Ohm's law without the boring part

Ohm's law is three letters: V = I × R. Most people learn it for a test, pass, and never really get it. Here's the version that sticks.

Start with the playground. Move the sliders and watch the dots. Faster dots means more current.

Push, squeeze, flow

• Voltage (V, volts) is the push. A 9 V battery pushes harder than a 1.5 V one.
• Resistance (R, ohms, Ω) is how hard the path pushes back.
• Current (I, amps) is how much actually flows. It's the result. You don't set it directly, you get it from the other two.

So: more push, more current. More resistance, less current. That's the whole idea. If it doesn't feel obvious yet, play with the sliders a bit more. Double the voltage and the current doubles. Double the resistance and it halves.

Three versions, one formula

• V = I × R when you want the voltage
• I = V ÷ R when you want the current
• R = V ÷ I when you want the resistance

You only need to remember the first one. The other two are the same thing moved around.

Watch the units

This is where almost every mistake happens. The formula works in volts, amps and ohms. Not milliamps, not kilohms. Convert first, then calculate.

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

Example: 9 V across 4.7 kΩ. 9 ÷ 4,700 = 0.0019 A, so about 1.9 mA. Divide 9 by 4.7 instead and you get 1.9 A, a thousand times wrong. The calculator in the playground takes 4.7k directly, so you can check yourself.

Three real examples

How much current flows?

5 V across a 220 Ω resistor. I = 5 ÷ 220 = 0.0227 A, about 23 mA.

Which resistor do I need?

You have 12 V and want about 50 mA. R = 12 ÷ 0.05 = 240 Ω. That's not a standard value, so take the next one up, 270 Ω. Now I = 12 ÷ 270 ≈ 44 mA. Close enough, and on the safe side.

What voltage is across it?

15 mA through 1 kΩ. V = 0.015 × 1,000 = 15 V. Now say your supply is only 9 V. Then 15 mA through 1 kΩ can't happen. The current will be lower, 9 mA at most. Ohm's law is also good for catching numbers that don't make sense.

Don't forget power

Power is how much energy turns into heat: P = V × I. 9 V and 20 mA gives 0.18 W. A 1/4 W resistor handles that, but it gets warm.

Put 12 V on a 10 Ω resistor and you get 1.2 A and 14.4 W. A small resistor in that spot will smoke. That's why every resistor has a power rating, and why the playground shows power next to current.

Where Ohm's law stops working

It works for resistors and wires. It doesn't work directly for LEDs, diodes and transistors. Their resistance changes with the voltage, so there's no single R to put in the formula.

That's exactly why an LED needs a resistor in front of it. The resistor follows Ohm's law, the LED doesn't. More on that in why your LED needs a resistor.