Ohm's Law

Q: What is an ohm?

One ohm ($\Omega$) is the resistance that lets 1 A flow when 1 V is across it. It is $1\ \Omega = 1\ \text{V} / 1\ \text{A}$.

In one sentence: Ohm’s law says the push on a wire, the voltage, equals the flow through it, the current, times how hard that flow is to get through, the resistance.

$V = I R$

Read it out loud: “V equals I times R. Voltage equals current times resistance.”

What each symbol means

Symbol	Meaning
$V$	Voltage, the electrical push across the part, measured in volts (V). More voltage pushes more current through.
$I$	Current, the flow of electric charge through the part, measured in amperes (A). One ampere is one coulomb of charge per second.
$R$	Resistance, how strongly the part opposes the flow, measured in ohms ( $\Omega$ ). A bigger number means less current for the same voltage.

What the formula is doing

Three quantities are linked here: voltage $V$ in volts (V), current $I$ in amperes (A) and resistance $R$ in ohms ( $\Omega$ ). Ohm’s law says that the voltage across a part equals the current through it multiplied by its resistance. If you know any two of the three, you can work out the third.

Rearranged, the same rule reads $I = \frac{V}{R}$ and $R = \frac{V}{I}$ . Those versions answer the questions people usually ask. Double the voltage on the same resistor and the current doubles. Keep the voltage the same and double the resistance, and the current is cut in half.

A resistor is the everyday part that follows this rule. Its resistance is set by its material and shape, and it does not change when you change the voltage. The unit of resistance is named after the physicist Georg Ohm.

Ohm’s law has limits. It describes ohmic parts, where the current rises in a straight line with the voltage. Diodes and LEDs are not ohmic. An LED drops about 2 V and then lets the current climb steeply, so the ratio $V / I$ is not a fixed number. For those parts you still use the voltage and current, but you need a separate curve or a series resistor to control the current.

An everyday picture

Think of water in a pipe. The voltage is the water pressure that pushes the water, the current is how much water flows past each second, and the resistance is how narrow the pipe is. Higher pressure pushes more water through. A narrower pipe lets less through for the same pressure. In this picture Ohm’s law reads: flow equals pressure divided by how narrow the pipe is, so the pressure needed for a given flow equals the flow times the narrowness.

Worked example: Choosing a resistor for an LED on a 5 V supply

A 5 V supply powers a red LED that drops 2 V when lit. The LED should run at 20 mA, which is the current the designer wants. The resistor in series with the LED takes the leftover voltage. What resistance should it be?

The resistor sees the supply voltage minus the LED voltage: $V_R = 5\ \text{V} - 2\ \text{V} = 3\ \text{V}$ .
Convert the current to amperes: $20\ \text{mA} = 0.02\ \text{A}$ .
Rearrange Ohm’s law to $R = \frac{V}{I}$ and fill in the numbers: $R = \frac{3\ \text{V}}{0.02\ \text{A}} = 150\ \Omega$ .
Check the power the resistor turns into heat: $P = V_R \times I = 3\ \text{V} \times 0.02\ \text{A} = 0.06\ \text{W}$ .

Answer: Use a 150 ohm resistor. It drops the leftover 3 V, so the LED gets its 2 V and the circuit carries 20 mA. The resistor turns about 0.06 W into heat, so a standard 1/4 W resistor is enough.

The numbers in this example are recomputed by script every time the site is built.

Common mistakes

Using milliamps as if they were amps. 20 mA is 0.02 A. Plugging in 20 gives a resistance 1000 times too small.
Using the full supply voltage instead of the voltage across the resistor. The LED takes its own share, so the resistor sees only the difference.
Treating an LED or a diode as a plain resistor. These parts are not ohmic, so one fixed resistance does not describe them.
Thinking that a bigger resistor lets more current through. For the same voltage, a bigger resistance gives less current.

Where you will meet it

Choosing the resistor for an LED, an indicator light or a button backlight so the current stays safe.
Working out the resistance of a wire, heater or sensor from a voltmeter and an ammeter reading.
Estimating the voltage lost along a long cable, which is the current times the cable resistance.
Designing the bias networks and dividers that set the operating point of transistors and sensors.

Questions people ask

Why is the formula V = I R and not I = V R?

Current goes up when the voltage goes up and goes down when the resistance goes up. So the voltage is on top when you solve for current, $I = \frac{V}{R}$ , and multiplying back gives $V = I R$ .

What is an ohm?

One ohm ( $\Omega$ ) is the resistance that lets 1 A flow when 1 V is across it. It is $1\ \Omega = 1\ \text{V} / 1\ \text{A}$ .

Does Ohm's law work for every device?

No. It works for ohmic parts such as ordinary resistors. LEDs, diodes and transistors do not follow a straight line, so you need their own datasheet curves for them.

If an LED has its own resistance, why does it still need a resistor?

Past its forward voltage, the current in an LED climbs very fast for a small change in voltage. A series resistor limits the current, so a small change in the supply does not destroy the LED.

Electric Power: Electric power tells you how fast a device uses energy, and you get it by multiplying the volts by the amps to get watts.
Resistors in Series and Parallel: Resistors in a line add up, and resistors side by side always give a total smaller than the smallest one.
Kirchhoff's Current Law: Kirchhoff’s current law says that whatever electricity flows into a junction has to flow out again, because nothing piles up there.