The Great Restrictor: Mastering Resistance & Ohm's Law

The Build

Let’s wire this up.

1. Components: 9V Battery, Breadboard, LED, Resistor.
2. Circuit:
   • Battery Positive (+) to Resistor.
   • Resistor to LED Anode (+, Long Leg).
   • LED Cathode (-, Short Leg) to Battery Negative (-).

Why this order? It actually doesn’t matter! The resistor can go before or after the LED. The current is the same everywhere in the loop (Day 2 Lesson!).

Step-by-Step

1. Snap your 9V battery into the power rails of the breadboard.
2. Insert the LED. remember which leg is which!
3. Bridge the gap between power and LED with your resistor.
4. LIGHT!

Verification: The Multimeter Test

Science isn’t about trusting math; it’s about verifying it.

Set your Multimeter to DC Current (A or mA mode). Remember Day 2? You must break the circuit to measure current.

1. Disconnect the wire going to the LED.
2. Put your Red Probe on the wire.
3. Put your Black Probe on the LED leg.
4. The current flows through your meter.

The Reading: If you used a $330\Omega$ resistor, you should see roughly: $I = 7V / 330\Omega = 0.021A$ or 21mA.

If you see 0.021, you have successfully manipulated the laws of physics to your will.

Advanced Concept: Series vs Parallel Resistance

Resistors behave very differently depending on how you connect them. This is the foundation of all circuit design.

Series Circuits (The Queue)

When you connect resistors end-to-end, they form a single path. The electrons have to trudge through the first resistor, and then the second one. It is like adding more kinks to the same hose. The resistance adds up.

$R_{total} = R_1 + R_2 + R_3 \dots$

Example: If you have two $220\Omega$ resistors in series: $R_{total} = 220 + 220 = 440\Omega$. This is useful if you don’t have the exact resistor value you need. Need $440\Omega$? Just chain two $220\Omega$s together!

Parallel Circuits (The Multi-Lane Highway)

When you connect resistors side-by-side, you create multiple paths for the electrons to flow. It is like opening a second lane on a highway. Even if the second lane is narrow (high resistance), it still improves the total traffic flow. Therefore, adding a resistor in parallel decreases the total resistance.

Formula: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}$

Example: Two $220\Omega$ resistors in parallel. $\frac{1}{R_{total}} = \frac{1}{220} + \frac{1}{220} = \frac{2}{220}$ $R_{total} = 110\Omega$ It cuts the resistance in half!

The Danger Zone: Power Rating (Wattage)

We mentioned that resistors convert electrical energy into heat. But how much heat can they handle? This is measured in Watts. Standard resistors in your kit are rated for 1/4 Watt (0.25W).

If you push more power than that, they will smoke, turn black, and fail (usually open circuit).

Calculating Power

$P = I \times V$ Substituting Ohm’s Law ($V=IR$), we get the two most useful forms:

1. $P = I^2 \times R$ (Use this if you know Current)
2. $P = V^2 / R$ (Use this if you know Voltage)

Let’s check our LED circuit:

• Current ($I$) = 0.021A
• Resistance ($R$) = $330\Omega$ $P = 0.021^2 \times 330$ $P = 0.000441 \times 330$ $P = 0.145 \text{ Watts}$

Verdict: $0.145W$ is less than $0.25W$. You are safe! But if you used a $10\Omega$ resistor at 9V… $P = 9^2 / 10 = 81 / 10 = 8.1 \text{ Watts}$ Result: Instant fire. Always check the wattage.

Know Your Tools: Types of Resistors

Not all resistors are created equal.

1. Carbon Film (Beige)

• Pros: Cheap, common.
• Cons: Noisy (electrically), not very precise (5% tolerance).
• Use: General purpose, LED limiting, pull-ups.

2. Metal Film (Blue)

• Pros: Precise (1% tolerance), stable, low noise.
• Cons: Slightly more expensive (cents vs fractions of cents).
• Use: Audio circuits, delicate sensors, amplifiers.

3. Wirewound (Cement/White)

• Pros: Can handle massive power (5W, 10W, 50W).
• Cons: Bulky, acts like an inductor (bad for high speed signals).
• Use: Power supplies, motor braking, heating elements.

Decoding the Bands (4-Band Code)

You don’t need to memorize this, but you should understand how to read it.

Example: Red - Red - Brown - Gold

• 1st Digit: Red (2)
• 2nd Digit: Red (2)
• Multiplier: Brown (x10)
• Tolerance: Gold (5%) Result: $22 \times 10 = 220\Omega$ (with $\pm 5\%$ precision).

Logic Essentials: Pull-up & Pull-down Resistors

This is a concept that confuses every beginner, but it is crucial for Arduino buttons.

The Floating Pin Problem: If you have an Arduino pin connected to a button, and the button is not pressed… what is the voltage? Is it 0V? Is it 5V? Answer: Neither. It is “floating”. It acts like an antenna, picking up static noise from the air. Your Arduino will read random 1s and 0s.

The Solution: We use a resistor (usually $10k\Omega$) to “pull” the voltage to a known state when the button is open.

1. Pull-Down: Connects the pin to GND through 10k.
   • Button Open: Pin reads LOW (held by resistor).
   • Button Closed: Pin reads HIGH (connected to 5V).
2. Pull-Up: Connects the pin to 5V through 10k.
   • Button Open: Pin reads HIGH (held by resistor).
   • Button Closed: Pin reads LOW (connected to GND).

Without these resistors, digital logic simply does not work.

Troubleshooting: When Resistors Go Bad

Resistors are generally reliable, but they do fail.

1. Open Circuit (Infinite $\Omega$): The most common failure. Usually caused by overpowering (burning out). The current stops completely.
2. Drift: Over time and with heat, the resistance value can change. A $100\Omega$ resistor might become $110\Omega$. In precise audio circuits, this ruins the sound.
3. Noise: Carbon resistors generate “Johnson Noise” due to thermal agitation. In high-gain microphone preamps, this sounds like a faint “hiss”. Metal film resistors are used to fix this.

// Simple Arduino Ohmmeter
// Connect Known Resistor (1k) between 5V and A0
// Connect Unknown Resistor between A0 and GND

const int sensorPin = A0;  // The middle of the voltage divider
const float Vin = 5.0;     // Input voltage
const float R_known = 1000.0; // Value of the known resistor (1k)

void setup() {
  Serial.begin(9600);
  Serial.println("Resistance Meter Ready...");
}

void loop() {
  int rawValue = analogRead(sensorPin);
  
  // Convert 0-1023 range to 0-5V
  float Vout = rawValue * (Vin / 1023.0);
  
  // Prevent division by zero if nothing is connected
  if (Vout > 0.1) {
    // Calculate Unknown Resistance
    float R_unknown = (Vout * R_known) / (Vin - Vout);
    
    Serial.print("Vout: ");
    Serial.print(Vout);
    Serial.print("V | Resistance: ");
    Serial.print(R_unknown);
    Serial.println(" Ohms");
  } else {
    Serial.println("No Resistor detected.");
  }
  
  delay(1000); // Update every second
}