 5 Ω, 10 Ω, and 15 Ω resistors, which has the LARGEST voltage drop?

7. What is the total resistance of 20 Ω, 30 Ω, and 50 Ω resistors connected in series?

8. Kirchhoff's Voltage Law states that the algebraic sum of the EMFs and voltage drops around any closed loop equals:

9. The reference (ground) point in a circuit is considered to be at:

10. An open circuit has what resistance?

11. Maximum power is transferred from a source to a load when:

12. In a parallel circuit, the voltage across each branch is:

13. Three 60 Ω resistors are connected in parallel. What is the equivalent resistance?

14. Kirchhoff's Current Law states that, counting currents entering a junction as positive and leaving as negative, their algebraic sum equals:

15. When one PARALLEL BRANCH opens, what happens to total resistance and total current?

16. Combination (series-parallel) circuits are solved by:

17. The bleeder current in a voltage divider is the current that flows:

18. To get both positive and negative voltages from a single DC source with a voltage divider, you:

19. At about what current does a one-second, 60 Hz shock reach the range where ventricular fibrillation (and likely death) occurs?

20. A coworker who was shocked is now clear of the source, unresponsive, and not breathing normally. What should you do?

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