Ohm's Law

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.

The Formula

Three variables, one relationship:

V = I × R

V — voltage in volts (V)
I — current in amperes (A)
R — resistance in ohms (Ω)

Rearrange for whatever you're solving:

Solving for	Formula	Use when you know
Voltage (V)	V = I × R	Current and resistance
Current (I)	I = V / R	Voltage and resistance
Resistance (R)	R = V / I	Voltage and current

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

What It's Actually Saying

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.

Units and Prefixes

Real circuits rarely use bare volts, amps, and ohms — you'll encounter prefixed units constantly:

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

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.

Worked Examples

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

Power

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 = V × I          (fundamental power formula)
P = I² × R        (when you know current and resistance)
P = V² / R        (when you know voltage and resistance)

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

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.

Series and Parallel Resistors

Ohm's Law applies to individual components and to combinations:

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)

Where It Doesn't Apply

Ohm's Law applies strictly to ohmic (resistive) components at constant temperature. These don't follow it:

Component	Behavior	Why it's non-linear
Diode / LED	Exponential I-V curve	Requires forward voltage threshold before conducting; ≈0.6–3.3V depending on type
Transistor (BJT)	Current-controlled	Collector current is β × base current, not V/R
Capacitor	Reactance (frequency-dependent)	Impedance = 1/(2πfC); drops at high frequency
Inductor	Reactance (frequency-dependent)	Impedance = 2πfL; rises at high frequency
Thermistor / bulb	Resistance changes with temperature	Technically ohmic at any instant, but R is not constant

References

• Horowitz & Hill — The Art of Electronics, 3rd ed. Chapter 1
• Scherz & Monk — Practical Electronics for Inventors, 4th ed.
• All About Circuits — DC Chapter 2 ↗