589  Electricity Fundamentals: Introduction

589.1 Learning Objectives

By the end of this section, you will be able to:

  • Explain Electrical Basics: Understand current, voltage, and resistance
  • Apply Ohm’s Law: Calculate voltage, current, resistance, and power
  • Read Circuit Diagrams: Interpret schematic symbols and connections
  • Understand Components: Differentiate between resistors, capacitors, and inductors
  • Design Simple Circuits: Apply electrical principles to IoT hardware

589.2 Prerequisites

Before diving into this chapter, you should be familiar with:

  • Basic Physics Concepts: Understanding atoms, electrons, and the concept of electric charge is helpful for grasping how electricity works at the fundamental level
  • Basic Mathematics: Familiarity with algebra and working with equations (solving for variables) is essential for applying Ohm’s Law and power calculations
  • IoT Reference Models: Basic awareness of IoT system architecture helps you understand where electrical principles apply in the hardware and device layer

589.3 For Kids: Electricity is Like Magic Water!

Imagine tiny invisible water drops flowing through wires!

589.3.1 The Magic River Inside Wires

Electricity is like a river of teeny-tiny invisible drops called electrons. They flow through wires like water flows through pipes!

Here’s a fun way to understand it:

Water World Electricity World
Water in a tank Batteries or power outlets
Water pipes Wires
Water pump pushing hard Voltage (how hard electrons push)
How much water flows Current (how many electrons flow)
A narrow part of the pipe Resistance (makes it harder to flow)

589.3.2 A Story About Light Bulb Village

Once upon a time, there was a village called Light Bulb Village. The villagers needed energy to glow! There was a magical mountain called Battery Mountain that pushed tiny glowing particles called electrons down through wire rivers to the village.

When Battery Mountain pushed really hard (high voltage), lots of electrons flowed and the light bulbs glowed super bright! When it pushed gently (low voltage), fewer electrons flowed and the bulbs were dimmer.

Some wire rivers were wide and smooth - electrons loved flowing through those! But some were narrow and bumpy (high resistance) - electrons had a harder time getting through.

589.3.3 Try This at Home!

Make a “Circuit” With Your Friends: 1. Stand in a circle holding hands 2. One person is the “Battery” - they squeeze the hand of the person next to them 3. That person passes the squeeze to the next person 4. The squeeze goes around the circle and back to the battery!

That’s how electricity works! The squeeze is like voltage, and it flows all the way around (a circle = a circuit).

589.3.4 Why Do IoT Devices Need Electricity?

Every smart device needs electricity to: - Think (the brain chip needs power) - Talk (sending messages uses energy) - Feel (sensors need a tiny bit of power) - Remember (saving information takes power)

That’s why batteries are so important for sensors that aren’t plugged in!

589.3.5 Key Words for Kids

Word What It Means
Electricity Invisible energy that flows through wires
Electron A teeny-tiny particle that carries electricity
Battery A container that stores electrical energy
Wire A path for electricity to flow through
Circuit A complete loop that electricity can flow around
Voltage How hard electricity is pushed (like water pressure)

589.3.6 Fun Fact!

Did you know? A single AA battery pushes electricity with 1.5 volts - just enough to make a small LED glow! But the outlet in your wall pushes with 120 volts (in the US) or 230 volts (in Europe) - that’s why we never touch outlets!

Electricity is like a river of invisible energy that flows through wires to power everything!

589.3.7 The Sensor Squad Adventure: The Magical Power River

One sunny morning, Sammy the Sensor woke up feeling very weak. “I can’t sense anything today!” Sammy said sadly. Bella the Battery hurried over with her shiny silver jacket. “Don’t worry, Sammy! I’ll share my magical energy river with you!”

Bella explained how she stores tiny invisible workers called electrons inside her. “When I connect to the wire, the electrons flow like a river from me, through the wire, through you, and back to me in a big circle!” Max the Microcontroller drew a picture: “See? The electrons go around and around in a loop - that’s called a circuit! If the circle is broken anywhere, the river stops flowing.”

Lila the LED started glowing brightly. “The electrons flowing through me make me light up! But if too many come at once, I get too hot!” Bella nodded wisely. “That’s why we use resistors - they’re like narrow parts of the pipe that slow down the electron river so nobody gets hurt.” Thanks to Bella’s energy river, Sammy could sense temperature again, Lila could glow safely, and Max could think and make decisions. The Sensor Squad was powered up and ready for action!

589.3.8 Key Words for Kids

Word What It Means
Electricity Invisible energy that flows through wires like water through pipes
Battery A container that stores electrical energy until you need it
Circuit A complete loop path for electricity to flow around
Voltage How hard the electricity is being pushed (like water pressure)
Current How much electricity is flowing (like how much water comes out)
Resistor A part that slows down electricity so things don’t get too hot

589.3.9 Try This at Home!

Build a Human Circuit!

