Ohm's law explained: how voltage, current and resistance relate

Ohm's law states that the current through a conductor is proportional to the voltage across it: V = I × R, where V is voltage in volts, I is current in amps and R is resistance in ohms. Rearrange it and you can find any one of the three values from the other two - which is why it's the first formula taught in every electronics course and the one working engineers still use most.

This guide covers the formula and its rearrangements, worked examples you can follow at the bench - including the classic LED resistor calculation - how power fits in, where Ohm's law stops applying, and how to measure all three quantities properly with a multimeter.

What is Ohm's law?

One relationship, three rearrangements. Which one you use depends on which value you're missing:

The traditional memory aid is the Ohm's law triangle: V on top, I and R side by side underneath. Cover the value you want and the layout of the remaining two tells you the operation - side by side means multiply, one above the other means divide. It works, but the intuition matters more than the mnemonic: voltage is the push, resistance is the opposition, and current is what results. Double the push and current doubles; double the opposition and current halves.

How do you use Ohm's law? Two worked examples

Sizing a resistor for an LED. A standard red LED drops about 2 V and runs comfortably at 10 mA. From a 5 V supply, the resistor has to absorb the difference: 5 − 2 = 3 V. Applying R = V ÷ I gives 3 ÷ 0.01 = 300 Ω — conveniently a standard value you'll find in any resistor kit. If the calculation lands between standard values, round up: slightly less current is safe, slightly more shortens the LED's life.

Finding current draw. A 6 Ω heating element across a 12 V supply draws I = V ÷ R = 12 ÷ 6 = 2 A. That single figure tells you most of what you need for the rest of the design: the fuse rating, the wire size and multiplying by the voltage - a 24 W power budget.

What is resistance and what affects it?

Resistance measures how strongly a material opposes current, and for a wire or track it comes down to three physical factors: the material's resistivity, the length of the path and its cross-sectional area. Resistance rises with length and falls as the conductor gets fatter - which is precisely why wire gauge matters in cable runs and why a long thin cable can quietly drop a volt or more before the load ever sees it.

Copper sits at the low-resistance end, which is why it dominates cabling. At the other end, alloys like nichrome are chosen because of their resistance: resistance wire turns opposition to current into useful heat in elements and heaters. In between sit the manufactured values of everyday metal film resistors, which set currents and divide voltages deliberately rather than incidentally.

Temperature is the complicating factor. Most metals gain resistance as they heat up, and some components exploit the effect - a thermistor's resistance changes so predictably with temperature that it works as a sensor. It also means a component's resistance in a running circuit isn't always what the cold measurement said it was.

How does power fit in?

Combining Ohm's law with the power formula P = V × I gives two more forms worth memorising: P = I² × R and P = V² ÷ R. These tell you how much heat a component has to survive, and they're where beginners most often get caught out.

Take a 100 Ω resistor placed straight across a 9 V battery. The current is only 90 mA, which sounds harmless, but P = V² ÷ R = 81 ÷ 100 = 0.81 W. A standard 0.25 W resistor will overheat and fail, possibly taking the smell of the workshop with it. The job calls for a power resistor rated at least 1 W, and good practice is to leave generous headroom — running any resistor near its limit shortens its life and shifts its value.

The I² term explains a lot of practical electronics. Because power scales with the square of current, doubling the current through the same resistance quadruples the heat. It's why high-current paths get thick tracks and fat cables, and why a loose, resistive connection gets hot enough to discolour.

Does Ohm's law apply to everything?

No — and knowing where it fails is as useful as knowing the formula. Ohm's law describes components whose resistance stays constant regardless of the applied voltage. Plenty of real devices don't behave that way:

• LEDs and diodes conduct almost nothing below their forward voltage, then current rises steeply - which is exactly why an LED needs a series resistor to set the current for it
• Filament lamps increase in resistance as the filament heats, so a bulb's cold resistance can be a tenth of its operating value
• Thermistors and other sensors change resistance with temperature, light or voltage by design

For AC circuits, the same V = I × R structure survives but resistance generalises to impedance, which includes the frequency-dependent opposition of capacitors and inductors. The arithmetic gains a frequency term, but the intuition - push, opposition, result - carries straight over.

How do you measure voltage, current and resistance?

Each measurement wants the meter connected differently, and mixing them up is the fastest way to blow a multimeter fuse. Voltage is measured in parallel, probes across the component, circuit powered. Current is measured in series, meaning the circuit is broken and the meter inserted into the path - and the probe usually moves to a dedicated current socket. Resistance is measured out of circuit: the meter injects its own small current, so the component should be isolated and the circuit unpowered, otherwise other parts in parallel will skew the reading.

A hand-held multimeter covers all three for general work; bench multimeters add resolution and accuracy for calibration and development, and decent test leads matter more than people expect - worn leads add resistance of their own, which the meter faithfully includes in the reading. For experimenting safely with the law itself, a bench power supply with adjustable voltage and a current limit is the ideal teaching tool: set a voltage, read the current, and watch the arithmetic hold.

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Frequently asked questions

What are the three forms of Ohm's law?

V = I × R to find voltage, I = V ÷ R to find current, and R = V ÷ I to find resistance. They're one relationship rearranged three ways - knowing any two of the values gives you the third.

How do I calculate the resistor for an LED?

Subtract the LED's forward voltage from the supply voltage, then divide by the desired current: R = (V_supply − V_LED) ÷ I. For a 2 V LED at 10 mA on a 5 V supply, that's 3 ÷ 0.01 = 300 Ω. Round up to the nearest standard value.

What happens to current if resistance doubles?

At a fixed voltage, the current halves - current and resistance are inversely proportional. Halve the resistance instead and the current doubles, which is why an accidental short circuit, where resistance falls to almost nothing, draws destructive current.

Why doesn't my measured resistance match the marked value?

Every resistor has a tolerance, typically ±1% for metal film and ±5% for carbon film, so a 1 kΩ part reading 995 Ω is in spec. Measuring in-circuit also skews readings, because parallel components provide alternative paths for the meter's test current.

Does Ohm's law work for AC circuits?

Yes, in generalised form: V = I × Z, where impedance Z replaces resistance and includes the frequency-dependent opposition of capacitors and inductors. For purely resistive AC loads like heaters, the ordinary form works unchanged.

Why does a filament bulb not obey Ohm's law?

Its resistance changes with temperature. The filament might measure a tenth of its operating resistance when cold, so current is highest at the moment of switch-on - which is why filament bulbs usually fail at the flick of the switch rather than mid-glow.

Put it into practice

From resistor kits for the classroom to bench instruments for development work, everything you need to apply the fundamentals is in one place.