Ohm's law

Ohm’s law is the single most useful relationship in all of electronics. It ties together the three quantities you measure constantly on a bench: voltage, current and resistance. Once you internalise it, you can predict how much current a part will draw, size a resistor, or work out why a component is getting hot.

The three quantities

Voltage (V), measured in volts, is the electrical potential difference that pushes charge around a circuit. A useful mental model is water pressure from a pump or the height of a raised tank.

Current (I), measured in amperes, is the rate at which charge flows past a point. One ampere is one coulomb of charge per second. In the water analogy it is the litres-per-second flowing through a pipe.

Resistance (R), measured in ohms (Ω), opposes that flow. A high-resistance part is like a narrow, constricted pipe; for the same pressure, less flows through.

The core equation

Ohm’s law states these three are linked by:

V = I x R

That is, the voltage across a component equals the current through it multiplied by its resistance. The equation rearranges three ways, and being fluent in all three is what makes it practical:

• Current: I = V / R
• Resistance: R = V / I
• Voltage: V = I x R

For example, place 12 V across a 6 Ω resistor and the current is I = 12 / 6 = 2 A. If instead you measure 5 V producing 0.25 A, the resistance must be R = 5 / 0.25 = 20 Ω.

Proportionality and the V-I graph

For an ohmic component, resistance stays constant, so current is directly proportional to voltage. Double the voltage and you double the current. If you plot voltage against current, you get a straight line through the origin, and its gradient is the resistance.

Not everything behaves this way. A filament lamp grows hotter as more current flows, raising its resistance, so its graph curves. A diode conducts freely in one direction and blocks the other, giving a sharply bent curve. These are non-ohmic components, and Ohm’s law only describes them at a single operating point, not across their whole range.

Power: where the energy goes

Current flowing through resistance transfers energy, usually as heat. The rate of that transfer is power, measured in watts (W):

P = V x I

So a device at 12 V drawing 2 A dissipates P = 12 x 2 = 24 W. By substituting Ohm’s law you get two more forms that are often more convenient:

• P = I^2 x R — use it when you know the current and resistance
• P = V^2 / R — use it when you know the voltage and resistance

These matter for component ratings. A resistor is sold with a power rating (a common through-hole part is rated 0.25 W). If your calculation says it will dissipate more than that, it will overheat and may char or fail. Suppose a 3 A current flows through a 4 Ω resistor: P = I^2 x R = 9 x 4 = 36 W. That part needs to be a chunky wirewound resistor with a heatsink, not a tiny 0.25 W one.

A complete worked example

A 9 V battery is connected across a 3 Ω load.

1. Current: I = V / R = 9 / 3 = 3 A
2. Power: P = V x I = 9 x 3 = 27 W

You can cross-check the power with a different form: P = I^2 x R = 3^2 x 3 = 9 x 3 = 27 W. The agreement confirms the working.

Why it matters in practice

Almost every design decision touches Ohm’s law. Choosing a current-limiting resistor for an LED, sizing the gate resistor on a transistor, working out the voltage drop along a long wire run, or estimating how warm a regulator will get — all of them start from V = I x R and P = V x I. Master these two equations and the units that go with them (volts, amperes, ohms, watts), and the rest of electronics has a solid foundation to build on.