  1. Gather 4-6 friends or family members
  2. Stand in a circle and hold hands
  3. One person is the “Battery” - they squeeze the hand of the person next to them
  4. Each person passes the squeeze to the next person around the circle
  5. The squeeze travels all the way around back to the battery!

What you learned: The squeeze is like voltage (the push), and it travels around the circuit (the circle of people). If anyone lets go of hands, the circuit is broken and the squeeze can’t travel anymore - just like electricity!

589.4 🌱 Getting Started (For Beginners)

Tip👋 New to Electricity? Start Here!

If terms like “voltage,” “current,” or “Ohm’s Law” sound intimidating, this section will make them crystal clear with everyday analogies.

589.4.1 Understanding Electricity: The Water Analogy

The easiest way to understand electricity is to think of it like water flowing through pipes:

%% fig-alt: "Water-electricity analogy diagram comparing water pressure to voltage, water flow to current, and pipe restriction to resistance"
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graph LR
    subgraph Water["Water System"]
        A["Water Tank<br/>(Pressure)"] -->|Flow Rate| B["Narrow Pipe<br/>(Restriction)"]
        B --> C["Water Output"]
    end

    subgraph Electrical["Electrical System"]
        D["Battery<br/>(Voltage)"] -->|Current| E["Resistor<br/>(Resistance)"]
        E --> F["LED Output"]
    end

    style Water fill:#E3F2FD,stroke:#2C3E50,stroke-width:2px
    style Electrical fill:#E8F5E9,stroke:#2C3E50,stroke-width:2px
    style A fill:#16A085,stroke:#2C3E50,stroke-width:2px,color:#fff
    style D fill:#16A085,stroke:#2C3E50,stroke-width:2px,color:#fff
    style B fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style E fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff

Figure 589.1: Water-electricity analogy diagram comparing water pressure to voltage, water flow to current, and pipe restriction to resistance

This decision tree variant helps you calculate and manage power consumption for battery-powered IoT devices - a critical practical application of electrical concepts.

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flowchart TD
    START([Battery Capacity<br/>e.g., 1000mAh]) --> Q1{Sleep Current?}

    Q1 -->|"<10µA (good)"| SLEEP_LOW["Deep Sleep Mode<br/>Mostly sleeping"]
    Q1 -->|">100µA (bad)"| SLEEP_HIGH["Light Sleep<br/>Battery drains faster"]

    SLEEP_LOW --> Q2{Active Current?}
    SLEEP_HIGH --> Q2

    Q2 -->|"ESP32: ~80mA"| ACTIVE["Active Time<br/>per cycle"]
    Q2 -->|"Wi-Fi TX: ~200mA"| ACTIVE

    ACTIVE --> CALC["Calculate:<br/>Avg = Sleep×T_sleep + Active×T_active"]

    CALC --> LIFE["Battery Life =<br/>Capacity ÷ Avg Current"]

    LIFE --> EX1["Example: 1000mAh<br/>10µA sleep, 80mA×1s/hour<br/>≈ 3.5 years!"]
    LIFE --> EX2["Example: 1000mAh<br/>100µA sleep, 200mA×10s/min<br/>≈ 5 days"]

    style START fill:#16A085,stroke:#2C3E50,color:#fff
    style SLEEP_LOW fill:#16A085,stroke:#2C3E50,color:#fff
    style SLEEP_HIGH fill:#E67E22,stroke:#2C3E50,color:#fff
    style CALC fill:#2C3E50,stroke:#16A085,color:#fff
    style EX1 fill:#16A085,stroke:#2C3E50,color:#fff
    style EX2 fill:#E67E22,stroke:#2C3E50,color:#fff

Figure 589.2: Practical application of Ohm’s Law for IoT: Power (P=V×I) determines battery life. The key insight is that sleep current (µA range) and duty cycle matter more than peak current. An ESP32 drawing 80mA continuously lasts only 12 hours, but sleeping 99% of the time extends to years.

