Electronics
Ohm's law explained
Ohm's law says the current through a resistor is proportional to the voltage across it: V = I × R. Voltage (V, in volts) is the push, current (I, in amps) is the flow, and resistance (R, in ohms) is the squeeze. Know any two and the third follows.
The rule
Rearrange it for whichever one you're missing:
- I = V over R: current from voltage and resistance
- R = V over I: resistance from voltage and current
More push, more flow. More squeeze, less flow. Double the voltage across the same resistor and the current doubles, so a graph of current against voltage is a straight line. Georg Ohm published that in 1827, and the rule carries his name.
Live experiment
Three dials, one law
A battery and a resistor in a loop, with a current meter. Set any two of push (V), flow (I) and squeeze (R) and the third works itself out. Then try the three goals underneath.
“Ohm's law” is lesson 5 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 4 before it first.
A worked example
A 9 V battery is connected across a 1 kΩ resistor. What current flows?
Sizing an LED resistor
The most common use of Ohm's law at a workbench is picking the resistor for an LED. The LED keeps a roughly fixed forward voltage for itself, and the resistor takes whatever is left:
Take 5 V from USB, a red LED that drops about 2.0 V, and a target of 15 mA:
200 Ω isn't in the common E12 range, so round up to the next value that is: 220 Ω gives about 13.6 mA. Rounding up keeps the current safely below your target.
Where it applies
Ohm's law describes resistors and wires very well. It doesn't describe everything: an LED's current isn't proportional to its voltage, and neither is a diode's. That's why you apply the law to the resistor and treat the LED's forward voltage as a fixed drop.
It also connects to power. Combine V = I × R with P = V × I and you get P = I² × R, which tells you how hot a resistor runs. That's the next thing to check once you've picked a value.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Ohm's law” is lesson 5 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 4 before it first.
Or start from the very first lesson, no account neededWork it out
- Ohm's law calculatorAny two of V, I and R give the third, and the power.
- Electrical power calculatorWatts from any two of V, I and R, and the resistor rating that stays cool.
- LED resistor calculatorThe resistor for one LED or a string, rounded to a value you can buy.
- Resistor colour code calculatorBands to ohms, or ohms to bands, on 4- and 5-band resistors.
- Voltage divider calculatorVout from two resistors, or the resistor for the Vout you need.
- Wire voltage drop calculatorVolts and watts lost in a cable, out and back, and the size that keeps it under 3%.
- Ohm's law practice problemsFind V, I or R, then the power, with the working for each.
- Units and prefixes practice problemsConvert mA, kΩ, µF, nF, pF, ms and mV, with the working for each.
- LED resistor practice problemsSize the resistor for one LED or a string, round to a standard value, check the power.
- Standard resistor values chartThe E12, E24 and E96 series, decade by decade, and which one to reach for.
- Electronics unit prefixes and conversionsp, n, µ, m, k, M and G, conversion tables, and what 4k7 or 2n2 means.
- Electronics formulas cheat sheetOhm's law to antenna length: every formula in the course, what it gives and where to learn it.
Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: Gets bigger. More push through the same squeeze means more flow. A stronger battery drives more current through the same resistor.
- Why not “Stays the same”? By Ohm's law, I = V ÷ R. With R fixed, raising V raises I in proportion.
- Why not “Gets smaller”? Current falls when the resistance goes up or the voltage goes down. A stronger battery is more voltage, which drives more current.
- Why not “Stops”? Current stops only when the loop is broken. A stronger battery pushes harder, so more current flows, not none.
Show the answer
Answer: To limit the current. Once an LED is on, a tiny rise in voltage causes a huge rise in current. The resistor sets a safe current.
- Why not “To store charge”? Storing charge is a capacitor's job. A resistor stores nothing: it turns some energy into heat as it limits the current.
- Why not “It doesn't need one”? Without one, an LED on a battery draws far too much current and burns out, because its current rises steeply with a small rise in voltage.
- Why not “To change its colour”? An LED's colour is set by the material it's made from. A resistor changes how much current flows, not the colour of the light.
Show the answer
Answer: 4. P = I² × R. Doubling I multiplies I² by 4.
- Why not “It doesn't change”? The resistance stays the same, but the power doesn't: P = I² × R, so doubling I multiplies P by four.
- Why not “½”? More current means more power, never less. With the same resistor, P = I² × R grows four times when I doubles.
- Why not “2”? Power goes with the square of the current, P = I² × R, so twice the current gives 2² = 4 times the power, not twice.
“Ohm's law” is lesson 5 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 4 before it first.
Questions people ask
What is Ohm's law in simple terms?
The current through a resistor is proportional to the voltage across it. Written out, V = I × R: voltage equals current times resistance. Know any two of the three and you can work out the third.
How do you find current with Ohm's law?
Divide the voltage by the resistance: I = V ÷ R. A 9 V battery across 1 kΩ gives 9 ÷ 1000 = 0.009 A, which is 9 mA. Volts divided by kilohms give milliamps directly.
Does Ohm's law work for LEDs?
Not directly. An LED's current isn't proportional to its voltage: it keeps a roughly fixed forward voltage, about 2 V for a red LED. Apply Ohm's law to the resistor in series with it, using the voltage that's left over.
Who discovered Ohm's law?
Georg Ohm, a German physicist, published it in 1827 after measuring how the current changed as he changed the length of wire in the circuit.
Related topics
- What is voltage?The push that makes charge flow: what a volt is, and why stacked cells add up.
- What is electric current?How much charge flows past a point each second, in amps, and why it's the same all round a loop.
- What is resistance?The squeeze on the flow, in ohms: how resistors set the current and protect an LED.
- Electrical power explained: P = V × IP = V × I: how fast energy turns into heat, and why a resistor has a power rating.