6  Electricity in Real IoT Circuits

6.1 Start Simple

Imagine a door sensor, an LED, and a relay sharing the same board. Each part needs the right voltage, a limited current path, and protection from the ways real wiring can be wrong. Start by naming the source, load, signal, and failure you are designing against before adding more components.

6.2 Learning Objectives

• Calculate LED current limiting resistor values using Ohm’s Law to prevent component damage in IoT circuits
• Design voltage dividers to interface 5V sensors with 3.3V microcontrollers using resistor ratio calculations
• Analyze power budget for battery-powered IoT devices by calculating duty cycles and average current consumption
• Build series and parallel resistor networks and measure voltage/current distribution using multimeters
• Select and configure passive components (resistors, capacitors, inductors) for real-world IoT applications including sensor pull-up resistors, signal filtering, and DC-DC converters

In 60 Seconds

Passive components (resistors, capacitors, inductors) shape circuit behavior without external power. Real-world IoT applications include LED current limiting, sensor pull-up resistors, and power budget calculations that determine battery life for deployed devices.

Key Concepts

• LED Current Limiting Resistor: Calculated as R = (Vsupply - Vf) / If; the LED forward voltage Vf is typically 1.8-2.0 V (red), 2.1-2.5 V (green/yellow), 3.0-3.5 V (blue/white); use If = 5-20 mA for standard indicator LEDs
• Voltage Divider for Sensor Interface: Two resistors in series produce an intermediate voltage: Vout = Vin x R2 / (R1 + R2); used to read resistive sensors (thermistors, LDRs) as voltage changes, and to drop 5 V sensor outputs to 3.3 V for MCU ADC inputs
• Pull-Up Resistor for Digital Inputs: A resistor from VCC to a digital input ensures the pin reads HIGH when no device is driving it; typical values: 4.7-10 kohm for I2C, 10-47 kohm for button inputs; prevents floating inputs from reading random values
• Battery Life Calculation: Runtime = Battery_capacity_mAh / Average_current_mA; for duty-cycled IoT devices: Iavg = Iactive x duty_fraction + Isleep x (1 - duty_fraction); essential for sizing batteries in wireless IoT sensor nodes
• Power Supply Decoupling: 100 nF ceramic capacitor in parallel with 10 uF electrolytic placed close to each IC’s power supply pins; ceramic absorbs high-frequency transients, electrolytic provides bulk charge for slow current demands; prevents supply noise from affecting circuit performance
• Fuse Protection: A fuse in series with the power supply that opens (breaks) when current exceeds its rated value; prevents fire and board damage from short circuits and overcurrent conditions; fuse current rating should be 20-50% above maximum normal operating current
• Circuit Protection Diode: A series diode protecting against reverse-polarity power supply connections; simple but effective for field-deployed devices where connectors may be accidentally reversed; adds one diode forward voltage drop (0.3-0.7 V) to the supply path
• Current Measurement with Shunt Resistor: A small value resistor (0.01-1 ohm) in series with the power supply enables current measurement via voltage sensing: I = V_shunt / R_shunt; allows monitoring of battery current without expensive current sensor ICs in low-cost IoT applications

For Beginners: Passive Components

Resistors, capacitors, and inductors are the three basic building blocks found in almost every electronic circuit. A resistor is like a narrow section of pipe that limits water flow (limits electrical current). A capacitor is like a small tank that stores and releases water (stores and releases electrical charge). An inductor is like a heavy flywheel that resists changes in flow. Together, they shape how electricity behaves in your IoT circuits.

Time: ~12 min | Level: Intermediate | Unit: P06.C04.U09

6.3 Why This Chapter Matters

• This is the chapter where electricity stops being abstract and starts turning into wiring decisions you will actually make on a board.
• If you build IoT devices, you will repeatedly size LED resistors, create voltage dividers, estimate battery life, and choose decoupling parts. These are not edge cases; they are routine design tasks.
• A student who understands this chapter can move from “I know the formula” to “I can choose a safe part value for a real circuit.”

6.4 How To Use This Chapter

• Read the LED resistor, voltage divider, and power-budget parts in order on a first pass. Those three topics cover most beginner IoT hardware decisions.
• When a formula appears, pause and substitute one set of numbers from your own project instead of only following the book’s numbers.
• Treat the component tables as design aids, not memorization targets. The goal is to know what each part is for and when to look it up.

Chapter Roadmap

This chapter turns electricity formulas into board-level decisions:

1. First you identify passive parts and why resistors, capacitors, and inductors appear in nearly every IoT circuit.
2. Then you use voltage dividers to make a 5V signal safe for a 3.3V microcontroller.
3. Next you apply the same ideas to LED current limiting, pull-ups, labs, and battery runtime.
4. Finally you use Kirchhoff checks and practice questions to catch shared-rail, loop-voltage, and component-rating mistakes.

Checkpoints recap the decisions you have just made, and anything titled “Deep dive” is optional on a first read.

Voltage Vera

“Before you blame the code, follow the current — most ‘bugs’ are a loose ground or a wrong resistor.”

Through this chapter’s circuits and labs, Vera’s habit is predict-then-probe: compute the value, put the meter on the node, and compare.

Phoebe’s Field Notes: Why the Same Three Laws Size the Board

Phoebe’s Why

Every practical circuit check in this chapter is a conservation statement. Voltage is energy per unit charge, current is charge flow per second, and resistance is the material’s opposition to that flow. When charges move around a closed loop, the energy supplied by the source must be used by the loads. When branches meet at a node, charge cannot pile up indefinitely, so incoming and outgoing currents balance. Battery life is the same bookkeeping stretched over time: count the average charge or energy taken each cycle, then compare it with what the cell can deliver.