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flowchart TB
    subgraph cause["CAUSE (Energy Source)"]
        V["VOLTAGE (V)<br/>Electrical Pressure<br/>Volts"]
    end

    subgraph resistance["OPPOSITION"]
        R["RESISTANCE (R)<br/>Restricts Flow<br/>Ohms (Ω)"]
    end

    subgraph effect["EFFECT (What Flows)"]
        I["CURRENT (I)<br/>Electron Flow<br/>Amps (A)"]
    end

    subgraph result["RESULT (Work Done)"]
        P["POWER (P)<br/>Energy Used<br/>Watts (W)"]
    end

    V -->|"pushes against"| R
    R -->|"limits"| I
    V -->|"V × I ="| P
    I -->|"I × R = V"| V

    style cause fill:#E8F5E9,stroke:#16A085
    style resistance fill:#FFF3E0,stroke:#E67E22
    style effect fill:#E3F2FD,stroke:#2C3E50
    style result fill:#FCE4EC,stroke:#9B59B6

Figure 589.3: Cause-and-effect view: Voltage (electrical pressure) is the CAUSE that pushes electrons. Resistance OPPOSES the flow. Current is the EFFECT (actual electron movement). Power is the RESULT (energy consumed). Understanding this hierarchy helps you troubleshoot: no current? Check voltage source first, then resistance path.

{fig-alt=“Electrical circuit diagram showing”Water System”, “Water Tank (Pressure)”, “Narrow Pipe (Restriction)” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}

Water Concept Electrical Equivalent Unit What It Means
Water pressure Voltage (V) Volts How hard electrons are “pushed”
Water flow rate Current (I) Amps How many electrons flow per second
Pipe narrowness Resistance (R) Ohms How much the flow is restricted

589.4.2 The Three Key Relationships

1. Higher pressure → More flow (Higher voltage → More current)

Low Voltage (3.3V)     High Voltage (12V)
    ─ ─ ─ → →           ═══════════→ → →
    Dim LED              Bright LED

2. Narrower pipe → Less flow (Higher resistance → Less current)

Low Resistance (100Ω)    High Resistance (10kΩ)
    ══════════→ → →        ─ ─ ─ →
    Bright LED             Dim LED

3. Ohm’s Law: V = I × R (The fundamental equation!)

%% fig-alt: "Ohm's Law triangle showing the relationship between Voltage (V), Current (I), and Resistance (R) with formulas V=I×R, I=V/R, and R=V/I"
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graph TD
    V["V<br/>Voltage (Volts)"]
    I["I<br/>Current (Amps)"]
    R["R<br/>Resistance (Ohms)"]

    V -->|"V = I × R"| IR["I × R"]
    I -->|"I = V / R"| VR["V / R"]
    R -->|"R = V / I"| VI["V / I"]

    style V fill:#16A085,stroke:#2C3E50,stroke-width:3px,color:#fff
    style I fill:#E67E22,stroke:#2C3E50,stroke-width:3px,color:#fff
    style R fill:#2C3E50,stroke:#16A085,stroke-width:3px,color:#fff
    style IR fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style VR fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style VI fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px

Figure 589.4: Ohm’s Law triangle showing the relationship between Voltage (V), Current (I), and Resistance (R) with formulas V=I×R, I=V/R, and R=V/I

{fig-alt=“Electrical circuit diagram showing”V Voltage (Volts)“,”I Current (Amps)“,”R Resistance (Ohms)” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}

589.4.3 Real-World IoT Example: LED Circuit

You want to light an LED with an Arduino (5V output). LEDs typically need 2V and 20mA.

%% fig-alt: "LED circuit diagram showing 5V Arduino output, current-limiting resistor calculation, and LED with voltage drop, demonstrating practical application of Ohm's Law"
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graph LR
    A["Arduino Pin<br/>5V"] -->|Current: 20mA| B["Resistor<br/>150Ω"]
    B --> C["LED<br/>Forward: 2V"]
    C --> D["Ground<br/>0V"]

    E["Calculation:<br/>R = (Vsupply - VLED) / I<br/>R = (5V - 2V) / 0.02A<br/>R = 150Ω"]

    style A fill:#16A085,stroke:#2C3E50,stroke-width:2px,color:#fff
    style B fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style C fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style D fill:#7F8C8D,stroke:#2C3E50,stroke-width:2px,color:#fff
    style E fill:#FFF9C4,stroke:#E67E22,stroke-width:2px,color:#000

Figure 589.5: LED circuit diagram showing 5V Arduino output, current-limiting resistor calculation, and LED with voltage drop, demonstrating practical applicatio…

{fig-alt=“Electrical circuit diagram showing”Arduino Pin 5V”, “Resistor 150Ω”, “LED Forward: 2V” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}

589.4.4 Self-Check: Understanding the Basics

Before continuing, make sure you can answer:

  1. If voltage increases, what happens to current? → Current increases (assuming resistance stays same)
  2. What does resistance do? → Limits/reduces current flow
  3. How do you calculate power? → P = V × I (Watts = Volts × Amps)
  4. Why do we need resistors with LEDs? → To limit current and prevent burning out the LED
ImportantWhy Electricity Matters for IoT

Every IoT device runs on electricity. Sensors, microcontrollers, communication modules, actuators - all require electrical power and understanding electrical principles. Without electricity, there is no IoT.

