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<h1>Resistors</h1>
<p>Resistors are the most common component in electronics — passive, two-terminal, and indifferent to polarity. They resist current flow, and by controlling current you control voltage drops, set bias points, protect other components, and build voltage dividers. There is almost no circuit that doesn't have at least one. Understanding resistors well means understanding a large portion of circuit behaviour.</p>

<h2>Types</h2>

<table>
  <thead><tr><th>Type</th><th>Adjustable?</th><th>Notes</th><th>Typical use</th></tr></thead>
  <tbody>
    <tr><td>Carbon film</td><td>No</td><td>Cheap, ±5–10% tolerance, noisy</td><td>Non-critical applications, rough prototyping</td></tr>
    <tr><td>Metal film</td><td>No</td><td>Better tolerance (±1%), lower noise, stable with temperature</td><td>Default for most signal work</td></tr>
    <tr><td>Wirewound</td><td>No</td><td>High power handling, but inductive — bad for RF</td><td>Power supplies, loads, high-wattage applications</td></tr>
    <tr><td>Potentiometer</td><td>Yes (continuous)</td><td>Three terminals — two ends and a wiper</td><td>Volume controls, user-adjustable bias</td></tr>
    <tr><td>Trimmer (trimpot)</td><td>Yes (one-time)</td><td>Screwdriver-adjustable, not meant for frequent use</td><td>Factory calibration, offset adjustment</td></tr>
    <tr><td>Thermistor (NTC)</td><td>No (temperature-dependent)</td><td>Resistance drops as temperature rises</td><td>Temperature sensing, inrush limiting</td></tr>
    <tr><td>Thermistor (PTC)</td><td>No (temperature-dependent)</td><td>Resistance rises with temperature — self-limiting</td><td>Overcurrent protection, resettable fuse</td></tr>
    <tr><td>LDR (photoresistor)</td><td>No (light-dependent)</td><td>Slow response, not for precision work</td><td>Simple light sensing, dusk/dawn switching</td></tr>
  </tbody>
</table>

<h2>Reading the Colour Code</h2>
<p>Through-hole resistors have coloured bands. The standard 4-band system encodes the value as two significant digits, a multiplier, and a tolerance band:</p>

<table>
  <thead><tr><th>Colour</th><th>Digit</th><th>Multiplier</th><th>Tolerance</th></tr></thead>
  <tbody>
    <tr><td>Black</td><td>0</td><td>×1</td><td>—</td></tr>
    <tr><td>Brown</td><td>1</td><td>×10</td><td>±1%</td></tr>
    <tr><td>Red</td><td>2</td><td>×100</td><td>±2%</td></tr>
    <tr><td>Orange</td><td>3</td><td>×1,000</td><td>—</td></tr>
    <tr><td>Yellow</td><td>4</td><td>×10,000</td><td>—</td></tr>
    <tr><td>Green</td><td>5</td><td>×100,000</td><td>±0.5%</td></tr>
    <tr><td>Blue</td><td>6</td><td>×1,000,000</td><td>±0.25%</td></tr>
    <tr><td>Violet</td><td>7</td><td>—</td><td>±0.1%</td></tr>
    <tr><td>Grey</td><td>8</td><td>—</td><td>±0.05%</td></tr>
    <tr><td>White</td><td>9</td><td>—</td><td>—</td></tr>
    <tr><td>Gold</td><td>—</td><td>×0.1</td><td>±5%</td></tr>
    <tr><td>Silver</td><td>—</td><td>×0.01</td><td>±10%</td></tr>
  </tbody>
</table>

<p>Example: <strong>Brown–Black–Red–Gold</strong> = 1, 0, ×100, ±5% = <strong>1,000 Ω (1 kΩ) ±5%</strong></p>
<p>In practice, just use a multimeter. Reading bands under poor lighting with colour-blind eyes is how mistakes happen. Measure first, trust the bands second.</p>

<h2>SMD Resistor Codes</h2>
<p>Surface-mount resistors use a different system — numbers printed directly on the package:</p>
<pre>
3-digit code: first two digits are significant figures, third is the multiplier exponent
  102 → 10 × 10² = 1,000 Ω (1 kΩ)
  471 → 47 × 10¹ = 470 Ω
  330 → 33 × 10⁰ = 33 Ω

4-digit code (±1% precision parts):
  1002 → 100 × 10² = 10,000 Ω (10 kΩ)
  4701 → 470 × 10¹ = 4,700 Ω (4.7 kΩ)

EIA-96 code (used on 0402/0201 parts — letter + two digits):
  01C → value 100 × multiplier C (×10) = 1,000 Ω
</pre>

<h2>Standard E-Series Values</h2>
<p>Resistors don't come in every value. The E-series defines a set of standard preferred values per decade:</p>

