Ohm's Law and Basic Circuit Theory
Ohm's Law (V = IR) relates voltage, current, and resistance in any circuit. This chapter covers the three forms of the equation, how power dissipation follows from it, and why it's the single most-used calculation in pedal building.
Unit prefixes: reading pF to MΩ without losing a zero
Before Ohm’s Law itself, one fluency the rest of this book assumes: component values are almost never written as a plain number of ohms or farads, they’re written with a prefix that shifts the decimal point by a factor of 1,000. Capacitors climb pF → nF → µF (picofarads to nanofarads to microfarads); resistors climb Ω → kΩ → MΩ (ohms to kilohms to megohms). Each arrow is ×1,000 in the same direction: 1,000pF = 1nF, 1,000nF = 1µF, and likewise 1,000Ω = 1kΩ, 1,000kΩ = 1MΩ. Misreading a value by one prefix — treating a 100nF capacitor as 100µF, or a 4.7kΩ resistor as 4.7Ω — is an error of three orders of magnitude, and it’s the single most common invisible beginner mistake, because the digits look identical and only the letter changed.
Ohm’s Law states that voltage equals current multiplied by resistance: V = IR. Every resistor value you pick and every bias point in a fuzz or overdrive circuit traces back to this one equation. It was published by Georg Ohm in 1827 and remains the starting point for reading any pedal schematic. (The LED current-limiting calculation — the other classic first use of this equation — is covered in book two, alongside the rest of footswitch and indicator wiring, once there’s an actual LED circuit on the page to apply it to.)
The three forms of V = IR
The equation rearranges into three usable forms depending on which two values you already know:
- V = I × R — find voltage when you know current and resistance
- I = V / R — find current when you know voltage and resistance
- R = V / I — find resistance when you know voltage and current
A 9V pedal circuit pulling 5mA through a 1kΩ resistor drops V = 0.005A × 1000Ω = 5V across that resistor. That single calculation is how you check whether a transistor’s bias point sits where a schematic says it should.
Power dissipation follows directly from Ohm’s Law
Power in watts is P = V × I, and substituting Ohm’s Law gives two more useful forms: P = I²R and P = V²/R. This matters when picking resistor wattage ratings — a standard pedal build uses 1/4-watt resistors, and exceeding that rating (rare in 9V circuits, common in tube-adjacent builds) causes the resistor to overheat and drift or fail.
Why this matters before touching a soldering iron
Every subsequent Fundamentals chapter assumes fluency with these three forms. Resistors and capacitors covers how resistance values are chosen in practice; reading schematics assumes you can mentally check a bias voltage against a resistor value without stopping to look up the formula.
Common mistake: confusing series and parallel resistance
Ohm’s Law applies to a single resistor or a single equivalent resistance — it does not by itself tell you how to combine multiple resistors. Series resistors add directly (R_total = R1 + R2 + …). Parallel resistors combine as 1/R_total = 1/R1 + 1/R2 + …. Applying V = IR to the wrong equivalent resistance is the most common arithmetic error in early schematic-reading, and it silently produces a bias point that’s off by a factor of two or more.