Note🔗 Cross-Hub Connections

Explore Related Learning Resources:

  • Simulations Hub: Try the interactive circuit simulators (TinkerCAD, Wokwi) to visualize current flow, test Ohm’s Law, and experiment with component values without physical hardware
  • Videos Hub: Watch curated video tutorials on electrical fundamentals, including SparkFun’s “Voltage, Current, Resistance” and ElectroBOOM’s entertaining electricity explanations
  • Quizzes Hub: Test your understanding of Ohm’s Law, power calculations, and circuit analysis with interactive quiz banks organized by difficulty level
  • Knowledge Gaps Hub: Address common misconceptions about current flow direction, voltage vs current confusion, and parallel vs series resistance calculations

Why These Connections Matter: Electricity is the foundation of all IoT systems. Interactive simulations help visualize abstract concepts like electron flow, while video tutorials provide alternative explanations for difficult topics. Regular quiz practice reinforces calculation skills essential for circuit design.

Warning⚠️ Common Misconception: “Higher Voltage Always Means More Danger”

The Misconception: Many beginners believe that voltage alone determines electrical danger, leading to fear of any high-voltage circuit.

The Reality: Current through the body causes harm, not voltage alone. A 10,000V static shock (0.001 mA, <1 µJ) causes discomfort but no injury, while 120V AC mains (100 mA through the heart) can be fatal.

Real-World Impact: In a 2019 incident, an IoT developer working with a 12V/30A power supply for LED strips received severe burns when a short circuit sent 25A through a screwdriver, which heated to 800°C in 0.5 seconds. The “low voltage” system delivered 360W of power (P = 12V × 30A), enough to weld metal. Meanwhile, the developer safely handled 5,000V piezoelectric igniters (used in IoT gas sensors) because they deliver only 0.001 mA.

Key Formula: Danger = Current × Duration. Human threshold: 1 mA (tingling), 10 mA (cannot let go), 100 mA (ventricular fibrillation). Even 5V USB can deliver 3A (enough to start fires in shorted cables).

Takeaway: Respect amperage ratings and power calculations (P = V × I), not just voltage numbers. A 5V/20A power supply is far more dangerous than a 100V/10 mA source.

NoteKey Concepts
  • Current (I): Flow of electric charge measured in Amperes (A); the rate at which electrons move through a conductor
  • Voltage (V): Electric potential difference measured in Volts (V); the “pressure” that pushes electrons through a circuit
  • Resistance (R): Opposition to current flow measured in Ohms (Ω); determines how much current flows for a given voltage
  • Ohm’s Law: Fundamental relationship V = I × R relating voltage, current, and resistance in electrical circuits
  • Power (P): Rate of energy consumption measured in Watts (W); calculated as P = V × I
  • Series vs Parallel: Circuit configurations affecting total resistance and voltage/current distribution
NoteKey Takeaway

In one sentence: V = IR and P = VI are the two equations that govern every electrical circuit–master them and you can design any IoT power system.

Remember this rule: Current kills, not voltage alone–always calculate both voltage AND current capacity when assessing circuit safety and component ratings.


589.5 What is Electricity?

⏱️ ~8 min | ⭐ Foundational | 📋 P06.C04.U01

Electricity is a form of energy - specifically, the energy associated with the movement of electrons between atoms.

589.5.1 Types of Energy

Before diving into electricity, let’s understand the broader context. Energy can be classified into six types:

Type Examples IoT Relevance
Mechanical Windmills, gears, motors Actuators, moving parts
Chemical Batteries, fuel cells Power sources
Electrical Circuits, sensors, microcontrollers Core of all IoT devices
Radiant Solar panels, LEDs, lasers Energy harvesting, displays
Nuclear Not typically used in IoT -
Sound Acoustic sensors, speakers Audio IoT applications

Key Principle: Energy cannot be created or destroyed, only transformed. IoT devices constantly transform energy from one form to another (chemical → electrical → light/motion/data).


589.6 Atoms and Electrons

⏱️ ~10 min | ⭐ Foundational | 📋 P06.C04.U02

Understanding electricity requires understanding atomic structure.