<table>
  <thead><tr><th>Series</th><th>Steps/decade</th><th>Tolerance</th><th>Values (×1 decade)</th></tr></thead>
  <tbody>
    <tr><td>E6</td><td>6</td><td>±20%</td><td>1.0, 1.5, 2.2, 3.3, 4.7, 6.8</td></tr>
    <tr><td>E12</td><td>12</td><td>±10%</td><td>1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2</td></tr>
    <tr><td>E24</td><td>24</td><td>±5%</td><td>Includes E12 + 1.1, 1.3, 1.6, 2.0, 2.4, 3.0, 3.6, 4.3, 5.1, 6.2, 7.5, 9.1</td></tr>
    <tr><td>E96</td><td>96</td><td>±1%</td><td>Precision work — full table in datasheets</td></tr>
    <tr><td>E192</td><td>192</td><td>±0.5%</td><td>High-precision instrumentation</td></tr>
  </tbody>
</table>

<p>When you calculate a needed resistance, round to the nearest standard value. If your calculation gives 237 Ω, use 240 Ω (E24) or 220 Ω depending on which direction is safer for your circuit.</p>

<h2>Power Rating</h2>
<p>Every resistor has a maximum power dissipation. Exceed it and the component overheats, drifts in value, and eventually fails — sometimes with smoke and a scorched PCB. The formula:</p>
<pre>
P = I² × R   or   P = V² / R   or   P = V × I
</pre>

<table>
  <thead><tr><th>Rating</th><th>Physical size</th><th>Typical application</th></tr></thead>
  <tbody>
    <tr><td>1/8 W</td><td>Small through-hole, most SMD</td><td>Signal circuits, low-current biasing</td></tr>
    <tr><td>1/4 W</td><td>Standard through-hole</td><td>General purpose — the default choice</td></tr>
    <tr><td>1/2 W</td><td>Larger through-hole</td><td>Moderate current, LED drivers, regulators</td></tr>
    <tr><td>1 W</td><td>Large through-hole or TO-220 mount</td><td>Higher current loads, power supplies</td></tr>
    <tr><td>2 W+</td><td>Wirewound or chassis-mount</td><td>Dummy loads, power dissipation, braking resistors</td></tr>
  </tbody>
</table>

<p><strong>Rule of thumb:</strong> derate to 50%. If you calculate 0.47 W, use a 1 W rated resistor. Running at the rated maximum shortens lifespan significantly.</p>

<h2>Common Circuit Applications</h2>

<h3>Current Limiting</h3>
<p>The most common use — protecting an LED or other component:</p>
<pre>
Supply: 5V
LED forward voltage (Vf): 2V
Desired current: 20mA

R = (V_supply - V_LED) / I
R = (5V - 2V) / 0.02A = 150Ω → use 150Ω or 180Ω

Power: P = I² × R = (0.02)² × 150 = 0.06W → 1/8W resistor is fine
</pre>

<h3>Voltage Divider</h3>
<p>Two resistors in series divide a voltage proportionally:</p>
<pre>
       Vin
        |
       [R1]
        |
       Vout ←── measured here
        |
       [R2]
        |
       GND

Vout = Vin × R2 / (R1 + R2)

Example: Vin=12V, R1=10kΩ, R2=10kΩ
Vout = 12 × (10k / 20k) = 6V
</pre>
<p>Voltage dividers only work well when the load impedance is much higher than the divider resistance (typically 10× or more). If the load draws significant current, the output voltage drops from the calculated value.</p>

<h3>Pull-up and Pull-down</h3>
<p>Ensures a digital pin has a defined logic state when nothing is actively driving it:</p>
<pre>
Pull-up:   resistor from VCC to the pin → pin reads HIGH when floating
Pull-down: resistor from pin to GND    → pin reads LOW when floating

Typical values: 4.7 kΩ to 10 kΩ
Lower values = stronger pull, more current, better noise immunity
Higher values = weaker pull, less current, may be too slow for fast signals
</pre>

<h2>Tolerance in Practice</h2>

<table>
  <thead><tr><th>Tolerance</th><th>Series</th><th>When it matters</th></tr></thead>
  <tbody>
    <tr><td>±20%</td><td>E6</td><td>Almost never acceptable in signal work. Fine for bulk current limiting.</td></tr>
    <tr><td>±10%</td><td>E12</td><td>Acceptable for non-critical applications</td></tr>
    <tr><td>±5%</td><td>E24</td><td>General purpose default — what most hobby kits use</td></tr>
    <tr><td>±1%</td><td>E96</td><td>Precision analog, feedback networks, reference circuits</td></tr>
    <tr><td>±0.1%</td><td>E192</td><td>Instrumentation, metering, high-precision ADC input dividers</td></tr>
  </tbody>
</table>

<h2>References</h2>
<ul>
  <li>Horowitz &amp; Hill — <em>The Art of Electronics</em>, 3rd ed. Chapter 1</li>
  <li>Scherz &amp; Monk — <em>Practical Electronics for Inventors</em>, 4th ed.</li>
  <li><a href="https://www.resistorguide.com/" target="_blank" rel="noopener">ResistorGuide.com — comprehensive resistor reference ↗</a></li>
  <li><a href="https://eepower.com/resistor-guide/resistor-standards-and-codes/resistor-color-code/" target="_blank" rel="noopener">EEPower — colour code reference ↗</a></li>
</ul>