The Derivation

Start from charge and energy:

\[V = \frac{W}{Q}\]

\[I = \frac{dQ}{dt}\]

Ohm’s law defines resistance for the linear parts used here:

\[R = \frac{V}{I}\]

The power rate follows from energy per charge times charge per time:

\[P = VI\]

For a series LED loop, Kirchhoff’s voltage law gives

\[V_s - V_f - IR = 0\]

\[R = \frac{V_s - V_f}{I}\]

For a divider, the same current flows through both resistors:

\[I = \frac{V_{in}}{R_1 + R_2}\]

The output is the drop across \(R_2\):

\[V_{out} = IR_2\]

\[V_{out} = V_{in}\frac{R_2}{R_1 + R_2}\]

A duty-cycled node uses time-weighted current:

\[I_{avg} = \sum I_i\frac{t_i}{T}\]

For mixed rails, compare battery energy with average power:

\[t = \frac{E_{battery}}{P_{avg}}\]

Worked Numbers: This Chapter’s Circuits

• LED resistor: with \(V_s = 5.00\) V, \(V_f = 2.00\) V, and \(I = 20.0\) mA, \(R = (5.00 - 2.00)/0.0200\) \(= 150\) \(\Omega\). If the lab uses \(220\) \(\Omega\) on the same 5 V source, \(I = 3.00/220\) \(= 13.6\) mA and \(P_R = I^2R\) \(= 0.0409\) W.
• Level-shift divider: the first \(1.0\) k\(\Omega\) + \(2.2\) k\(\Omega\) trial gives \(I = 5.00/3.20\) k\(\Omega\) \(= 1.56\) mA and \(V_{out} = 1.56\) mA \(\times 2.2\) k\(\Omega\) \(= 3.44\) V. Changing to \(1.5\) k\(\Omega\) + \(2.2\) k\(\Omega\) gives \(I = 1.35\) mA and \(V_{out} = 2.97\) V.
• DHT22 example: \(1.8\) k\(\Omega\) + \(3.3\) k\(\Omega\) gives \(V_{out} = 5.00(3.3/5.1)\) \(= 3.24\) V, \(I = 5.00/5.1\) k\(\Omega\) \(= 0.980\) mA, and \(P = VI\) \(= 4.90\) mW.
• Five-minute power cycle: ESP32 average is \(160(2.6/300) + 0.010(297.4/300)\) \(= 1.40\) mA; DHT22 is \(1.5(2/300)\) \(= 0.0100\) mA; LoRa transmit plus sleep is \(120(0.5/300)+0.001(299.5/300)\) \(= 0.201\) mA; LED is \(20(0.5/300)\) \(= 0.0333\) mA. Total \(= 1.64\) mA, so \(2000/1.64\) \(= 1220\) h \(= 50.8\) days.
• Shared rail and heater: two \(4.7\) k\(\Omega\) pull-ups at 3.3 V draw \(2(3.3/4700)\) \(= 1.40\) mA, so the 3.3 V rail total is \(80 + 1 + 10 + 1.40\) \(= 92.4\) mA. With the 5 V, 150 mA MQ-135 heater included, average active power is \(1055\) mW; a 2000 mAh, 3.7 V cell stores \(7.40\) Wh, so continuous active runtime is \(7.40/1.055\) \(= 7.01\) h. Duty-cycling the heater to 30 s per 300 s drops it to 15.0 mA and supports the chapter’s roughly 19.5 h estimate if the other loads remain active.

First stop: name the passive parts before calculating with them. A resistor, capacitor, and inductor each changes circuit behavior in a different way, so the table below is a parts map for the design choices that follow.

Passive components don’t require external power and don’t generate power.

6.4.1 Comparison Table

Component	Property	Unit	Symbol	Function	IoT Application
Resistor	Resistance	Ohm (Ω)		Limits current	LED current limiting, pull-up/down
Capacitor	Capacitance	Farad (F)		Stores charge	Power smoothing, filtering
Inductor	Inductance	Henry (H)		Stores magnetic energy	DC-DC converters, RF circuits

6.4.2 Capacitors

Function: Store electrical energy as electric charge (like tiny, fast-charging batteries)

Typical Values:

• µF (microfarad): 10^-6 F - Power supply decoupling
• nF (nanofarad): 10^-9 F - Signal filtering
• pF (picofarad): 10^-12 F - High-frequency circuits

IoT Applications:

• Smoothing power supply voltage for microcontrollers
• Filtering noise from sensor signals
• Energy storage for low-power devices

6.4.3 Inductors

Function: Store energy as magnetic fields when current flows

Typical Values:

• mH (millihenry): 10^-3 H - Power inductors
• µH (microhenry): 10^-6 H - RF circuits

IoT Applications:

• DC-DC converters (boost/buck regulators)
• EMI filtering
• Wireless charging coils

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6.5 IoT Voltage Dividers

A voltage divider is one of the most fundamental circuits in IoT systems, allowing you to interface sensors operating at different voltages with microcontrollers. When you connect two resistors in series between a voltage source and ground, the voltage divides proportionally based on the resistor values.

Step 1: Identify the Basic Principle

Consider a 5V sensor connected to a 3.3V microcontroller. Connecting them directly would damage the microcontroller’s input pin. A voltage divider solves this:

• Signal path: 5V source, then R1 (1kΩ), then V_out, then R2 (2.2kΩ), then ground.