%% fig-alt: "Atomic structure diagram showing nucleus with protons and neutrons at center, surrounded by electron shells with orbiting electrons"
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graph TB
    subgraph Nucleus["Nucleus (Center)"]
        P["⊕ Protons<br/>(Positive +)"]
        N["◯ Neutrons<br/>(Neutral)"]
    end

    subgraph Shell1["Inner Electron Shell"]
        E1["⊖ Electron"]
        E2["⊖ Electron"]
    end

    subgraph Shell2["Outer Electron Shell"]
        E3["⊖ Electron"]
        E4["⊖ Electron"]
        E5["⊖ Electron"]
    end

    Nucleus -.->|"10,000× smaller"| Shell1
    Shell1 -.-> Shell2

    style Nucleus fill:#E67E22,stroke:#2C3E50,stroke-width:3px
    style Shell1 fill:#E8F5E9,stroke:#16A085,stroke-width:2px,stroke-dasharray: 5 5
    style Shell2 fill:#E3F2FD,stroke:#16A085,stroke-width:2px,stroke-dasharray: 5 5
    style P fill:#E74C3C,stroke:#2C3E50,stroke-width:2px,color:#fff
    style N fill:#7F8C8D,stroke:#2C3E50,stroke-width:2px,color:#fff
    style E1 fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style E2 fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style E3 fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style E4 fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style E5 fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff

Figure 589.6: Atomic structure diagram showing nucleus with protons and neutrons at center, surrounded by electron shells with orbiting electrons

{fig-alt=“Electrical circuit diagram showing”Nucleus (Center)“,”⊕ Protons (Positive +)“,”◯ Neutrons (Neutral)” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}

Key Components: - Protons (+): Positively charged particles in the nucleus - Neutrons (neutral): Neutral particles in the nucleus - Electrons (-): Negatively charged particles orbiting the nucleus

The electron cloud occupies a volume 10,000× larger than the nucleus!

Detailed cross-section diagram of atomic structure showing central nucleus containing protons and neutrons, surrounded by multiple electron orbital shells at increasing distances, with electrons depicted as small particles orbiting the nucleus
Figure 589.7: The structure of an atom showing nucleus and electron shells

589.6.1 How Electricity Works

Electricity occurs when electrons jump from one atom to another.

%% fig-alt: "Electron flow diagram showing electrons moving from atom to atom through a conductor, creating electric current from negative to positive"
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graph LR
    A["Atom 1<br/>(Excess ⊖)"] -->|"⊖ jumps"| B["Atom 2"]
    B -->|"⊖ jumps"| C["Atom 3"]
    C -->|"⊖ jumps"| D["Atom 4<br/>(Deficit ⊖)"]

    E["Negative (-)<br/>Excess Electrons"] -.->|"Electrons flow this way"| F["Positive (+)<br/>Deficit Electrons"]

    style A fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style B fill:#7F8C8D,stroke:#2C3E50,stroke-width:2px,color:#fff
    style C fill:#7F8C8D,stroke:#2C3E50,stroke-width:2px,color:#fff
    style D fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style E fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff
    style F fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff

Figure 589.8: Electron flow diagram showing electrons moving from atom to atom through a conductor, creating electric current from negative to positive

{fig-alt=“Electrical circuit diagram showing”Atom 1 (Excess ⊖)“,”Atom 2”, “Atom 3” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}

Electrical Charge: - Negative (-): Material with excess electrons - Positive (+): Material with deficit of electrons

Schematic illustration of electron flow in a complete electrical circuit, showing electrons moving from negative terminal through conductor to positive terminal, with arrows indicating direction of electron movement and conventional current flow
Figure 589.9: Electron flow in an electrical circuit

Detailed illustration of electron flow in a circuit showing atoms with valence electrons, conductor material with free electrons, direction of electron movement from negative to positive terminal, and conventional current direction (opposite to electron flow) with voltage source providing the driving force

Electron flow in circuits from CP IoT System Design Guide
Artistic visualization of electron flow through conductor showing copper wire cross-section with free electrons moving from negative to positive terminal, current direction arrows, and voltage source providing electrical pressure to drive electron movement
Figure 589.10: Electrons flow through conductors from negative to positive terminals when voltage creates an electric field. In metals, free valence electrons move through the atomic lattice, carrying charge from the power source through the load and back to complete the circuit.
Geometric collection of basic circuit diagrams showing series and parallel resistor configurations, voltage divider, current divider, and simple LED circuit with component values and current flow directions for IoT circuit fundamentals
Figure 589.11: These fundamental circuit configurations form the building blocks for IoT sensor and actuator interfaces. Series circuits share current while dividing voltage, and parallel circuits share voltage while dividing current. Understanding these patterns enables quick analysis of sensor signal conditioning circuits.
Artistic illustration of miniaturized electronic components used in IoT sensors including SMD resistors, ceramic capacitors, chip inductors, micro LEDs, MEMS sensors, and tiny connectors with size comparisons to common objects like rice grains
Figure 589.12: Miniaturized electronic components enable compact IoT sensor designs. Surface mount devices (SMD) reduce size dramatically compared to through-hole parts, allowing sensors to fit in wearables, implantables, and space-constrained industrial installations while maintaining full functionality.

