Ohm’s Law is the foundation of electrical engineering and electronics. Discovered by German physicist Georg Ohm in 1827, it describes the fundamental relationship between voltage, current, and resistance in an electrical circuit. Whether you are wiring a home, designing a circuit board, building an LED project, or just trying to understand your electricity bill, Ohm’s Law is the starting point.
Ohm’s Law states that voltage equals current multiplied by resistance:
| Variable | Symbol | Unit | What It Measures |
|---|---|---|---|
| Voltage | V | Volts (V) | Electrical “pressure” pushing current through a circuit |
| Current | I | Amperes (A) | Flow rate of electric charge |
| Resistance | R | Ohms (Ω) | Opposition to current flow |
The formula can be rearranged to solve for any variable: V = I × R, I = V ÷ R, R = V ÷ I. Use the Ohm’s Law Calculator to solve any configuration instantly.
The water analogy: Think of voltage as water pressure, current as flow rate (gallons per minute), and resistance as the pipe diameter. Higher pressure (voltage) pushes more water (current) through a pipe. A narrower pipe (more resistance) reduces flow. This analogy is imperfect but helps build intuition for how the three quantities interact.
Finding current: A 12V battery powers a circuit with 4Ω resistance. How much current flows? I = V ÷ R = 12 ÷ 4 = 3 amperes.
Finding resistance: An LED requires 20 milliamps (0.020A) of current at 2V, powered by a 5V source. What resistor is needed? The resistor must drop the remaining voltage: 5V − 2V = 3V. R = V ÷ I = 3 ÷ 0.020 = 150Ω. Use the LED Resistor Calculator for quick LED circuit design.
Finding voltage: A toaster draws 10A through a heating element with 12Ω resistance. What voltage does it operate at? V = I × R = 10 × 12 = 120V — standard U.S. household voltage.
Electrical power measures the rate of energy consumption. It relates to Ohm’s Law through several equivalent formulas:
| Formula | When to Use | Example |
|---|---|---|
| P = V × I | You know voltage and current | 120V × 10A = 1,200W |
| P = I² × R | You know current and resistance | 10² × 12 = 1,200W |
| P = V² ÷ R | You know voltage and resistance | 120² ÷ 12 = 1,200W |
All three formulas give the same answer — choose whichever matches the variables you know. Power is measured in watts (W). 1,000 watts = 1 kilowatt (kW).
Resistors use colored bands to indicate their resistance value. Each color represents a digit or multiplier:
| Color | Digit | Multiplier |
|---|---|---|
| Black | 0 | ×1 |
| Brown | 1 | ×10 |
| Red | 2 | ×100 |
| Orange | 3 | ×1,000 |
| Yellow | 4 | ×10,000 |
| Green | 5 | ×100,000 |
| Blue | 6 | ×1,000,000 |
| Violet | 7 | — |
| Grey | 8 | — |
| White | 9 | — |
A resistor with brown-black-red bands reads: 1 (brown), 0 (black), ×100 (red) = 1,000Ω = 1kΩ. The Resistor Color Code Calculator decodes any resistor instantly.
In a series circuit, components are connected end-to-end. The same current flows through every component, and resistances add up directly: Rtotal = R1 + R2 + R3. Three 100Ω resistors in series give 300Ω total resistance. Voltage divides proportionally across each component based on its share of total resistance.
In a parallel circuit, components share the same voltage but current splits between paths. Total resistance follows: 1/Rtotal = 1/R1 + 1/R2 + 1/R3. Three 100Ω resistors in parallel give 1/R = 3/100, so R = 33.3Ω — lower than any individual resistor. This is why parallel circuits carry more current: adding parallel paths reduces overall resistance.
A standard U.S. household circuit is rated for 15 or 20 amps at 120 volts. Using Ohm’s Law, a 15-amp circuit can deliver P = 120 × 15 = 1,800 watts. Plugging in a 1,500W space heater and a 500W vacuum cleaner (2,000W total) on the same circuit exceeds the limit and will trip the breaker. Understanding this calculation prevents overloaded circuits and potential fire hazards.
A 9V battery with an internal capacity of 500 milliamp-hours (mAh) powering a device that draws 50mA will last approximately 500 ÷ 50 = 10 hours. If the device has 180Ω resistance, current draw is I = 9 ÷ 180 = 0.05A = 50mA, confirming the estimate. Reducing current draw (increasing resistance or reducing voltage demand) directly extends battery life.
Most cars use a 12V electrical system. A 60W headlight bulb draws I = P ÷ V = 60 ÷ 12 = 5 amps. Four headlights draw 20A. The car’s alternator must supply enough current for all electrical loads simultaneously: headlights, radio, AC blower motor, heated seats, and charging the battery. Modern vehicles have 100–200 amp alternators to handle these demands.
Mixing units. Ohm’s Law requires volts, amps, and ohms. Milliamps (mA) must be converted to amps (divide by 1,000) before plugging into formulas. 20mA = 0.020A, not 20A.
Ignoring internal resistance. Real batteries have internal resistance that reduces the voltage available to the circuit. A 9V battery under load might deliver only 8.5V due to internal resistance, affecting all calculations downstream.
Confusing series and parallel rules. Resistances add in series (total goes up) but combine reciprocally in parallel (total goes down). Mixing up these rules produces dramatically wrong results.
Calculate circuits instantly. Use the free Ohm’s Law Calculator for voltage, current, and resistance, the LED Resistor Calculator for LED projects, and the Resistor Color Code Calculator to decode resistors — no signup required.
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