Step 2: Calculate the Output Voltage

The voltage divider equation determines V_out:

\[ \begin{aligned} V_{out} &= V_{in} \times \frac{R_2}{R_1 + R_2} \end{aligned} \]

For our example: \[ \begin{aligned} V_{out} &= 5V \times \frac{2.2k\Omega}{1k\Omega + 2.2k\Omega} \\ &= 5V \times \frac{2.2}{3.2} \\ &= 3.44V \end{aligned} \]

This is still slightly high for a 3.3V MCU (exceeds absolute maximum rating). Adjust R1 to 1.5kΩ:

\[ \begin{aligned} V_{out} &= 5V \times \frac{2.2k\Omega}{1.5k\Omega + 2.2k\Omega} \\ &= 5V \times \frac{2.2}{3.7} \\ &= 2.97V \end{aligned} \]

Now the signal is safely within the 0-3.3V range.

Step 3: Consider Current Draw

Voltage dividers constantly draw current (wasted power). Total resistance should be high enough to minimize current:

\[ \begin{aligned} I_{divider} &= \frac{V_{in}}{R_1 + R_2} \\ &= \frac{5V}{3.7k\Omega} \\ &= 1.35 \text{ mA} \end{aligned} \]

For battery-powered devices, increase resistor values proportionally (15kΩ + 22kΩ) to reduce current to 135 µA while maintaining the same voltage ratio.

Step 4: Account for Loading Effects

The MCU input pin has input impedance (typically >100kΩ for GPIO, ~1MΩ for ADC). If the divider resistance is too high, the input impedance creates a parallel path that affects the output voltage. General rule: keep total divider resistance below 1/10 of the input impedance.

Real-World Application Example

The DHT22 temperature/humidity sensor outputs 5V logic levels. To interface with an ESP32 (3.3V GPIO): - Use 1.8kΩ for R1 and 3.3kΩ for R2 - Output voltage: V_out = 5V x (3.3 / 5.1) = 3.24V - Divider current: 5V / 5.1kΩ = 0.98 mA - Power loss: 5V x 0.98mA = 4.9 mW

This simple two-resistor circuit protects expensive microcontrollers from overvoltage damage in mixed-voltage IoT systems.

Vera’s Probe Points

• Measure: V_out at the DHT22 divider midpoint feeding the ESP32 pin.
• Expect: 3.24 V from 5 V through 1.8 kΩ and 3.3 kΩ; 0.98 mA divider current.
• Wrong?: loading — divider resistance above about 1/10 of the pin’s input impedance drags the node off the calculated value.

Voltage Divider Value Trials

viewof vdiv_vin = Inputs.range([1, 24], {value: 5, step: 0.1, label: "Input voltage (V)"})
viewof vdiv_r1 = Inputs.range([100, 100000], {value: 1800, step: 100, label: "R1 (Ω)"})
viewof vdiv_r2 = Inputs.range([100, 100000], {value: 3300, step: 100, label: "R2 (Ω)"})

vdiv_vout = vdiv_vin * vdiv_r2 / (vdiv_r1 + vdiv_r2)
vdiv_current = vdiv_vin / (vdiv_r1 + vdiv_r2) * 1000
vdiv_power = vdiv_vin * vdiv_current
vdiv_safe = vdiv_vout <= 3.3

html`<div style="background: var(--bs-light, #f8f9fa); padding: 1rem; border-radius: 8px; border: 1px solid var(--bs-border-color, #dee2e6); font-family: inherit;">
<p><strong>Output voltage:</strong> ${vdiv_vout.toFixed(2)} V ${vdiv_safe ? "(safe for 3.3V MCU)" : "(WARNING: exceeds 3.3V!)"}</p>
<p><strong>Divider current:</strong> ${vdiv_current.toFixed(2)} mA</p>
<p><strong>Power dissipation:</strong> ${vdiv_power.toFixed(2)} mW</p>
<p style="color: var(--bs-secondary, #6c757d); font-size: 0.9em;"><em>For battery operation, scale both resistors up by 10× (${(vdiv_r1/100).toFixed(0)}kΩ + ${(vdiv_r2/100).toFixed(0)}kΩ) to reduce current to ${(vdiv_current/10).toFixed(2)} mA.</em></p>
</div>`

Checkpoint: Voltage Dividers

You now know:

• A 5V sensor needs level shifting before it reaches a 3.3V GPIO pin.
• The 1kΩ plus 2.2kΩ trial still gives 3.44V, while 1.5kΩ plus 2.2kΩ gives 2.97V.
• Scaling the same ratio from 1.35 mA divider current down to 135 µA matters for battery-powered devices.

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6.6 Real-World Applications in IoT

Time: ~15 min | Level: Intermediate | Unit: P06.C04.U10

The divider example protected one input pin. The next question is how the same current, voltage, and resistance checks show up in ordinary IoT outputs and buses.

6.6.1 Application 1: Fan Speed Control

Concept: Adjust resistance to control motor current

Figure 6.1: Fan speed control circuit showing variable resistor controlling current flow to motor, demonstrating speed regulation through resistance adjustment

6.6.2 Application 2: LED Current Limiting

Problem: LEDs will burn out if connected directly to power supply

Solution: Add a resistor to limit current

Example Calculation:

• Power supply: 5V
• LED forward voltage: 2V (typical red LED)
• Desired current: 20mA (0.02A)

\[ \begin{aligned} R &= \frac{V_{supply} - V_{LED}}{I} \\ &= \frac{5V - 2V}{0.02A} \\ &= 150\Omega \end{aligned} \]

Use a 150Ω or 220Ω resistor (standard value)

6.6.3 Application 3: Sensor Pull-up Resistors

Why needed: Many IoT sensors have open-drain outputs that need pull-up resistors

Typical values: 4.7kΩ or 10kΩ

Application: I2C communication (covered in Chapter 4)

Checkpoint: Everyday Applications

You now know:

• A red LED on a 5V supply with a 2V forward drop and 20 mA target current needs about 150Ω.
• A 150Ω or 220Ω standard resistor is the practical choice in the LED example.
• I2C and button inputs use pull-ups such as 4.7kΩ or 10kΩ so idle lines do not float.

