Every time you flip a light switch, charge a phone, or dim a lamp, Ohm's Law is quietly doing the math. Here's what it actually says — and why it matters.
In 1827, German physicist Georg Simon Ohm published the relationship between voltage, current and resistance. It became known as Ohm's Law, and it remains the single most useful equation in electronics — the foundation for designing circuits, choosing components, and understanding what happens inside anything that plugs in.
Voltage
The electrical push that drives charge around a circuit. Measured in volts (V).
Current
The rate at which charge flows through a component. Measured in amperes (A).
Resistance
How strongly a component opposes the flow of current. Measured in ohms (Ω).
What Is Ohm's Law?
V = I × ROhm's Law states that the current through a conductor between two points is directly proportional to the voltage across those two points, and inversely proportional to the resistance between them. In plain words: push harder and more flows; make the path harder and less flows.
The law holds for ohmic conductors — metallic wires and resistors at constant temperature — where resistance stays fixed. Components like diodes and filament lamps have resistance that changes with voltage or temperature, so they don't follow a straight-line rule.
Rearranged, the same relationship gives current from voltage and resistance, or resistance from voltage and current:
Try it below: adjust the voltage and resistance, and watch the current — and the flow of charge in the diagram — respond instantly.
The moving dots represent charge carriers. More voltage or less resistance means more current — exactly as Ohm's Law predicts.
Voltage, Current & Resistance Explained
These three quantities are easy to mix up. The cleanest way to tell them apart is to think about what each one actually measures.
- Voltage (V) — the energy transferred per unit charge, or the "electrical pressure" driving the current. A 9 V battery provides more push than a 1.5 V cell.
- Current (I) — the number of coulombs of charge passing a point per second. It's the flow rate, not the energy.
- Resistance (R) — a measure of how much a component restricts current for a given voltage. High resistance means less current for the same push.
Imagine water flowing through a pipe: voltage is the pump pressure, current is the flow rate, and resistance is the narrowness of the pipe. Squeeze the pipe and less water flows for the same pressure — that's increasing resistance.
Units at a glance
| Quantity | Symbol | Unit | Unit abbreviation |
|---|---|---|---|
| Voltage | V | volt | V |
| Current | I | ampere | A |
| Resistance | R | ohm | Ω |
The V-I Graph
Plot voltage on the vertical axis against current on the horizontal axis. For a component obeying Ohm's Law, the result is a straight line through the origin — the signature of proportionality.
The gradient of that line equals the resistance. A steeper line means a higher resistance: more volts are needed for each ampere. A shallower line means a lower resistance and a bigger current for the same voltage.
| Voltage (V) | Resistance (Ω) | Current (A) | What changed |
|---|---|---|---|
| 6 | 6 | 1.0 | Baseline case |
| 12 | 6 | 2.0 | Voltage doubled → current doubled |
| 12 | 12 | 1.0 | Resistance doubled → current halved |
| 24 | 12 | 2.0 | Both doubled → current unchanged |
A filament lamp's resistance rises as it heats up, so its V-I graph curves. A diode conducts in only one direction and has a sharp turn-on voltage. These components still follow physics — they just don't obey Ohm's Law because their resistance isn't constant.
Ohm's Law Worked Examples
These three examples cover the standard ways Ohm's Law shows up in problems and in real circuit design.
Example 1 — finding current
A 12 V battery is connected across a 4 Ω resistor. What current flows?
- Start from the rearranged formula: I = V / R
- Substitute the values: I = 12 V ÷ 4 Ω
- Solve: I = 3 A
Example 2 — finding resistance
A current of 0.5 A flows when 6 V is applied across a component. What is its resistance?
- Start from the rearranged formula: R = V / I
- Substitute the values: R = 6 V ÷ 0.5 A
- Solve: R = 12 Ω
Example 3 — finding voltage
A 2 A current flows through a 15 Ω resistor. What voltage is across it?
- Start from the base formula: V = I × R
- Substitute the values: V = 2 A × 15 Ω
- Solve: V = 30 V
An LED rated at 2 V and 20 mA needs to run from a 9 V supply. The resistor must drop 7 V at 0.02 A, so R = 7 ÷ 0.02 = 350 Ω. This is Ohm's Law doing real design work.
Ohm's Law in Series & Parallel Circuits
Ohm's Law applies to individual components and to whole circuits — but the rules for combining resistances depend on how components are wired.
- Series: resistances add directly. The same current flows through every component, and the supply voltage is divided across them.
- Parallel: the total resistance is less than the smallest individual resistance. The voltage is the same across every branch, and the current splits between them.
| Circuit type | Resistance rule | Current | Voltage |
|---|---|---|---|
| Series | R total = R₁ + R₂ + … | Same through each component | Divided across components |
| Parallel | 1/R total = 1/R₁ + 1/R₂ + … | Splits between branches | Same across each branch |
Real-World Applications of Ohm's Law
Ohm's Law isn't just a classroom formula — it's the basis for how electrical systems are designed, protected and controlled.
- Fuses and circuit breakers: sized by the current they must carry, calculated from the supply voltage and circuit resistance.
- Household wiring: cable thickness is chosen so resistance stays low enough to deliver current without dangerous heating.
- Dimmer switches: vary resistance to change current, which changes the brightness of a lamp.
- Electric heaters: a high-resistance element draws a controlled current, converting electrical energy into heat.
- Battery selection: matching a battery's internal resistance to a device avoids excessive voltage drop under load.
- Sensors and strain gauges: tiny resistance changes are read as voltage changes using Ohm's Law.
Ohm's Law is an excellent approximation for most conductors at constant temperature, but it is not a fundamental law of nature. Semiconductors, superconductors and plasma all behave differently — yet even there, the relationship between voltage, current and resistance remains a starting point for analysis.