Study guide
4.2 Electricity: Ohm's Law & Series/Parallel Circuits
NAPT Navy Advanced Programs Test 2026
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1 Introduction
About the NAPT & Navy Nuclear Field Program NFa & NFb Qualification Routes and Scoring How to Use This Guide
2 Chapter 1: Mathematics I — Arithmetic & Algebra
1.1 Arithmetic, Fractions, Decimals & Percentages 1.2 Ratios, Proportions & Unit Conversions 1.3 Algebra I: Linear Equations & Inequalities 1.4 Algebra II: Exponents, Radicals & Quadratic Equations
3 Chapter 2: Mathematics II — Geometry, Trigonometry & Word Problems
2.1 Geometry: Area, Volume & Right Triangles 2.2 Trigonometry Basics 2.3 Word Problems & Multi-Step Reasoning
4 Chapter 3: Physics I — Mechanics & Energy
3.1 Kinematics & Motion 3.2 Forces & Newton's Laws 3.3 Work, Energy & Power
5 Chapter 4: Physics II — Thermodynamics, Electricity & Waves
4.1 Thermodynamics & Heat Transfer 4.2 Electricity: Ohm's Law & Series/Parallel Circuits 4.3 Kirchhoff's Laws & Magnetism 4.4 Waves, Fluids & Pressure
6 Chapter 5: Chemistry I — Atomic Structure & Reactions
5.1 Atomic Structure & the Periodic Table 5.2 Chemical Bonding & Reactions 5.3 Stoichiometry & the Mole Concept
7 Chapter 6: Chemistry II — Gas Laws, Solutions & Thermochemistry
6.1 Gas Laws 6.2 Solutions, Acids & Bases 6.3 States of Matter & Thermochemistry
8 Chapter 7: Nuclear Science
7.1 Atomic & Nuclear Structure, Isotopes 7.2 Radioactivity, Decay & Half-Life 7.3 Nuclear Fission, Chain Reactions & Critical Mass 7.4 Reactor Basics & Radiation Safety
9 Chapter 8: Administration Boundaries & Editorial Review
8.1 Administration Boundaries & Personal Readiness 8.2 Integrated Review & Local Practice
4.2 Electricity: Ohm's Law & Series/Parallel Circuits
Key Takeaways Explain This Topic AI
Ohm's Law: V = IR (voltage equals current times resistance); rearrange to I = V/R or R = V/I to solve for any unknown quantity.
Electrical power has three equivalent formulas — P = VI = I²R = V²/R — all three give the same answer for the same circuit.
In a series circuit, current is identical everywhere and total resistance is the sum of all resistors (R_total = R1 + R2 + ...); voltage divides across each resistor.
In a parallel circuit, voltage is identical across every branch and total resistance comes from 1/R_total = 1/R1 + 1/R2 + ...; current divides among the branches.
Total resistance in a parallel circuit is always smaller than the smallest individual resistor in that circuit.
Last updated: August 2026
Editorial Scope
Ohm's law and simple series/parallel circuits are standard introductory electricity topics. They appear here as transferable STEM review, not because the Navy has published them as NAPT content or tied them to a particular rating task.
The Three Core Quantities
Voltage (V) , measured in volts, is the electrical potential difference that pushes current through a circuit — think of it as the electrical push that drives charge from one point to another.
Current (I) , measured in amperes (amps, A), is the rate of flow of electric charge through a circuit.
Resistance (R) , measured in ohms (Ω), is a material's opposition to the flow of current.
Ohm's Law ties these together: V = IR . Rearranged algebraically, this relationship also gives I = V/R and R = V/I ; all three forms are useful in the local circuit exercises.
- Quantity Symbol Unit Solve For It
- Voltage V volt (V) V = IR
- Current I ampere (A) I = V/R
- Resistance R ohm (Ω) R = V/I
Worked Example: A 12V battery is connected to a 4Ω resistor. What current flows through the circuit?
- I = V/R = 12 V ÷ 4 Ω = 3 A
- Power in Electrical Circuits
Electrical power (P), measured in watts (W), is the rate at which a circuit converts electrical energy into another form (heat, light, motion). Three equivalent formulas calculate it, and all three must give the same answer for the same circuit:
P = VI = I²R = V²/R
Worked Example: Using the circuit above (12V, 3A, 4Ω), find the power dissipated.
- P = VI = 12 V × 3 A = 36 W
- Check with P = I²R = (3 A)² × 4 Ω = 9 × 4 = 36 W ✓
Both formulas agree: the resistor dissipates 36 W .
Series Circuits
A series circuit connects components end-to-end along a single path, so current has only one route to follow. Three rules define series behavior:
- Current is identical at every point in the circuit: I_total = I1 = I2 = I3…
- Total resistance is the sum of all individual resistances: R_total = R1 + R2 + R3…
Voltage divides across each resistor in proportion to its resistance, and the individual voltage drops always add up to the source voltage.
Worked Example: A 20V battery is connected in series with two resistors, R1 = 6Ω and R2 = 4Ω. Find the total resistance, the current, and the voltage drop across each resistor.
R_total = R1 + R2 = 6 + 4 = 10 Ω I = V/R_total = 20 V ÷ 10 Ω = 2 A V1 = I × R1 = 2 A × 6 Ω = 12 V V2 = I × R2 = 2 A × 4 Ω = 8 V
Check: V1 + V2 = 12 + 8 = 20 V, matching the source voltage exactly. This check — that the voltage drops always sum to the source voltage — is a preview of Kirchhoff's Voltage Law, covered in the next section.
Parallel Circuits
A parallel circuit connects components across the same two nodes, giving current multiple paths to follow. Parallel rules are essentially the mirror image of series rules:
Voltage is identical across every branch, and equal to the source voltage.
Total current is the sum of the currents in each branch: I_total = I1 + I2 + I3…
Total resistance is found from the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3… — and total resistance is always smaller than the smallest individual resistor.
Worked Example: A 12V source is connected to two resistors in parallel, R1 = 6Ω and R2 = 3Ω. Find the total resistance and the current through each branch.
1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so R_total = 2 Ω I_total = V/R_total = 12 V ÷ 2 Ω = 6 A I1 = V/R1 = 12 V ÷ 6 Ω = 2 A I2 = V/R2 = 12 V ÷ 3 Ω = 4 A
Check: I1 + I2 = 2 + 4 = 6 A, matching the total current calculated directly.
- Property Series Circuit Parallel Circuit
- Current Same through every component Divides among branches
- Voltage Divides across components Same across every branch
- Total resistance R_total = R1 + R2 + … 1/R_total = 1/R1 + 1/R2 + … (always less than smallest resistor)
- If one path opens Entire circuit stops working Other branches keep working
Parallel wiring also illustrates why opening one branch need not interrupt every other branch.
Continue to section 4.3, where Kirchhoff's Laws generalize these same series and parallel rules to circuits with multiple loops and junctions that cannot be solved with series/parallel reduction alone.