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<h1>Ohm's Law</h1>
<p>Ohm's Law is the foundation of circuit analysis. It describes the relationship between voltage, current, and resistance — three quantities you'll be thinking about constantly in any electronics work. Formulated by Georg Simon Ohm in 1827, it's still the first tool you reach for when analysing any resistive circuit. Get comfortable with it early and everything else becomes easier.</p>

<h2>The Formula</h2>
<p>Three variables, one relationship:</p>
<pre>
V = I × R

V — voltage in volts (V)
I — current in amperes (A)
R — resistance in ohms (Ω)
</pre>
<p>Rearrange for whatever you're solving:</p>

<table>
  <thead><tr><th>Solving for</th><th>Formula</th><th>Use when you know</th></tr></thead>
  <tbody>
    <tr><td>Voltage (V)</td><td>V = I × R</td><td>Current and resistance</td></tr>
    <tr><td>Current (I)</td><td>I = V / R</td><td>Voltage and resistance</td></tr>
    <tr><td>Resistance (R)</td><td>R = V / I</td><td>Voltage and current</td></tr>
  </tbody>
</table>

<p>The triangle diagram is a common memory aid — cover the quantity you want and the arrangement of the remaining two tells you the formula:</p>

<svg viewBox="0 0 240 160" width="240" height="160" style="display:block;margin:1rem 0;" aria-label="Ohm's Law triangle">
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  <polygon points="120,10 20,150 220,150" fill="none" stroke="#9aacbe" stroke-width="2"/>
  <line x1="120" y1="80" x2="20" y2="80" stroke="#9aacbe" stroke-width="1.5" stroke-dasharray="4 3"/>
  <line x1="120" y1="80" x2="220" y2="80" stroke="#9aacbe" stroke-width="1.5"/>
  <line x1="120" y1="10" x2="120" y2="150" stroke="#9aacbe" stroke-width="1.5"/>
  <text x="120" y="55" text-anchor="middle" font-family="'Roboto Mono',monospace" font-size="22" font-weight="bold" fill="#7db85a">V</text>
  <text x="65" y="128" text-anchor="middle" font-family="'Roboto Mono',monospace" font-size="22" font-weight="bold" fill="#7eb8e0">I</text>
  <text x="175" y="128" text-anchor="middle" font-family="'Roboto Mono',monospace" font-size="22" font-weight="bold" fill="#f0aa3f">R</text>
  <text x="120" y="90" text-anchor="middle" font-family="'Roboto Mono',monospace" font-size="9" fill="#6b7a8d">cover to solve</text>
</svg>

<h2>What It's Actually Saying</h2>
<p>Voltage is pressure. Current is flow. Resistance is restriction. Ohm's Law says that if you push harder (more voltage) through the same restriction (same resistance), more current flows. If you narrow the restriction (more resistance) without changing the pressure, less flows. These relationships are linear and proportional — double the voltage, double the current. That linearity is what makes Ohm's Law so useful and so clean to work with.</p>

<h2>Units and Prefixes</h2>
<p>Real circuits rarely use bare volts, amps, and ohms — you'll encounter prefixed units constantly:</p>

<table>
  <thead><tr><th>Quantity</th><th>Unit</th><th>Common prefixes</th><th>Example</th></tr></thead>
  <tbody>
    <tr><td>Voltage</td><td>Volt (V)</td><td>mV (millivolts), kV</td><td>3.3 V logic, 12 mV noise floor</td></tr>
    <tr><td>Current</td><td>Ampere (A)</td><td>mA (milliamps), µA (microamps)</td><td>20 mA LED, 500 µA sleep current</td></tr>
    <tr><td>Resistance</td><td>Ohm (Ω)</td><td>kΩ (kilohms), MΩ (megohms)</td><td>10 kΩ pull-up, 1 MΩ input impedance</td></tr>
  </tbody>
</table>

<p>Always convert to base units before calculating: 20 mA = 0.02 A, 10 kΩ = 10,000 Ω. Forgetting this is the source of most arithmetic errors.</p>

