Ohm's law

On the first page you saw that current flows only around a closed loop. This page is about how much current flows, which is the most useful single fact in electronics. It depends on two things, voltage and resistance, and Ohm's law ties the three together.

Voltage, current and resistance

Voltage is the difference in electrical pressure between two points, measured in volts (V). A battery creates a voltage between its terminals: about 1.5 V for an AA cell, 9 V for the rectangular battery. Voltage is always measured between two points, never at a single point.

Current is the amount of charge flowing past a point each second, measured in amps (A) or milliamps (mA). It is the result of the voltage pushing charge through the circuit.

Resistance is how strongly a part opposes the current, measured in ohms (Ω). Large values are written in kilohms (kΩ, thousands of ohms) and megohms (MΩ, millions). A resistor is a part made to have a known resistance.

A common comparison is water in a pipe: voltage is the water pressure, current is how much water flows, and resistance is how narrow the pipe is. The comparison helps at first, but don't push it too far. Electricity doesn't leak out of an open wire the way water leaks out of an open pipe.

The formula

Ohm's law says that the voltage across a resistor equals the current through it multiplied by its resistance: V = I × R. The letter I stands for current. Rearranged, the same law gives the other two values:

• V = I × R to find the voltage
• I = V ÷ R to find the current
• R = V ÷ I to find the resistance

In words: with the same resistance, twice the voltage gives twice the current. With the same voltage, twice the resistance gives half the current. Try it in the tool, the dots move faster when more current flows.

The moving circuit and the calculator below it start with different resistors. At 9 V and 470 Ω, the moving circuit shows about 19.1 mA. The calculator starts at 9 V and 450 Ω, so it shows 20 mA. Enter 470 Ω in the calculator to compare the same circuit.

Converting units first

The formula only works with volts, amps and ohms. If a value is in milliamps or kilohms, convert it before you calculate. Forgetting this is the most common mistake, and it gives answers that are wrong by a factor of a thousand.

• 20 mA = 0.02 A
• 4.7 kΩ = 4,700 Ω
• 1 MΩ = 1,000,000 Ω

For example, 9 V across 4.7 kΩ: 9 ÷ 4,700 = 0.0019 A, which is 1.9 mA. Dividing 9 by 4.7 instead would give 1.9 A, a thousand times too much. The calculator above accepts values like 4.7k and 1M, so you can check your own sums.

Three worked examples

Finding the current

A 220 Ω resistor is connected to 5 V. The current is 5 ÷ 220 = 0.0227 A, about 23 mA.

Finding the resistance

You have a 12 V supply and want about 50 mA to flow. The resistance needed is 12 ÷ 0.05 = 240 Ω. Resistors are only sold in certain standard values, and 240 Ω is not a common one, so you would pick the next value up, 270 Ω. With 270 Ω the current is 12 ÷ 270, about 44 mA. How the standard values work is explained on the colour code page.

Finding the voltage

If 15 mA flows through 1 kΩ, the voltage across it is 0.015 × 1,000 = 15 V. If your supply is only 9 V, that situation can't happen, because there isn't enough voltage to push 15 mA through 1 kΩ. The current will be at most 9 mA. Ohm's law is useful for spotting impossible numbers like this, too.

Where Ohm's law doesn't apply directly

Ohm's law describes resistors and wires well. Some parts don't have a fixed resistance at all. A diode or an LED lets almost no current through below a certain voltage and then lets a lot through, so there is no single resistance to put into the formula. You will meet those parts in the diodes guide, and you will see that the trick is always to put a resistor next to them and apply Ohm's law to the resistor.

Current through a resistance also produces heat. How much, and when it becomes a problem, is the subject of the next page.