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6.7 Hands-On Labs

Time: ~30 min | Level: Advanced | Unit: P06.C04.U11

You have seen the calculations; now the chapter asks you to measure them. The labs keep the same pattern: predict first, wire carefully, then compare the meter reading with the expected value.

6.7.1 Lab 1: Build Your First LED Circuit

Objective: Build a basic LED circuit with current limiting resistor.

Materials Needed (or use TinkerCAD simulator):

• 1× LED (any color)
• 1× 220Ω resistor
• 1× Push button switch
• 1× 9V battery (or 5V USB power)
• Breadboard and jumper wires

Circuit Diagram:

Figure 6.2: Basic LED circuit breadboard diagram showing battery, resistor, LED, and button switch connections for hands-on learning

Instructions:

1. Connect resistor to positive battery terminal
2. Connect LED positive (long leg) to other end of resistor
3. Connect LED negative (short leg) to one terminal of button
4. Connect other button terminal to battery negative
5. Press button → LED lights up!

Measurements to Record:

• Measure voltage across the LED using multimeter
• Measure current through the circuit
• Calculate and verify resistance using Ohm’s Law

Expected Learning:

• Current only flows when circuit is complete
• Resistor limits current to safe level for LED
• Practice reading circuit diagrams
• Verify Ohm’s Law with real measurements

---

6.7.2 Sensor Voltage Divider Lab

Objective: Create a voltage divider to scale down 5V to 3.3V for microcontroller ADC input.

Materials Needed:

• 1× 1kΩ resistor (R1)
• 1× 2kΩ resistor (R2)
• 1× 5V power supply (or USB)
• Multimeter
• Breadboard and jumper wires

Circuit Diagram:

Figure 6.3: Voltage divider circuit diagram showing two resistors in series dividing 5V input down to a 3.3V measurement point.

Instructions:

1. Connect R1 (1kΩ) from 5V to middle point
2. Connect R2 (2kΩ) from middle point to ground
3. Measure output voltage at middle point
4. Calculate expected voltage: \(V_{out} = 5V \times \frac{2kΩ}{1kΩ + 2kΩ} = 3.33V\)
5. Compare calculated vs measured values

Expected Learning:

• Voltage dividers reduce voltage proportionally
• Essential for interfacing 5V sensors with 3.3V microcontrollers
• Predict output voltage from resistor ratio values

Extension:

• Try different resistor values (4.7kΩ and 10kΩ)
• Calculate current through the divider
• Determine power dissipation

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6.7.3 IoT Power Budget Lab

Objective: Calculate total power consumption and estimate battery life for a battery-powered IoT sensor.

Scenario: Environmental sensor with these components: - ESP32 microcontroller: 160mA active, 10µA deep sleep - DHT22 sensor: 1.5mA when reading - LoRa radio: 120mA transmit, 15mA receive, 1µA sleep - Status LED: 20mA when on

Operating cycle (every 5 minutes):

1. Wake from sleep (0.1s)
2. Read sensor (2s)
3. Transmit data (0.5s)
4. Return to sleep (297.4s)

Instructions:

1. Calculate duty cycles:
   • Active time: 2.6s per 300s = 0.87%
   • Sleep time: 297.4s per 300s = 99.13%
2. Calculate average current for each component:
   • ESP32: (160mA × 0.0087) + (0.01mA × 0.9913) = 1.40mA
   • DHT22: 1.5mA × (2/300) = 0.01mA
   • LoRa: (120mA × 0.5/300) + (0.001mA × 299.5/300) = 0.20mA
   • LED: 20mA × (0.5/300) = 0.03mA
   • Total average: 1.64mA
3. Calculate battery life:
   • Battery: 2000mAh Li-ion (3.7V)
   • Battery life: 2000mAh / 1.64mA ≈ 1220 hours ≈ 51 days
4. Use Python PowerBudget calculator to verify

Expected Learning:

• Duty cycle dramatically affects battery life
• Sleep modes are critical for IoT devices
• Power budget analysis guides component selection

Vera’s Probe Points

• Measure: the node’s supply current across one full 5-minute cycle.
• Expect: 1.64 mA average, so the 2000 mAh battery gives about 1220 hours — 51 days.
• Wrong?: a sleep mode not engaging — the ESP32 at 160 mA active versus 10 µA asleep is the whole budget.

Checkpoint: Lab Evidence

You now know:

• The voltage-divider lab predicts 3.33V from 5V using 1kΩ and 2kΩ resistors.
• The power-budget lab turns a 5 minute cycle into 1.64 mA average current.
• A 2000 mAh battery at that average current is about 1220 hours, or about 51 days.

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6.7.4 Series vs Parallel Lab

Series and Parallel Circuits

What you’ll do: Use the sliders below to compare series and parallel resistor networks and see how voltage, current, and total resistance change.