<h2>Worked Examples</h2>

<table>
  <thead><tr><th>Problem</th><th>Known values</th><th>Formula</th><th>Answer</th></tr></thead>
  <tbody>
    <tr><td>Current through a 4Ω resistor on a 12V supply</td><td>V=12, R=4</td><td>I = V/R</td><td>3 A</td></tr>
    <tr><td>Voltage drop across 10Ω with 2A flowing</td><td>I=2, R=10</td><td>V = I×R</td><td>20 V</td></tr>
    <tr><td>Resistor to limit LED to 20mA on 5V (LED Vf=2V)</td><td>V=3, I=0.02</td><td>R = V/I</td><td>150 Ω → use 180 Ω</td></tr>
    <tr><td>Current draw of a 60W lamp on 120V AC</td><td>P=60, V=120</td><td>I = P/V</td><td>0.5 A</td></tr>
    <tr><td>Resistance of a wire with 0.1V drop at 1A</td><td>V=0.1, I=1</td><td>R = V/I</td><td>0.1 Ω</td></tr>
  </tbody>
</table>

<h2>Power</h2>
<p>Closely related to Ohm's Law — power dissipation matters whenever you're choosing components. Pick the wrong power rating and you'll have a smoking resistor:</p>
<pre>
P = V × I          (fundamental power formula)
P = I² × R        (when you know current and resistance)
P = V² / R        (when you know voltage and resistance)
</pre>

<table>
  <thead><tr><th>Scenario</th><th>Values</th><th>Power</th><th>Component needed</th></tr></thead>
  <tbody>
    <tr><td>100mA through 47Ω</td><td>I=0.1A, R=47Ω</td><td>0.47 W</td><td>1/2 W or 1 W resistor</td></tr>
    <tr><td>5V across 1kΩ</td><td>V=5, R=1000</td><td>25 mW</td><td>1/8 W resistor fine</td></tr>
    <tr><td>12V 500mA motor</td><td>V=12, I=0.5</td><td>6 W</td><td>MOSFET with adequate power rating</td></tr>
  </tbody>
</table>

<p>The rule: always calculate dissipation, then choose a component rated at least 2× that value. Heat degrades components over time even below the rated maximum.</p>

<h2>Series and Parallel Resistors</h2>
<p>Ohm's Law applies to individual components and to combinations:</p>
<pre>
Series (same current through each):
  R_total = R1 + R2 + R3 + ...
  V_total = V1 + V2 + V3 + ...

Parallel (same voltage across each):
  1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
  I_total = I1 + I2 + I3 + ...

Two resistors in parallel shortcut:
  R_total = (R1 × R2) / (R1 + R2)
</pre>

<h2>Where It Doesn't Apply</h2>
<p>Ohm's Law applies strictly to ohmic (resistive) components at constant temperature. These don't follow it:</p>

<table>
  <thead><tr><th>Component</th><th>Behavior</th><th>Why it's non-linear</th></tr></thead>
  <tbody>
    <tr><td>Diode / LED</td><td>Exponential I-V curve</td><td>Requires forward voltage threshold before conducting; ≈0.6–3.3V depending on type</td></tr>
    <tr><td>Transistor (BJT)</td><td>Current-controlled</td><td>Collector current is β × base current, not V/R</td></tr>
    <tr><td>Capacitor</td><td>Reactance (frequency-dependent)</td><td>Impedance = 1/(2πfC); drops at high frequency</td></tr>
    <tr><td>Inductor</td><td>Reactance (frequency-dependent)</td><td>Impedance = 2πfL; rises at high frequency</td></tr>
    <tr><td>Thermistor / bulb</td><td>Resistance changes with temperature</td><td>Technically ohmic at any instant, but R is not constant</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.allaboutcircuits.com/textbook/direct-current/chpt-2/voltage-current-resistance-relate/" target="_blank" rel="noopener">All About Circuits — DC Chapter 2 ↗</a></li>
</ul>
