Ohm’s Law & the LED Driver Circuit

class: center, middle, inverse, title-slide

.title[
# Ohm’s Law & the LED Driver Circuit
]
.subtitle[
## Programmable Electronics — Unit 1
]
.date[
### Class 2 and beyond
]

---

# Learning Targets

.lt-box[
- Develop the intuition behind how electricity works.
- Apply Ohm's law (`$V = IR$`) to calculate the resistor value needed to safely light an LED.
- Read a resistor's value directly off its color bands.
- Build a working LED driver circuit on a breadboard from a schematic.
]

.eu-label[Essential Understanding:] What electricity is. What current, voltage, and resistance are. How to use Ohm's law in a basic LED driver circuit.

---

# Agenda

.agenda-box[
1. What is electricity? Electrons and current
2. How electrons flow: conductors and the water-tank analogy
3. What an LED needs, and why it needs a resistor
4. Ohm's law: deriving the resistor value
5. Reading resistor color bands
6. Build: LED driver circuit on the breadboard
7. Measure & verify
8. Homework
]

---
class: center, middle

# What is electricity?

# What makes electrons move?

Talk it over with your partner for one minute before we define anything.

---

# Electrons and current

- Matter is made of atoms: a nucleus of protons (+) and neutrons, surrounded by electrons (–).
- Normally, an atom's protons and electrons balance out — but electrons in the outermost shell can be knocked loose and made to move.
- **Current** (`$I$`) is a *rate*: how many electrons flow past a point every second, measured in amps (A).
  - One amp means about `$6.242 \times 10^{18}$` electrons pass that point every second — roughly 6.24 quintillion.

---

.pull-left.w55[
- A circuit only works if it's a closed loop: source → path → load → back to source.
- Break the loop anywhere — open the switch — and current stops everywhere at once, not just past the break.
]
.pull-right.w40[
<img src="assets/circuit-battery-switch.gif" alt="A battery, lightbulb, and switch; closing the switch completes the circuit and current flows." width="100%"/>
.footnote[Image: SparkFun Electronics, CC BY-SA 4.0]
]

---

# How electrons flow

.pull-left.w50[
- In a **conductor** (copper, silver, most metals), the outermost electrons are loosely held and free to drift from atom to atom.
- In an **insulator** (rubber, plastic, glass), electrons are held tightly — nothing moves.
- Apply voltage across a conductor, and free electrons drift steadily in one direction: that drift *is* the current.
]
.pull-right.w45[
<img src="assets/electron-flow.gif" alt="A simplified model of electrons drifting through atoms to create current." width="100%"/>
.footnote[Image: SparkFun Electronics, CC BY-SA 4.0]
]

---

# Voltage: the water-tank analogy

.pull-left.w45[
<img src="assets/water-tank-voltage.png" alt="Voltage is like the pressure created by the water." width="100%"/>
.footnote[Image: SparkFun Electronics, CC BY-SA 4.0]
]
.pull-right.w50[
- Picture a water tank raised above the ground, with a hose at the bottom.
- The **water** in the tank represents the electrons available to flow.
- The **pressure** at the end of the hose is like voltage (`$V$`) — it's what pushes those electrons through a circuit.
- Drain the tank and the pressure drops — just like a battery's voltage sags as it runs down.
]

---

# Current and resistance: same analogy

.pull-left.w45[
<img src="assets/water-tank-two-pressures.png" alt="Two tanks at the same pressure, but one has a narrower hose than the other." width="100%"/>
.footnote[Image: SparkFun Electronics, CC BY-SA 4.0]
]
.pull-right.w50[
- Two tanks, same pressure (voltage), but one hose is narrower.
- **Flow rate** through the hose is like current (`$I$`).
- The narrow hose "resists" the flow more than the wide one — that's **resistance** (`$R$`), measured in ohms (`$\Omega$`).
- Same voltage, more resistance → less current. This is the relationship Ohm's law makes exact.
]

---
class: medium-font

# Putting the analogy together

.center[
<img src="assets/water-tank-equivalents.png" alt="Two tanks at the same 1-volt pressure: a 1-ohm hose passes 1 amp, a 2-ohm hose passes only 0.5 amp." style="max-height: 340px;"/>
]

Same pressure (voltage) in both tanks. Double the resistance, and the flow (current) is cut in half — that's Ohm's law, before we've written a single equation. Next, we make it exact.

.footnote[Image: SparkFun Electronics, CC BY-SA 4.0]

---
class: center, middle

# LED Driver circuit

Putting voltage, current, and resistance to work in a very simple circuit.

---

# What is an LED, really?
.pull-left.w60[
- LED = Light-Emitting Diode. A diode only lets current flow **one direction**.
- An LED has a **forward voltage** (`$V_f$`) — roughly fixed, depends on color:
  - Red ≈ 2.0 V, Green ≈ 2.1 V, Blue/White ≈ 3.0–3.2 V
- Below `$V_f$`: effectively no current flows, no light.
- Above `$V_f$`: current rises **very fast** for a tiny increase in voltage.

