Voltage dividers

Given a 9V battery and a sensor that wants 3V, how do you get there?

You could buy a "3V regulator". Or you could put two resistors in a row, tap the middle, and do math.

The setup

9V ──[ R1 ]──┬──[ R2 ]── GND
             │
           V_out

The output voltage at the tap is:

V_out = V_in × R2 / (R1 + R2)

For 9V → 3V, pick R1 = 2 × R2. So R1 = 10kΩ, R2 = 5kΩ works. Or 20kΩ + 10kΩ. The ratio is what matters, not the absolute values.

Why big resistors?

In the lab above you could also use R1 = 2Ω, R2 = 1Ω. Math checks out — 3V still appears at the tap. But those resistors would draw 3 amps continuously, heating up and wasting power.

Rule of thumb for low-power dividers: use kilohms or higher.

Companion lab

@exosynk/voltage-divider-demo has this exact circuit. Click any wire or pin to see the voltage / current readout. Try:

Change R1 from 10k to 20k. V_out should drop to 1.8V. Verify with the multimeter.
Swap both to 100Ω. Circuit still works, but now it burns 90 mW continuously — check the battery drain estimate.

When dividers break

Voltage dividers assume almost no current flows out of the tap. The moment you connect a "load" that draws real current, the math gets messier (you've added a third resistor in parallel). That's why most real designs use op-amp buffers or dedicated regulators — but dividers are everywhere in low-power signal work.

Voltage dividers: how two resistors split a signal