Ohm's law explained with worked examples

Ohm's law is the first rule anyone learns about electricity, and it is also one of the most useful. It links three quantities, voltage, current and resistance, so that if you know two of them you can find the third. It also leads straight to power, which is what you pay for on an energy bill. This guide explains each quantity in plain terms, shows the formulas and how to rearrange them, works through examples from a kettle and an LED to simple series and parallel circuits, and points out the limits of the law. It is an explanation for learning and for planning, not a substitute for a qualified electrician on any mains job.

By Valtrinity. Updated 18 October 2026.

Voltage, current and resistance

Voltage, measured in volts (V), is the push that drives electric charge around a circuit. Think of it as pressure. A bigger voltage pushes harder.

Current, measured in amperes or amps (A), is the rate at which charge flows. In the pressure analogy, it is how much water flows through a pipe each second. Resistance, measured in ohms (symbol Ω), is how much a component opposes that flow, like a narrow section of pipe.

The relationship between them, found by Georg Ohm in the 1820s, is simple for many everyday materials: for a given resistance, doubling the voltage doubles the current. Materials that follow this rule are called ohmic. A plain resistor is the standard example.

The formula and its three forms

Ohm's law is written V = I × R, where V is voltage in volts, I is current in amps and R is resistance in ohms. Rearranged, I = V ÷ R and R = V ÷ I.

A memory aid is a triangle with V at the top and I and R side by side at the bottom. Cover the quantity you want: if you cover V, you see I next to R, so multiply. If you cover I, you see V over R, so divide.

Always use base units. If a current is given in milliamps, divide by 1,000 to turn it into amps. If a resistance is in kilohms, multiply by 1,000 to get ohms. Most wrong answers come from forgetting this step.

Basic worked examples

A 12 V battery is connected across a 4 Ω resistor. The current is 12 ÷ 4, which is 3 A.

A component draws 0.5 A when 9 V is applied. Its resistance is 9 ÷ 0.5, which is 18 Ω.

A 47 Ω resistor carries 0.2 A. The voltage across it is 0.2 × 47, which is 9.4 V.

Now with a conversion: a 2.2 kΩ resistor is connected to 5 V. 2.2 kΩ is 2,200 Ω, so the current is 5 ÷ 2,200, which is 0.00227 A, or 2.27 mA. Working in milliamps is natural for electronics, because the amounts are small.

Power: the formulas that go with it

Power, measured in watts (W), is the rate at which energy is used. The basic formula is P = V × I. Combine it with Ohm's law and you get two more forms: P = I² × R, and P = V² ÷ R.

For the 12 V battery and 4 Ω resistor above, the current is 3 A, so the power is 12 × 3, which is 36 W. Using the other forms: 3² × 4 is 9 × 4, which is 36 W, and 12² ÷ 4 is 144 ÷ 4, which is 36 W. All three agree.

Power in a resistor turns into heat. That is why resistors have a power rating, such as a quarter of a watt, and why a component run beyond its rating gets hot and can fail. Always pick a resistor whose rating is comfortably above the calculated power.

UK mains examples

The nominal supply voltage in the UK is 230 V. A kettle rated at 2,200 W (2.2 kW) draws a current of P ÷ V, which is 2,200 ÷ 230, or 9.57 A. Its resistance when running is V ÷ I, which is 230 ÷ 9.57, or about 24 Ω.

A 3 kW heater draws 3,000 ÷ 230, which is 13.04 A. UK plugs are fitted with fuses of 3 A, 5 A or 13 A, and the 13 A fuse is the largest. Appliances that draw close to that limit are made to a rating that suits it, which is why you rarely see a plug-in appliance above about 3 kW.

To work out running cost, convert watts to kilowatts and multiply by the hours and the price per kilowatt hour. The 2.2 kW kettle running for 10 minutes uses 2.2 × (10 ÷ 60), which is 0.367 kWh. At an example price of 28 pence per kWh, that is about 10 pence. Check your own tariff for the current price.

Series and parallel circuits

In a series circuit the components are joined one after another, and the same current flows through each. The total resistance is the sum. A 100 Ω and a 220 Ω resistor in series give 320 Ω. Connected to 9 V, the current is 9 ÷ 320, which is 0.028 A, or 28 mA. The voltage across the 100 Ω resistor is 0.028 × 100, which is 2.8 V, and across the 220 Ω resistor is 6.2 V, so the voltages add up to 9 V.

In a parallel circuit the components share the same two connection points, so each has the same voltage and the currents add. For two resistors, the total resistance is the product divided by the sum. Two 100 Ω resistors in parallel give (100 × 100) ÷ 200, which is 50 Ω. A 100 Ω and a 220 Ω resistor give 22,000 ÷ 320, which is 68.75 Ω. The total is always lower than the smallest resistor.

This is why plugging more appliances into a circuit raises the total current: each new device adds a parallel path.

A practical example: choosing a resistor for an LED

An LED needs a resistor to limit the current. Suppose you have a 5 V supply and a red LED that drops about 2 V and is happy with 20 mA. The resistor must drop the remaining 3 V. R = V ÷ I = 3 ÷ 0.02, which is 150 Ω.

The power in the resistor is 3 × 0.02, which is 0.06 W, well within the rating of a quarter-watt resistor. If 150 Ω is not available, the next higher standard value, such as 180 Ω, gives a slightly lower current of 3 ÷ 180, or 16.7 mA, which is still fine and slightly longer lasting.

Note the limits of the law. It applies to ohmic parts. LEDs, diodes and filament bulbs do not have a constant resistance, so a single resistance figure does not describe them, which is why we treated the LED's drop as a fixed voltage. Mains wiring should always be left to a qualified electrician.

Tools mentioned in this guide

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