Electronics
Voltage divider explained
A voltage divider is two resistors in series across a supply. The point between them, the tap or output, sits at a fraction of the supply set by the resistors' ratio: Vout = Vin × R2 ÷ (R1 + R2). It's how circuits make a smaller voltage from a bigger one, for signals and references.
The formula
With R1 on top and R2 on the bottom, the same current flows through both, so each drops its share of the supply. The output is the bottom resistor's share:
Example: 5 V across 1 kΩ (top) and 1.5 kΩ (bottom).
Only the ratio sets the output: 10 kΩ and 15 kΩ give 3 V too, while drawing ten times less current.
Live experiment
Slide the tap
A 10 kΩ track across a 9 V battery, with a sliding tap. Hit the three target voltages, then plug a 10 kΩ gadget into the tap and watch its voltage sink: at the middle, 4.5 V falls to 3.6 V.
“Voltage dividers” is lesson 7 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 13 before it first.
Potentiometers
A potentiometer is a divider you can adjust: a resistive track with a sliding contact, the wiper. Wire the track's ends across a supply and the wiper gives anything from 0 V to the full supply. It's what's inside a volume knob, and it's the classic way to feed a microcontroller's analog input.
A load pulls it down
Connect something to the tap and the output sinks, because the load draws its current through the top resistor. Seen from its output, a divider acts like a battery behind a resistor, its Thevenin equivalent:
- Vth: the output with nothing connected
- Rth = R1 ∥ R2: the two resistors in parallel
The load then forms a second divider with Rth. Example: 10 kΩ and 10 kΩ on 12 V give 6 V behind 5 kΩ. A 100 kΩ load gets:
As a rule of thumb, the output sags by about Rth ÷ RL, here 5%.
Choosing values
Smaller resistors sag less but waste more: 1 kΩ and 1 kΩ on 12 V sag to only 5.97 V under that load, but draw 6 mA instead of 0.6 mA. And a divider can't power a lamp or a motor: Rth sits in series with the load and the output collapses. Dividers are for signals; for power, use a regulator.
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.
“Voltage dividers” is lesson 7 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 13 before it first.
Or start from the very first lesson, no account neededWork it out
- Voltage divider calculatorVout from two resistors, or the resistor for the Vout you need.
- Voltage divider practice problemsFind Vout, pick R2 for a target and work out loading, with the working for each.
- 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: goes up. Brighter light shrinks the LDR's resistance, so it drops less of the 5 V and more of it lands on A0. The reading climbs, to about 937 by a sunny window.
- Why not “flips between 0 and 1023”? analogRead gives a smooth range of values, not just two. The divider's output moves gradually as the light changes, so the reading does too.
- Why not “stays at 512”? 512 is only the reading when both halves happen to be equal. As the LDR's resistance changes, so does the share A0 gets.
- Why not “goes down”? That's what happens with the LDR at the bottom. On top, its falling resistance takes a smaller share of the 5 V, so more lands on A0.
Show the answer
Answer: A resistance alone gives no voltage: the divider turns it into one A0 can read. A0 measures voltage. The divider makes the voltage at the middle depend on the LDR's resistance.
- Why not “To protect the LDR”? Protection isn't the job. Paired with the fixed resistor, the LDR's changing resistance becomes a changing voltage at the middle, which A0 can read.
- Why not “To make it brighter”? An LDR doesn't give out light, it only senses it. The fixed resistor is there to turn its resistance into a voltage.
- Why not “It doesn't”? On its own an LDR only changes resistance, and A0 measures voltage. Without a second resistor there's no middle point whose voltage follows the light.
Show the answer
Answer: Close to 1023, but never quite. The small LDR takes only a little of the 5 V, so the 10 kΩ, and A0, get most of it: about 937. Reaching 1023 would need the LDR to be 0 Ω.
- Why not “Exactly 1023”? A full 1023 would need the LDR to be 0 Ω. Even under 1 kΩ it still takes a small share of the 5 V, so the reading stays just below.
- Why not “Exactly 512”? 512 is the reading when the two resistors are equal. With the LDR far smaller than 10 kΩ, A0 gets well over half.
- Why not “Close to 0”? That would need the LDR to be much bigger than the 10 kΩ. Here it's much smaller, so most of the 5 V lands on A0.
“Voltage dividers” is lesson 7 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 13 before it first.
Questions people ask
What is the voltage divider formula?
Vout = Vin × R2 ÷ (R1 + R2), with R1 between the supply and the output and R2 between the output and ground. The output is the bottom resistor's share of the total resistance, times the supply.
Can I use a voltage divider to power something?
Not well. Seen from its output, the divider is a voltage behind R1 ∥ R2, and that resistance sits in series with whatever you connect, so a load that draws real current drags the output down. Dividers are for signals and reference voltages, not for powering motors, lamps or boards.
How do I choose the resistor values?
Only the ratio sets the output, so pick the ratio first, then the size. Smaller resistors sag less under a load but waste more current; larger ones waste less but sag more. Keep the load at least ten to a hundred times the divider's resistors.
Is a potentiometer a voltage divider?
Yes. A potentiometer is a resistive track with a sliding contact, the wiper. Connect the track's ends across a supply and the wiper gives any voltage from 0 V to the full supply. That's what's inside a volume knob.
Related topics
- Ohm's law explainedV = I × R: set any two of voltage, current and resistance and the third follows.
- Series vs parallel circuitsOne path or many: what stays the same, what adds up, and how to combine resistors.
- How Arduino analogRead worksHow analogRead turns 0–5 V into 0–1023, and how to scale it for analogWrite.