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.
Ohm’s Law states that voltage equals current multiplied by resistance: V = IR. It was published by Georg Ohm in 1827, it’s the single most-used calculation in pedal building, and every resistor value you pick and every bias point in a fuzz or overdrive circuit traces back to this one equation. Before working with it directly, though, there’s a notational fluency every pedal schematic assumes you already have.
Unit prefixes: reading pF to MΩ without losing a zero
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.
(The LED current-limiting calculation — the other classic first use of Ohm’s Law — is covered in the Assembly book, 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.