What you’ll learn:

• How resistors combine in series vs parallel
• How voltage and current distribute in each configuration
• When to use series vs parallel in real IoT circuits

Estimated time: 12 minutes

viewof network_vin = Inputs.range([1, 12], {value: 5, step: 0.1, label: "Supply voltage (V)"})
viewof network_r1 = Inputs.range([100, 10000], {value: 1000, step: 100, label: "R1 (Ω)"})
viewof network_r2 = Inputs.range([100, 10000], {value: 1000, step: 100, label: "R2 (Ω)"})
viewof network_r3 = Inputs.range([100, 10000], {value: 1000, step: 100, label: "R3 (Ω)"})

series_total_r = network_r1 + network_r2 + network_r3
series_total_i = network_vin / series_total_r
series_total_i_ma = series_total_i * 1000
series_v1 = series_total_i * network_r1
series_v2 = series_total_i * network_r2
series_v3 = series_total_i * network_r3

parallel_total_r = 1 / ((1 / network_r1) + (1 / network_r2) + (1 / network_r3))
parallel_i1 = network_vin / network_r1
parallel_i2 = network_vin / network_r2
parallel_i3 = network_vin / network_r3
parallel_total_i = parallel_i1 + parallel_i2 + parallel_i3
parallel_total_i_ma = parallel_total_i * 1000

smallest_parallel_branch = Math.min(network_r1, network_r2, network_r3)

html`<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(260px, 1fr)); gap: 1rem; margin: 1rem 0;">
  <section style="background: #fff4e8; border: 1px solid #f0c8a0; border-radius: 10px; padding: 1rem;">
    <h4 class="depth-l1" style="margin-top: 0; color: #8a3b12;">Series network</h4>
    <p><strong>Total resistance:</strong> ${series_total_r.toFixed(0)} Ω</p>
    <p><strong>Total current:</strong> ${series_total_i_ma.toFixed(2)} mA</p>
    <p><strong>Voltage across R1:</strong> ${series_v1.toFixed(2)} V</p>
    <p><strong>Voltage across R2:</strong> ${series_v2.toFixed(2)} V</p>
    <p><strong>Voltage across R3:</strong> ${series_v3.toFixed(2)} V</p>
    <p style="margin-bottom: 0;"><strong>Key rule:</strong> the same current flows through every resistor in series.</p>
  </section>
  <section style="background: #edf6ff; border: 1px solid #b7d6f5; border-radius: 10px; padding: 1rem;">
    <h4 class="depth-l1" style="margin-top: 0; color: #0d4976;">Parallel network</h4>
    <p><strong>Total resistance:</strong> ${parallel_total_r.toFixed(1)} Ω</p>
    <p><strong>Total current:</strong> ${parallel_total_i_ma.toFixed(2)} mA</p>
    <p><strong>Branch current through R1:</strong> ${(parallel_i1 * 1000).toFixed(2)} mA</p>
    <p><strong>Branch current through R2:</strong> ${(parallel_i2 * 1000).toFixed(2)} mA</p>
    <p><strong>Branch current through R3:</strong> ${(parallel_i3 * 1000).toFixed(2)} mA</p>
    <p style="margin-bottom: 0;"><strong>Key rule:</strong> every branch sees the full supply voltage of ${network_vin.toFixed(1)} V.</p>
  </section>
</div>`

html`<div style="background: var(--bs-light, #f8f9fa); border: 1px solid var(--bs-border-color, #dee2e6); border-radius: 10px; padding: 1rem; margin-bottom: 1rem;">
  <h4 class="depth-l1" style="margin-top: 0;">What to notice</h4>
  <ul style="margin-bottom: 0;">
    <li>Series resistance becomes <strong>${series_total_r.toFixed(0)} Ω</strong>, so the source current stays relatively small.</li>
    <li>Parallel resistance drops to <strong>${parallel_total_r.toFixed(1)} Ω</strong>, which is lower than the smallest branch resistor (${smallest_parallel_branch.toFixed(0)} Ω).</li>
    <li>In series, larger resistors take a larger share of the voltage drop because the same current passes through all three parts.</li>
    <li>In parallel, the branch with the smallest resistance carries the largest current because it provides the easiest path for charge flow.</li>
  </ul>
</div>`

Interactive Challenges:

Try these experiments:

1. Series Resistance Challenge: Set all three resistors to 1kΩ. Confirm that the series total becomes 3kΩ and the source current drops to about 1.67mA at 5V.
   Hint

   For series: R_total = R1 + R2 + R3 = 1kΩ + 1kΩ + 1kΩ = 3kΩ. Resistances simply add up in series.
2. Parallel Resistance Challenge: Keep all three resistors at 1kΩ and compare the parallel total. Is it higher or lower than one resistor by itself?
   Hint

   For equal resistors in parallel: R_total = R / n = 1kΩ / 3 ≈ 333Ω. Parallel resistance is always LOWER than any individual resistor.
3. Current Distribution Challenge: Change only R3 to 2.2kΩ. Watch what happens to current in series versus current in each parallel branch. What pattern do you see?
   Hint

   Series: Current is the SAME everywhere (Kirchhoff’s Current Law). Parallel: Current DIVIDES among branches, but sum equals total current.
4. Voltage Division Challenge: Make R1 = 470Ω, R2 = 1kΩ, and R3 = 2.2kΩ. Compare the voltage across each resistor in series, then compare that with the parallel case.
   Hint

   Series: total resistance is 470Ω + 1kΩ + 2.2kΩ = 3.67kΩ, so current is about 1.36mA. Voltage drops are proportional to resistance: about 0.64V, 1.36V, and 3.00V. Parallel: each resistor still has the full 5V across it, but branch currents differ.

Part A: Series Configuration

Figure 6.4: Series resistor circuit showing three 1kΩ resistors connected end-to-end with total resistance of 3kΩ and total current of 1.67mA.

