Building a voltage divider, and why it's everywhere

If you've used a thermistor, photoresistor, force-sensitive resistor, slide pot, flex sensor, or moisture sensor — you've used a voltage divider, whether you knew it or not. The pattern is the same every time: two resistors in series, one of them variable, the chip reads the junction voltage.

The maths is a fraction

The formula is famous: Vout = Vin · R2 / (R1 + R2). Two resistors, one ratio. When R1 = R2, Vout is half of Vin. When R1 ≫ R2, Vout is small. When R1 ≪ R2, Vout is most of Vin. Nothing in here cares about absolute resistance, only the ratio.

That's why a 10 kΩ thermistor and a 10 kΩ fixed resistor give you the best dynamic range: as the temperature changes, the thermistor's value sweeps from ~5 kΩ to ~30 kΩ, and the ratio (and so the Vout) changes most around the fixed-resistor value.

Why it's everywhere

Almost every analog sensor cheaper than $5 is just a variable resistor wrapped in interesting physics. A photoresistor's resistance falls as light hits it. A thermistor's resistance falls as it warms. A flex sensor's resistance rises as it bends. Build the divider, read the junction with analogRead, and you've sampled the physical world. The same eight cents of resistor pattern, over and over.