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Calculate the output voltage of a two-resistor voltage divider circuit. Find the correct R1 and R2 values to produce any desired output voltage from any input supply. Used in sensor interfaces, ADC references, and level shifting.
The voltage divider is perhaps the simplest analog circuit — just two resistors — yet it solves a remarkable variety of problems in electronics design. Signal level shifting, sensor biasing, reference voltage generation, and impedance matching all rely on the voltage divider principle. Mastering its design and limitations is fundamental to analog electronics.
A voltage divider (also called a potential divider) uses two resistors in series to produce a fraction of the input voltage. It is one of the most fundamental and widely used circuits in electronics. Applications include sensor biasing, ADC input scaling, microcontroller level shifting (5V to 3.3V), and setting reference voltages.
With R1 connected from Vin to the output node, and R2 from the output node to ground, the output voltage follows: Vout = Vin × R2 / (R1 + R2). The voltage is divided in proportion to the resistor values. If R1 = R2, Vout = Vin/2.
The voltage divider formula assumes no current is drawn from the output. When a load (like a microcontroller input) is connected, it creates a parallel resistance with R2, reducing Vout. For accurate division, the load resistance should be at least 10× R2. A low-impedance buffer (op-amp follower) eliminates loading effects.
| Application | R1 | R2 | Vout |
|---|---|---|---|
| 5V → 3.3V level shift | 10kΩ | 20kΩ | 3.33V |
| 12V → 5V reference | 14kΩ | 10kΩ | 5V |
| Battery monitor (12V→3.3V) | 27kΩ | 10kΩ | 3.2V |
| NTC thermistor bias | 10kΩ | NTC | Variable |
Voltage dividers appear in virtually every electronic system. From sensor interfaces to ADC input scaling, from battery monitoring to audio volume controls — understanding when and how to use a voltage divider correctly prevents common design mistakes.
Microcontrollers typically have 3.3V or 5V ADC inputs. To monitor a 12V lead-acid battery, a voltage divider scales it down: R1=27kΩ, R2=10kΩ gives Vout = 12×10/37 = 3.24V — within 3.3V ADC range. At full charge (14.4V): Vout = 3.89V — exceeds ADC range, so use R1=33kΩ for a safer scale. Always add protection diodes on ADC inputs.
NTC (Negative Temperature Coefficient) thermistors are used in a voltage divider configuration. With a fixed resistor (equal to thermistor value at 25°C) and 3.3V supply: Vout varies from ~0.3V (hot) to ~3V (cold). The ADC reads Vout, the microcontroller calculates thermistor resistance, then uses Steinhart-Hart equation to find temperature. Used in printers, 3D printers, and HVAC systems.
A potentiometer is a variable voltage divider. Rotating the wiper changes the ratio R2/(R1+R2), scaling the audio signal voltage. Log-taper potentiometers (audio taper) are used for volume controls because human hearing perceives loudness logarithmically — a linear taper pot sounds like most volume change happens at the top of the dial.