Instructions:

1. Connect three 1kΩ resistors in series
2. Measure total resistance: Expected = 3kΩ
3. Calculate current: I = 5V / 3kΩ = 1.67mA
4. Measure voltage across each resistor (should be ~1.67V each)

Part B: Parallel Configuration

Figure 6.5: Parallel resistor circuit showing three 1kΩ resistors connected side-by-side with total resistance of 333Ω and total current of 15mA

Instructions:

1. Connect three 1kΩ resistors in parallel
2. Measure total resistance: Expected = 333Ω (1kΩ/3)
3. Calculate total current: I = 5V / 333Ω = 15mA
4. Measure current through each resistor (should be ~5mA each)

Comparison Table:

Configuration	Total Resistance	Total Current	Voltage per Resistor	Current per Resistor
Series	3kΩ	1.67mA	1.67V	1.67mA
Parallel	333Ω	15mA	5V	5mA

Expected Learning:

• Series: Resistance adds, current stays same
• Parallel: Resistance decreases, current divides
• Determine when to use each configuration in IoT circuits

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The series and parallel lab showed how current and voltage split in small networks. The next layer is to use Kirchhoff’s Laws when several real loads share the same supply.

6.8 Deep dive: Kirchhoff Laws in IoT

When IoT circuits get more complex than a single loop – for example, a sensor node with an MCU, LED indicator, and pull-up resistor all sharing a power supply – you need Kirchhoff’s Laws to predict voltage and current at every point.

6.8.1 Kirchhoff’s Current Law (KCL)

The Rule: Total current entering a node equals total current leaving that node. Current cannot appear or disappear – it must flow somewhere.

Why IoT Engineers Care: KCL tells you how much current your battery must supply when multiple components share a power rail.

6.8.2 Kirchhoff’s Voltage Law (KVL)

The Rule: The sum of all voltages around any closed loop in a circuit equals zero. Every volt the battery provides must be “used up” by components in the loop.

Why IoT Engineers Care: KVL tells you the voltage at every point in the circuit, which is critical for ensuring sensors and MCUs receive the correct operating voltage.

6.8.3 ESP32 Sensor Node Power

Scenario: You are designing a battery-powered air quality sensor node with these components on a shared 3.3V rail:

• ESP32-C3 microcontroller: draws 80 mA when active
• BME280 environmental sensor (I2C with 4.7 kOhm pull-ups): draws 1 mA
• Status LED (green, V_forward = 2.1V) with current-limiting resistor: target 10 mA
• MQ-135 gas sensor heater: draws 150 mA from a separate 5V rail

The power comes from a 3.7V LiPo battery through a 3.3V LDO regulator (AMS1117-3.3).

Step 1: Apply KCL at the 3.3V Power Node

All components connect to the 3.3V rail. By KCL, the total current the regulator must supply equals the sum of all branch currents:

\[ \begin{aligned} I_{total} &= I_{ESP32} + I_{BME280} \\ &\quad + I_{LED} + I_{pullups} \end{aligned} \]

Calculate the pull-up resistor current. Two 4.7 kOhm pull-ups (SDA and SCL) connect from 3.3V to the I2C lines. When the line is pulled low (logic 0):

\[ \begin{aligned} I_{pullup} &= \frac{V}{R} \\ &= \frac{3.3V}{4.7\text{k}\Omega} \\ &= 0.70 \text{ mA per line} \end{aligned} \]

Both lines pulled low simultaneously (worst case):

\[ \begin{aligned} I_{pullups} &= 2 \times 0.70 \\ &= 1.4 \text{ mA} \end{aligned} \]

Total 3.3V rail current:

\[ \begin{aligned} I_{total} &= 80 + 1 + 10 + 1.4 \\ &= 92.4 \text{ mA} \end{aligned} \]

Step 2: Apply KVL to the LED Loop

Trace a loop from the 3.3V rail through the current-limiting resistor, through the LED, to ground:

\[ \begin{aligned} V_{supply} - V_{resistor} - V_{LED} &= 0 \end{aligned} \]

\[ \begin{aligned} 3.3V - V_{resistor} - 2.1V &= 0 \end{aligned} \]

\[ \begin{aligned} V_{resistor} &= 3.3V - 2.1V \\ &= 1.2V \end{aligned} \]

Now find the resistor value for 10 mA:

\[ \begin{aligned} R &= \frac{V_{resistor}}{I_{LED}} \\ &= \frac{1.2V}{0.01A} \\ &= 120\Omega \end{aligned} \]

Use a standard 120 Ohm resistor. Verify power dissipation:

\[ \begin{aligned} P_{resistor} &= I^2 \times R \\ &= (0.01)^2 \times 120 \\ &= 0.012 \text{ W} \end{aligned} \]

A standard 1/8 W (0.125 W) resistor is sufficient.

Step 3: Apply KVL to Check Regulator Headroom

The LDO regulator needs a minimum dropout voltage of 1.0V (AMS1117 datasheet). Apply KVL to the battery-regulator loop:

\[ \begin{aligned} V_{battery} - V_{dropout} - V_{output} &= 0 \end{aligned} \]

\[ \begin{aligned} V_{battery(min)} &= V_{dropout} + V_{output} \\ &= 1.0V + 3.3V \\ &= 4.3V \end{aligned} \]

But a LiPo battery drops to 3.0V when discharged. At 3.5V battery:

\[ \begin{aligned} V_{available} &= 3.5V - 3.3V \\ &= 0.2V < 1.0V \text{ dropout} \end{aligned} \]

Problem found by KVL: The regulator cannot maintain 3.3V output when the battery drops below 4.3V. A LiPo spends most of its discharge curve between 3.5-3.8V, so the LDO will drop out frequently.

