Ohm's Law: Voltage, Current and Resistance

If you learn only one equation in electricity, make it Ohm's law. It connects the three most fundamental quantities in any electrical circuit — voltage, current and resistance — and it underlies the design of virtually every electronic device you own.

The three quantities

To understand Ohm's law, picture electric charge flowing through a wire like water flowing through a pipe. Voltage is the pressure pushing the charge along, measured in volts. Current is the rate at which charge flows, measured in amperes. Resistance is how much the wire opposes that flow, measured in ohms. A narrow, restrictive pipe is like a high resistance; a wide, open one is a low resistance.

The law

Ohm's law states that the voltage across a conductor equals the current through it multiplied by its resistance:

From this one relationship you can find any of the three quantities if you know the other two. Rearranged, current equals voltage divided by resistance — which tells you that for a fixed voltage, more resistance means less current. Increase the push or lower the resistance, and more current flows.

A worked example

Suppose a 9-volt battery is connected across a 300-ohm resistor. How much current flows? Rearranging Ohm's law, current equals voltage divided by resistance: 9 divided by 300, which is 0.03 amperes, or 30 milliamperes. If you swapped in a 100-ohm resistor instead, the current would triple to 90 milliamperes — lower resistance, more flow.

Power in circuits

Ohm's law pairs naturally with the electrical power equation. Power — the rate at which electrical energy is converted to heat, light or motion — equals voltage times current. Combining this with Ohm's law gives several useful forms, including power equals current squared times resistance. This is why a short circuit (very low resistance) draws an enormous current and can generate dangerous heat, and why electrical engineers care so much about resistance in high-current systems.

Ohmic and non-ohmic materials

Ohm's law is not a universal law of nature in the way Newton's laws are — it is a property that many materials happen to obey. A material is called "ohmic" if its resistance stays constant regardless of the voltage applied; ordinary metal wires are a good example. But many components are "non-ohmic": the resistance of a filament lamp rises as it heats up, and a diode lets current flow easily in one direction while blocking it in the other. For these, the simple straight-line relationship breaks down, though Ohm's law still describes each instant locally.

Series and parallel

Real circuits combine many resistors. When resistors are placed in series, one after another, their resistances simply add up, and the same current flows through all of them. When they are placed in parallel, side by side, the total resistance is less than any individual one, because the current has multiple paths to take. These two rules, built on Ohm's law, let engineers analyse circuits of almost any complexity.

Why it matters

Every time you choose a resistor to protect an LED, size a fuse, or work out why a device runs hot, you are using Ohm's law. It is the first tool reached for in electronics, the bridge between the abstract idea of voltage and the practical reality of current and heat. Simple as it is, it never stops being useful.

Key takeaways

• Voltage is electrical pressure, current is rate of flow, resistance is opposition to flow.
• Ohm's law, V = IR, links all three; rearrange it to find any one.
• Electrical power equals voltage times current, explaining heat in circuits.
• Ohmic materials have constant resistance; many real components do not.