What is Ohm’s law?

Before you switch on a lamp, can you tell how much electricity will flow through it? You can, with one simple rule. It is called Ohm’s law, and it is one of the most useful rules about electricity.

Three things to know first

Ohm’s law connects three ideas you may have met already:

• Voltage is the push that makes electricity flow. It is measured in volts (V).
• Current is how much electricity flows past each second. It is measured in amperes, or amps (A).
• Resistance is how much something holds the flow back. It is measured in ohms (Ω).

In formulas, each of them gets a letter: V for voltage, I for current and R for resistance. In Slovakia, Germany and some other countries, voltage is written with the letter U instead.

The rule

Here is Ohm’s law:

$$I = \frac{V}{R}$$

In words: the current ($I$) equals the voltage ($V$) divided by the resistance ($R$). With a division sign, you can write it as I = V ÷ R.

The rule tells us two things:

• More push, more flow. If the voltage doubles, the current doubles too.
• More resistance, less flow. If the resistance doubles, the current drops to half.

Ohm’s law playground

Change the push and the resistance. The current is always the push divided by the resistance.

Push (voltage)

12 V

Resistance

6 Ω

Current 2.00 A

Power 24 W

Try a real device: Torch bulbPhone chargingLED lampToasterKettle

Let’s calculate!

Example 1. A car battery gives a push of 12 volts. We connect it to a coil of wire with a resistance of 6 ohms. How much current flows?

$$I = \frac{V}{R} = \frac{12\ \text{V}}{6\ \Omega} = 2\ \text{A}$$

Twelve divided by six is two, so a current of 2 amps flows around the circuit.

Example 2. An electric kettle is plugged into a 230-volt socket. Its heating part has a resistance of about 26 ohms. How much current flows?

$$I = \frac{230\ \text{V}}{26\ \Omega} \approx 9\ \text{A}$$

That is about 9 amps, which is a big current. It makes the heating part very hot, very fast.

Turning the rule around

Ohm’s law can also find the voltage or the resistance. You only need to turn it around:

• To find the voltage, multiply the current by the resistance: V = I × R.
• To find the resistance, divide the voltage by the current: R = V ÷ I.

Here is a trick to remember all three. Draw a triangle with V at the top, and I and R side by side at the bottom. Cover the letter you want to find. What is left tells you what to do.

Example 3. A current of half an amp (0.5 A) flows through a resistor of 6 ohms. A resistor is a small part made to have a certain resistance. What voltage pushes the current?

$$V = I \times R = 0.5\ \text{A} \times 6\ \Omega = 3\ \text{V}$$

That is the push of two ordinary AA batteries, with 1.5 volts each.

Example 4. A toaster in a 230-volt socket lets 4 amps flow. What is its resistance?

$$R = \frac{V}{I} = \frac{230\ \text{V}}{4\ \text{A}} = 57.5\ \Omega$$

So the toaster’s hot wires have a resistance of about 58 ohms.

Who was Ohm?

Georg Simon Ohm was a German teacher who loved experiments. In the 1820s, he taught mathematics and physics at a school in the city of Cologne. Next to his teaching, he ran experiments with electric circuits.

He made wires of different lengths and thicknesses and measured the current in each one. He built much of his equipment himself. Again and again, the current followed the same simple pattern.

In 1827, he described his rule in a book. At first, many scientists ignored it, and some even made fun of it. In 1841, the Royal Society in London gave him a famous science prize, the Copley Medal. Today, the unit of resistance carries his name.

Go deeper: Not everything follows Ohm’s law for grown-ups and the extra curious

Ohm’s law works very well for metal wires that stay at the same temperature. Their resistance stays the same whatever the voltage, so a graph of current against voltage is a straight line. Such things are called ohmic. Many things are non-ohmic:

• A light bulb filament. As it heats up, its resistance rises. A cold filament can have more than ten times less resistance than a glowing one. So when an old-style bulb is switched on, a big rush of current flows for a moment. That is why such bulbs often fail at the moment they are switched on.
• An LED. Below about 2 volts (for a red LED) or 3 volts (for a white one), hardly any current flows. Above that, a tiny increase in voltage makes the current shoot up. That is why an LED always needs a resistor or a special circuit to limit its current.

You can still work out $R = V / I$ at any moment, but for these parts R keeps changing, so one number cannot describe them.

Even the water picture has limits. Water flowing slowly and smoothly through a thin pipe follows a rule very like Ohm’s law. But when water rushes and swirls, twice the push gives less than twice the flow.

Go deeper: How Ohm got a steady push for grown-ups and the extra curious

The batteries of the 1820s gave a push that grew weaker as they worked. So Ohm switched to a thermocouple: two different metals, bismuth and copper, joined at both ends. He kept one joint in boiling water and the other in ice. The difference in temperature made a small, steady voltage.

To measure the current, he hung a magnetised needle on a thin wire above the circuit. The bigger the current, the more the needle turned. His results fit a simple formula. In today’s letters, it reads $V = I \times R$.

Check yourself

A 12-volt battery is connected to a heating wire of 4 ohms. How much current flows?

48 amps 3 amps 8 amps

Show the answer

3 amps — Current = voltage ÷ resistance = 12 ÷ 4 = 3 amps.

Check yourself

The resistance stays the same, but the voltage doubles. What happens to the current?

It drops to half It stays the same It doubles

Show the answer

It doubles — Current = voltage ÷ resistance. With the same resistance, twice the push gives twice the current.