Solution: Replace the LDO with a buck-boost regulator (e.g., TPS63000) that can maintain 3.3V output from inputs as low as 2.5V.

Vera’s Probe Points

• Measure: the regulator’s input and output while the battery discharges.
• Expect: 3.3 V out only while the input stays above 4.3 V (3.3 V plus the 1.0 V AMS1117 dropout).
• Wrong?: the LiPo itself — it spends most of its discharge between 3.5 and 3.8 V, below the dropout line.

Step 4: Total Power Budget

Component	Voltage	Current	Power
ESP32-C3 (active)	3.3V	80 mA	264 mW
BME280 sensor	3.3V	1 mA	3.3 mW
Status LED	3.3V	10 mA	33 mW
I2C pull-ups	3.3V	1.4 mA	4.6 mW
MQ-135 heater	5.0V	150 mA	750 mW
Total		242.4 mA	1,055 mW

With a 2000 mAh LiPo at 3.7V (7.4 Wh), battery life during continuous active mode:

\[ \begin{aligned} \text{Battery life} &= \frac{7.4 \text{ Wh}}{1.055 \text{ W}} \\ &\approx 7 \text{ hours} \end{aligned} \]

This confirms the MQ-135 heater dominates power consumption (71%). Duty-cycling it (heat 30s, read, sleep 270s) would reduce average heater current to 15 mA. If the rest of the 3.3V rail stayed continuously active, the same table gives roughly 19.5 hours; longer runtimes require the MCU, sensor, and indicator loads to sleep too.

Key Takeaway from Kirchhoff’s Laws

KCL answered: “Can my regulator handle the total current?” (92.4 mA – yes, AMS1117 supports up to 1A).

KVL answered: “Does my LED get the right current?” (yes, 120 Ohm resistor) AND revealed a hidden problem: “Will the LDO maintain output as the battery discharges?” (no – must switch to buck-boost).

These two laws catch problems that Ohm’s Law alone cannot: KCL catches overcurrent on shared rails, and KVL catches voltage headroom failures in multi-component loops.

Checkpoint: Kirchhoff Checks

You now know:

• The shared 3.3V rail example totals 92.4 mA before the separate 5V heater load.
• The LED loop needs a 120 Ohm resistor for a 10 mA target from a 3.3V rail with a 2.1V LED drop.
• The AMS1117 dropout check needs 4.3V input, so a 3.7V LiPo cannot hold 3.3V across most of its discharge curve.

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6.9 Quiz 3

Test your understanding of electricity fundamentals with these questions.

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Key Takeaway

Passive components (resistors, capacitors, inductors) shape every IoT circuit: resistors limit current and create voltage dividers, capacitors filter noise and store energy, and inductors enable efficient power conversion. The power budget calculation (average current = sum of duty-cycle-weighted component currents) is the single most important analysis for battery-powered IoT deployments.

For Kids: Meet the Sensor Squad!

Sammy the Sensor and friends learn about building real circuits!

Sammy the Sensor was excited – today was Build Day! The Sensor Squad was going to build their very first LED circuit. “First, we need a resistor,” said Max the Microcontroller, holding up a tiny striped cylinder. “Without it, Lila could get hurt!”

Lila the LED looked worried. “Hurt? How?” Max explained: “If too much electricity flows through you, you’ll burn out – like eating too much candy too fast gives you a tummy ache. The resistor is like a speed bump that slows the electricity down to a safe amount.”

Bella the Battery was ready to power everything. “I have 9 volts of energy!” she announced proudly. Max did some quick math: “Lila needs about 2 volts, so the resistor needs to handle 7 volts. Using Ohm’s Law – that’s V divided by I – we need a 220 ohm resistor to keep the current at a safe 20 milliamps.”

They connected everything on the breadboard: Bella to the resistor, the resistor to Lila, and Lila back to Bella through a button switch. When Sammy pressed the button – POP – Lila lit up bright red! “I’m glowing!” Lila cheered. “And I feel perfectly safe thanks to that resistor!”

“That’s the magic of circuits,” said Max. “Every part has a job: Bella provides energy, the resistor keeps everyone safe, and the button gives us control. That’s how EVERY LED in your toys, phones, and smart home gadgets works!”

6.9.1 Key Words for Kids

Word	What It Means
Resistor	A part that slows down electricity, like a speed bump for electrons
Capacitor	A tiny bucket that stores electricity and releases it quickly
LED	A special light that runs on very little electricity
Breadboard	A board with holes where you plug in parts to build circuits
Voltage Divider	Two resistors that share voltage, like splitting a pizza between friends
Battery Life	How long a battery lasts before it runs out of energy

6.10 Electrical Concept Map

Base Concept	Builds To	Requires Understanding Of	Applied In
Voltage (V)	Current flow, Power	Ohm’s Law	Voltage dividers, Battery selection
Current (I)	Power consumption, Heat	Ohm’s Law, KCL	Power budgets, Component ratings
Resistance (R)	Voltage drop, Power loss	Ohm’s Law	Pull-up resistors, Current limiting
Power (P = V × I)	Battery life, Heat dissipation	Voltage, Current	Component selection, Thermal management
Ohm’s Law (V=IR)	All circuit analysis	Voltage, Current, Resistance	Every IoT circuit design
Series Circuits	Voltage dividers	Ohm’s Law, KVL	Sensor level shifters, Multi-cell batteries
Parallel Circuits	Current distribution	Ohm’s Law, KCL	Redundant sensors, LED arrays
Capacitors	Filtering, Energy storage	Charge, Voltage	Power supply decoupling, Signal conditioning
Inductors	DC-DC converters	Magnetic fields, Energy	Buck/boost regulators, RF circuits
KVL	Loop analysis	Series circuits, Voltage	Power rail debugging, LED current limiting
KCL	Node analysis	Parallel circuits, Current	I2C pull-ups, Multi-load power budgets
Power Budgets	Battery life calculation	Power, Current, Duty cycle	IoT deployment planning

Key Insight: Every IoT electrical design decision starts with Ohm’s Law (V=IR) and branches into power analysis (P=VI), circuit topology (series/parallel), and component selection (passive elements). Kirchhoff’s Laws (KVL and KCL) tie these concepts together for complete circuit analysis.