If you connect an LED straight to a supply above roughly 3 V with nothing else in the circuit, current keeps rising until the LED burns out.
]
.pull-right.w30[
<img src="assets/led-fvoltage.png" alt="." height="500"/>
]
---

# The fix: a current-limiting resistor

.pull-left.w30[
- Put a resistor in series with the LED.
- The resistor "absorbs" the extra voltage the LED doesn't use, and limits the current to a safe value.
- This is the **LED driver circuit** — the simplest one you'll build all semester, and the one every other circuit today builds on.
]
.pull-right.w60[
<img src="assets/LED-driver.png" alt="A working LED circuit with a current-limiting resistor in series." width="100%"/>
Supply → Resistor → LED → Ground

]

---
# Exercises

1. Calculate the **nominal** current that is being applied to your LED, considering:
   - Source Voltage of `$6V$` (`$4 \times 1.5 V$`)
   - Resistance of `$220 Ω$`

class: center, middle

### How to know the value of the resistor we need to light the LED safely? What would we need to know?

### How many electrons pass through the LED in one second? How can we figure this out?

Talk it over with your partner for one minute.

---
# Ohm's Law

`$$V = IR$$`

Where:
- `$V$` = voltage, in volts
- `$I$` = current, in amps
- `$R$` = resistance, in ohms (`$\Omega$`)

Solved for resistance, since we're picking `$R$`:

`$$R = \frac{V}{I}$$`

---
# LED datasheet

### Current
<img src="assets/led-current-datasheet.jpeg" alt="." width="100%"/>
---

### Voltage
<img src="assets/led-voltage-datasheet.jpg" alt="" width="100%"/>

---
# Sizing the resistor for an LED

The resistor only sees the voltage the LED *doesn't* use, and needs to pass the current we want the LED to run at:

`$$R = \frac{V_{supply} - V_{f}}{I_{LED}}$$`

**Worked example:** 5 V supply, red LED (`$V_f \approx 2.0\,\text{V}$`), target current 15 mA:

`$$R = \frac{5\,\text{V} - 2.0\,\text{V}}{0.015\,\text{A}} = \frac{3\,\text{V}}{0.015\,\text{A}} = 200\,\Omega$$`

We'll round **up** to the nearest resistor we actually have (e.g. 220 Ω) — rounding up means *less* current than calculated, which is the safe direction.

---

# Try it yourself

With your partner, calculate `$R$` for:

1. A 9 V supply, green LED (`$V_f = 2.1\,\text{V}$`), target current 15 mA.
2. A 5 V supply, blue LED (`$V_f = 3.0\,\text{V}$`), target current 20 mA.

Show your work in your notebook: the formula, the numbers plugged in, and the final answer rounded up to a standard resistor value.

---

# Reading a resistor: the color code

Resistors are too small to print numbers on, so they use **color bands** instead. A standard 4-band resistor:

- Band 1: 1st digit
- Band 2: 2nd digit
- Band 3: multiplier (how many zeros)
- Band 4: tolerance (how close to the stated value it actually is)

---

# Digit colors

<div style="line-height: 2.6;">
Black = 0
Brown = 1
Red = 2
Orange = 3
Yellow = 4
Green = 5
Blue = 6
Violet = 7
Gray = 8
White = 9
</div>

Band 3 (multiplier) reuses this same color scale as "×10^n" — Black is ×1, Brown is ×10, Red is ×100, and so on — plus two colors unique to the multiplier band:
Gold = ×0.1
Silver = ×0.01

---

# Worked example: reading a resistor

**Yellow – Violet – Red – Gold**

- Band 1 (Yellow) = 4
- Band 2 (Violet) = 7
- Band 3 (Red) = ×100
- Band 4 (Gold) = ±5% tolerance

`$$47 \times 100 = 4{,}700\,\Omega = 4.7\,\text{k}\Omega$$`

So this resistor is **4.7 kΩ, ±5%**.

---

# Your turn: decode these

Work in your notebook. For each, give the value in ohms and the tolerance.

1. Red – Red – Brown – Gold
2. Brown – Black – Orange – Gold
3. Green – Blue – Red – Silver
4. Orange – Orange – Black – Gold

*(Answers reviewed together before we start building.)*

---

# Video: reading resistor color bands

*Swap in your own video's embed link — copy the "Embed" URL from YouTube's Share menu and drop the ID after `/embed/`.*

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# Build: LED driver circuit

With your partner:

1. Pick an LED and read its likely `$V_f$` from the reference sheet.
2. Calculate the resistor value for a 5 V supply and 15 mA target current.
3. Find a resistor close to that value and **decode its bands** to confirm before you use it — don't trust the bin label.
4. Build the circuit on your breadboard: supply → resistor → LED (long leg to resistor) → ground.
5. Power on. It should light without getting hot.

---

# Measure & verify

Using the multimeter:

- Measure the actual voltage across the resistor.
- Measure the actual voltage across the LED.
- Calculate the actual current from the resistor's voltage and its resistance (`$I = V/R$`).

Record all three numbers in your notebook next to your prediction. If they don't match closely, that's not a failure — that's data. Where do you think the difference came from?

---
class: center, middle

# Homework

.hw-box[
- Finish decoding the four practice resistors if you didn't in class.
- In your notebook, write the LED driver formula from memory and explain each term.
- Bring your notebook and kit — next class we measure series and parallel networks.
]