Source: CP IoT System Design Guide, Chapter 3 - Sensing and Actuation

Artistic illustration of electron flow in a conductor showing: copper wire cross-section with crystalline lattice structure, free valence electrons drifting from negative terminal toward positive terminal under voltage influence, collision path with atoms causing resistance, and arrows indicating conventional current direction opposite to actual electron movement.

Electron Flow Artistic Visualization

Electron drift creates current: Free electrons move through the conductor’s atomic lattice from negative to positive terminal.

  • Electrical Potential: The difference in charge between two points

Nature seeks equilibrium: Electrons flow from negative to positive, balancing the charge difference.

NoteImportant Convention

Physically: Electrons flow from negative (-) to positive (+) By Convention: We analyze circuits as if current flows from positive (+) to negative (-)

This historical convention is used in all circuit analysis and design.


589.7 The Big Three: Current, Voltage, Resistance

⏱️ ~12 min | ⭐⭐ Intermediate | 📋 P06.C04.U03

589.7.1 Electric Current (I)

Definition: The flow of electrons between atoms, measured in Amperes (A).

  • 1 Ampere = 1 Coulomb of charge flowing per second
  • 1 Coulomb = 6.24 × 1018 electrons (6.24 quintillion!)

Water Analogy: Think of current like water flowing through a pipe - the amount of water flowing per second.

589.7.2 Voltage (V)

Definition: The difference in electric charge between two points, measured in Volts (V).

  • Greater voltage = greater “pressure” pushing electrons
  • Creates the “force” that drives current flow

Water Analogy: Think of voltage like water pressure - the higher the pressure difference, the more water flows.

589.7.3 Resistance (R)

Definition: The opposition to current flow in a material, measured in Ohms (Ω).

  • Good conductors (copper, gold): Low resistance
  • Insulators (rubber, plastic): High resistance
  • Resistors: Components specifically designed to provide resistance

Water Analogy: Think of resistance like pipe diameter - narrow pipes resist flow more than wide pipes.


Question 4: You’re building a 3-stage voltage divider to create reference voltages for a multi-ADC sensor system. Using 12V input, you need 9V, 6V, and 3V taps. You select three resistors in series: R1=100Ω (12V to 9V), R2=220Ω (9V to 6V), R3=330Ω (6V to ground). Your multimeter reads incorrect tap voltages. Before checking connections, what is the total circuit resistance affecting current flow?

  • 217Ω (parallel combination)
  • 550Ω (partial sum of R2+R3)
  • 650Ω (series sum: R1+R2+R3)
  • 54Ω (reciprocal sum for parallel)

💡 Explanation: Series resistors add directly: R_total = 100Ω + 220Ω + 330Ω = 650Ω. Circuit current: I = V/R_total = 12V / 650Ω = 18.5mA flows through all resistors. Voltage drops: V_R1 = I × R1 = 18.5mA × 100Ω = 1.85V (NOT 3V expected!). V_R2 = 18.5mA × 220Ω = 4.07V. V_R3 = 18.5mA × 330Ω = 6.1V. Actual tap voltages: 12V - 1.85V = 10.15V (not 9V), 10.15V - 4.07V = 6.08V, 6.08V - 6.1V ≈ 0V. Why voltage divider failed: Equal voltage steps (3V each) require resistors proportional to voltage drops with SAME current. For 3V steps from 12V: Use equal resistors! R1 = R2 = R3 = 1kΩ each. Then: I = 12V / 3kΩ = 4mA. Each resistor drops 4mA × 1kΩ = 4V… still wrong for 3V steps. Correct design for 9V, 6V, 3V taps: R1 = 1kΩ (12V→9V, 3V drop), R2 = 1kΩ (9V→6V, 3V drop), R3 = 2kΩ (6V→3V, 3V drop), R4 = 1kΩ (3V→0V, 3V drop). Total = 5kΩ. I = 12V/5kΩ = 2.4mA. Drops: 2.4V, 2.4V, 4.8V, 2.4V. Key lesson: Voltage divider output depends on load current. Unloaded divider calculations assume infinite load impedance. ADC inputs (~1MΩ) negligibly load the divider, but incorrect resistor ratios give wrong voltages.

589.8 Resistors

⏱️ ~10 min | ⭐ Foundational | 📋 P06.C04.U04

Resistors are passive components that control current flow in circuits.