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6.11 Op-Amp Front-End Contracts

The main chapter above stays focused on passive-component applications: LED resistors, voltage dividers, pull-ups, power budgets, and Kirchhoff checks. For the deeper design contract behind op-amp buffers, non-inverting gain, comparators, virtual-short assumptions, supply-rail limits, and gain-bandwidth trade-offs, continue to Op-Amp Sensor Front-End Contracts.

Chapter Summary

Electricity is the foundation of all IoT systems, driven by the flow of electrons through conductors. Understanding the relationship between voltage (electrical “pressure”), current (flow rate), and resistance (opposition to flow) through Ohm’s Law (V = I × R) is essential for designing and troubleshooting IoT circuits. Power consumption (P = V × I) determines battery life and energy requirements for IoT deployments.

Circuit configurations significantly impact system behavior: series circuits share current but divide voltage, while parallel circuits share voltage but divide current. Series configurations are useful for voltage division and cumulative resistance, while parallel configurations provide redundancy and current distribution. Understanding these principles enables proper component selection and circuit design.

Passive components shape circuit behavior without requiring external power: resistors limit current and create voltage dividers, capacitors store energy and filter signals, and inductors resist changes in current. Real-world circuits combine these components to condition sensor signals, filter noise, store energy, and protect sensitive electronics.

Practical application of electrical principles includes power budget calculations (ensuring battery capacity meets device requirements), voltage regulation (maintaining stable supply despite load variations), and component selection (choosing resistor wattage, capacitor voltage ratings). Safety margins (typically 2×) prevent component failure and ensure long-term reliability in IoT deployments.

6.12 Practice: Match and Order

6.13 See Also

Within This Module:

• Electricity Introduction - Foundational concepts of voltage, current, and resistance
• Ohm’s Law Deep Dive - Advanced worked examples for IoT applications including heaters, motors, and complete power budgets
• Common Electricity Pitfalls - Unit confusion, voltage drops, power limits, and AC vs DC mistakes

Related Topics:

• Electronics: Doping & Diodes - Active semiconductor devices built on electrical principles
• Electronics: Transistor Selection - Choosing BJT vs MOSFET for IoT switching and amplification
• Power Management - System-level power architecture and battery optimization
• Op-Amp Sensor Front-End Contracts - Buffer divider outputs, amplify sensor signals, and respect op-amp feedback limits
• Analog-to-Digital Conversion - How electrical signals become digital data
• Sensor Interfacing - Electrical considerations for connecting sensors to microcontrollers

External Resources:

• All About Circuits - Ohm’s Law - Interactive tutorials with circuit simulators
• SparkFun Learn - Voltage, Current, Resistance - Beginner-friendly explanations with visual aids
• TI Power Management Fundamentals - Industry reference for power circuit design

Common Pitfalls

LED Resistor Current Error

Many beginners size LED resistors for the maximum rated current (20 mA) because it is listed prominently in the datasheet. At 20 mA, LEDs are near their thermal limits and consume unnecessary power. Use 5-10 mA for indicator LEDs — they are still clearly visible and last orders of magnitude longer. Size the resistor for your chosen If, not the maximum rated If.

2. Voltage Divider Loading Error

When a load (ADC input, voltmeter, next stage circuit) is connected to the voltage divider output, it appears in parallel with R2 and changes the voltage. If the load resistance is comparable to R2, the output voltage drops significantly below the calculated value. Use an operational amplifier buffer if the load impedance is too low to maintain divider accuracy.

Battery Rated vs Usable Capacity

Battery rated capacity (mAh on the label) assumes discharge to a cutoff voltage (typically 2.5-3.0 V for Li-ion, 1.0 V for alkaline). Devices with brownout reset voltages of 2.8-3.0 V stop working before the battery is fully discharged. Usable capacity is typically 80-90% of rated capacity. Apply this derating factor to battery life calculations for realistic estimates.

Reverse Diode Voltage Drop

A series protection diode drops 0.3-0.7 V off the supply voltage. A 3.3 V system with a diode sees 2.6-3.0 V at the circuit. For 3.3 V logic that requires VCC > 2.7 V minimum, this can bring the supply dangerously close to the minimum operating voltage. Account for diode drops in power supply headroom calculations, or use a P-channel MOSFET for near-zero-drop reverse protection.

Label the Diagram

6.14 What’s Next

Next Chapter	Why It Matters
Electronics: Doping & Diodes	Progress from passive components to active semiconductor devices — learn how doping creates diodes and transistors that enable amplification, switching, and complex IoT functionality
Ohm’s Law Deep Dive	Return to the foundational equations with advanced worked examples for IoT applications including heaters, motors, LED calculations, I2C pull-ups, and complete power budget analysis
Common Electricity Pitfalls	Avoid the most common mistakes in IoT circuit design: unit confusion, voltage drops, power limits, and AC vs DC errors

Code Challenge