Ohm's Law Explained: Voltage, Current, Resistance, and Power
Master Ohm's Law from first principles. Learn how voltage, current, resistance, and power interact, with clear formulas, worked examples, and a complete reference table.
Ohm's Law is the single most important relationship in all of electrical engineering. Once you understand it, circuit behavior transforms from mystery into a clear, predictable system. Whether you are a hobbyist building your first LED circuit or a licensed electrician sizing a sub-panel, these four quantities describe everything happening inside a conductor.
The Four Electrical Quantities
Every electrical circuit is completely described by four interacting quantities. You only ever need two of them to solve for the other two.
| Symbol | Quantity | Unit | Analogy |
|---|---|---|---|
| V | Voltage | Volts (V) | Water pressure |
| I | Current | Amperes (A) | Volume flow rate |
| R | Resistance | Ohms (Ω) | Pipe narrowness |
| P | Power | Watts (W) | Pressure × flow rate |
Think of a water pipe: voltage is the pressure pushing water through, current is how much flows per second, resistance is how narrow the pipe is, and power is the total work done by moving that water.
Ohm's Law: The Core Formula
The fundamental relationship, published by Georg Simon Ohm in 1827:
V = I × R
Rearranged to solve for any variable:
- Voltage: V = I × R
- Current: I = V / R
- Resistance: R = V / I
Worked Example 1
A 12V battery drives current through a 6-ohm resistor. How much current flows?
I = V / R = 12 / 6 = 2 Amperes
Worked Example 2
A circuit draws 5A from a 120V source. What is the total resistance?
R = V / I = 120 / 5 = 24 Ohms
The Power Equation
P = V × I
Combining this with Ohm's Law gives all 12 derived formulas:
| To Find | Using V + I | Using V + R | Using I + R |
|---|---|---|---|
| V | — | V = I × R | V = P / I |
| I | I = P / V | I = V / R | — |
| R | R = V² / P | — | R = P / I² |
| P | P = V × I | P = V² / R | P = I² × R |
Why Resistance Creates Heat
When current forces its way through resistance, energy dissipates as heat (Joule's First Law):
Q = I² × R × t
Where Q is heat in Joules, I is current in Amps, R is resistance in Ohms, and t is time in seconds. This is why undersized wires overheat and why circuit breakers protect against overloads.
Practical Example: LED Resistor Sizing
Given a 9V source, LED forward voltage 2.1V, desired current 20 mA:
- Voltage across resistor: 9 - 2.1 = 6.9V
- Required resistance: R = 6.9 / 0.020 = 345 Ω → use 330 Ω or 360 Ω standard
- Power dissipated: P = 0.020² × 345 = 0.138 W → safe with a 1/4W resistor
Quick Reference Table
| Voltage (V) | Current (A) | Resistance (Ω) | Power (W) |
|---|---|---|---|
| 5 V | 1 A | 5 Ω | 5 W |
| 12 V | 2 A | 6 Ω | 24 W |
| 24 V | 4 A | 6 Ω | 96 W |
| 120 V | 10 A | 12 Ω | 1,200 W |
| 120 V | 15 A | 8 Ω | 1,800 W |
| 240 V | 20 A | 12 Ω | 4,800 W |
Use our Ohm's Law Calculator to solve any combination instantly.
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