Practical Ohm's Law applications diagram for IoT circuits showing four common scenarios: LED current limiting resistor calculation (Vsupply - Vforward) / I_desired, voltage divider for sensor level shifting with R1 and R2 formula Vout = Vin x R2/(R1+R2), pull-up resistor sizing for I2C bus with typical values 4.7k-10k ohms, and power dissipation calculation P = I squared times R with heat sink considerations. Each scenario includes circuit schematic, component values, and step-by-step calculation example.

Ohm’s Law applications in IoT circuits
Figure 589.13: AI-generated Ohm’s Law practical applications for IoT circuit design

Understanding Ohm’s Law (V = I x R) is fundamental to designing every IoT circuit. From calculating LED resistor values to sizing pull-ups for I2C buses, these calculations determine whether your circuits work reliably or fail in the field.

Common Resistor Types:

Type Application Range
Carbon Film General purpose 1Ω - 10MΩ
Metal Film Precision circuits 0.1Ω - 1MΩ
Wire Wound High power 0.01Ω - 100kΩ
Surface Mount (SMD) Compact PCBs 0.1Ω - 10MΩ
Variable (Potentiometer) Adjustable resistance 100Ω - 1MΩ

Circuit Symbols:

Collection of various resistor types including carbon film resistors with color bands, metal film precision resistors, large wire-wound power resistors, small surface-mount SMD resistors, and adjustable potentiometers showing different sizes and form factors
Figure 589.14: Different kinds of resistors
Standard electrical schematic symbols for resistors showing American zigzag style symbol and international rectangular box symbol, plus variable resistor arrow notation and photoresistor light-sensitive symbol
Figure 589.15: Common symbols for resistors in circuit diagrams
Collection of basic electrical circuit schematic diagrams showing series and parallel configurations with batteries, resistors, switches, and loads, using standard electrical symbols and connection lines
Figure 589.16: Electric circuit diagrams and schematics

%% fig-alt: "Resistor types comparison showing fixed, variable, and specialized resistors with their applications and typical values"
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graph TB
    Resistors["Resistor Types"]

    Resistors --> Fixed["Fixed Resistors"]
    Resistors --> Variable["Variable Resistors"]
    Resistors --> Special["Specialized Resistors"]

    Fixed --> F1["Carbon Film<br/>General purpose<br/>1Ω - 10MΩ"]
    Fixed --> F2["Metal Film<br/>Precision circuits<br/>0.1Ω - 1MΩ"]
    Fixed --> F3["SMD<br/>Compact PCBs<br/>0.1Ω - 10MΩ"]

    Variable --> V1["Potentiometer<br/>Adjustable<br/>100Ω - 1MΩ"]
    Variable --> V2["Trimmer<br/>One-time tuning<br/>10Ω - 100kΩ"]

    Special --> S1["Thermistor<br/>Temperature sensing<br/>1kΩ - 100kΩ"]
    Special --> S2["Photoresistor<br/>Light detection<br/>10Ω - 1MΩ"]

    style Resistors fill:#16A085,stroke:#2C3E50,stroke-width:3px,color:#fff
    style Fixed fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style Variable fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style Special fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style F1 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style F2 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style F3 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style V1 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style V2 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style S1 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style S2 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px

Figure 589.17: Resistor types comparison showing fixed, variable, and specialized resistors with their applications and typical values

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flowchart LR
    subgraph protect["PROTECTION"]
        R1["LED Current Limit<br/>330Ω @ 10mA<br/>Prevents burnout"]
        R2["GPIO Protection<br/>10kΩ series<br/>Limits ESD damage"]
    end

    subgraph sense["SENSING"]
        R3["Thermistor<br/>10kΩ NTC<br/>Temp varies resistance"]
        R4["Photoresistor<br/>10kΩ-1MΩ<br/>Light varies resistance"]
        R5["Force Sensor<br/>1kΩ-100kΩ<br/>Pressure varies R"]
    end

    subgraph condition["SIGNAL CONDITIONING"]
        R6["Voltage Divider<br/>10k/10k = 50%<br/>Level shifting 5V→2.5V"]
        R7["Pull-up/down<br/>4.7kΩ-10kΩ<br/>Default logic state"]
    end

    subgraph adjust["CALIBRATION"]
        R8["Trimmer Pot<br/>10kΩ<br/>One-time tuning"]
        R9["Gain Adjust<br/>100kΩ pot<br/>Op-amp gain control"]
    end

    style protect fill:#FCE4EC,stroke:#E74C3C
    style sense fill:#E8F5E9,stroke:#16A085
    style condition fill:#E3F2FD,stroke:#2C3E50
    style adjust fill:#FFF3E0,stroke:#E67E22

Figure 589.18: IoT application view: Resistors serve four main purposes in IoT circuits. PROTECTION: Current limiting for LEDs and GPIO. SENSING: Variable resistance sensors for temperature, light, force. SIGNAL CONDITIONING: Voltage dividers and pull-ups for logic levels. CALIBRATION: Trimmers for one-time adjustments. Know your purpose to choose the right resistor.

