Voltage Dividers
Two resistors that turn any voltage into any smaller voltage — the most-reused pattern in electronics.
Builds on: 1.5 Series & Parallel2.1 Kirchhoff's Laws
Deriving it in three lines
Stack two resistors between a supply and ground and tap the midpoint. Series rules (Lesson 1.5): I = Vin/(R₁+R₂). The output is just R₂’s share: Vout = I·R₂. Substitute:
The ratio is everything, the absolute values secondary: 1 k/1 k divides exactly like 100 k/100 k (the difference is how much current the divider itself wastes — larger values sip, smaller values gulp but are stiffer under load).
Where you’ll meet it
- Sensors: swap R₂ for a thermistor or photoresistor and Vout becomes a voltage that tracks temperature or light — this is how microcontrollers read the analog world.
- Volume knobs: a potentiometer is a resistor with a sliding tap — a divider whose ratio you turn. Audio has ridden on this for a century.
- Level shifting: feeding a 5 V signal to a 3.3 V input? A divider scales it down. Reference voltages, biasing — dividers everywhere.
The loading trap
The formula assumes nothing is connected to the output. Attach a load and it sits in parallel with R₂, lowering the effective bottom resistance — and the output sags. Rule of thumb: keep the load at least 10× R₂, or account for the parallel combination explicitly.
Never try to power a motor or bright LED “at 4.5 V” from a divider — the load collapses the ratio and the resistors burn your energy as heat. For signals and references, dividers; for power, regulators (a great advanced-unit topic).
⚡ Lab — The Ratio Machine
A live divider with an optional 10 kΩ load on its output.
- Set R₁ = R₂ and confirm the output is exactly half of any input.
- Attach the load with R₂ = 10 k — watch the sag. Now set R₁, R₂ = 1 k. Stiffer?
- Switch to potentiometer mode and ride the wiper from 0 to 100%.