{fig-alt=“Electrical circuit diagram showing”Resistor Types”, “Fixed Resistors”, “Variable Resistors” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}


589.9 Circuit Diagrams

⏱️ ~8 min | ⭐ Foundational | 📋 P06.C04.U05

Circuit diagrams (schematics) are visual representations of electrical circuits using standardized symbols.

589.9.1 Basic Circuit Example: Light Switch

%% fig-alt: "Simple light switch circuit diagram showing battery, switch, and lamp in series, demonstrating open and closed circuit states"
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graph LR
    subgraph Open["Switch Open (OFF)"]
        B1["+ Battery -"] -.->|"No current"| S1["Switch<br/>(Open)"]
        S1 -.-> L1["Lamp<br/>(OFF)"]
        L1 -.-> B1
    end

    subgraph Closed["Switch Closed (ON)"]
        B2["+ Battery -"] -->|"Current flows"| S2["Switch<br/>(Closed)"]
        S2 --> L2["💡 Lamp<br/>(ON)"]
        L2 --> B2
    end

    style Open fill:#FFEBEE,stroke:#2C3E50,stroke-width:2px
    style Closed fill:#E8F5E9,stroke:#2C3E50,stroke-width:2px
    style B1 fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style B2 fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style S1 fill:#7F8C8D,stroke:#2C3E50,stroke-width:2px,color:#fff
    style S2 fill:#16A085,stroke:#2C3E50,stroke-width:2px,color:#fff
    style L1 fill:#f4f4f4,stroke:#2C3E50,stroke-width:2px
    style L2 fill:#16A085,stroke:#2C3E50,stroke-width:2px,color:#fff

Figure 589.19: Simple light switch circuit diagram showing battery, switch, and lamp in series, demonstrating open and closed circuit states

{fig-alt=“Electrical circuit diagram showing”Switch Open (OFF)“,”+ Battery -“,”Switch (Open)” including voltage, current, resistance relationships, component connections, and signal flow for understanding sensor power requirements and circuit fundamentals in IoT applications.”}

How it works: - Switch Open: No path for electrons → Lamp OFF - Switch Closed: Complete circuit → Current flows → Lamp ON

SparkFun Tutorial: How to Read a Schematic

Learn to interpret circuit diagrams, component symbols, and connections.

Mathematical representation of Ohm's Law showing the three fundamental equations: V equals I times R, I equals V divided by R, and R equals V divided by I, arranged in a triangle diagram for easy reference
Figure 589.20: Ohm Law equation relating voltage, current, and resistance
Visual explanation of Ohm's Law with practical examples showing how voltage, current, and resistance interact in real circuits, including sample calculations and circuit diagrams demonstrating the relationship between the three electrical quantities
Figure 589.21: Ohm Law visualization and applications

Ohm's Law triangle diagram showing the mathematical relationship between Voltage (V), Current (I), and Resistance (R), with the three formulas V=IR, I=V/R, and R=V/I, plus worked examples showing calculations for LED current limiting and resistor sizing in IoT circuits

Ohm’s Law from CP IoT System Design Guide

Source: CP IoT System Design Guide, Chapter 3 - Sensing and Actuation

Visual guide to Ohm's Law applications showing circuit analysis examples, power calculations, and practical scenarios including sensor current draw calculations, LED resistor selection, and motor control circuit analysis for IoT prototyping

Ohm’s Law practical applications from CP IoT System Design Guide

Source: CP IoT System Design Guide, Chapter 3 - Sensing and Actuation

Artistic illustration of Ohm's Law triangle diagram with V (Voltage in Volts) at the top, I (Current in Amps) and R (Resistance in Ohms) at the bottom, showing the three derived formulas: V=IxR for calculating voltage, I=V/R for calculating current, and R=V/I for calculating resistance, with arrows indicating the relationships.

Ohm’s Law Artistic Visualization

The Ohm’s Law triangle: Cover the unknown variable to reveal the formula using the other two.

Artistic visualization of Ohm's Law practical applications showing: LED current limiting circuit calculation (selecting proper resistor), sensor power consumption analysis, motor current draw prediction, and voltage divider design for level shifting, each with worked example calculations using V=IR formulas.

Ohm’s Law Applications Artistic Visualization

Practical applications: From LED circuits to sensor power budgets, Ohm’s Law solves real IoT design challenges.


589.10 Ohm’s Law: The Foundation of Electronics