A voltage divider is a circuit of two or more resistors in series across a voltage source, where the voltage across one resistor is a fixed fraction of the source voltage. For two resistors, V_out = V_in × R₂ / (R₁ + R₂), where V_out is taken across R₂.
Learning objectives
- Apply the two-resistor voltage divider formula.
- Calculate the divider current and the power dissipated in each resistor.
- Explain how a connected load changes the output voltage.
- Choose sensible resistor values for a given load and accuracy.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
Dividers are common in sensor circuits, reference settings and signal scaling. But a divider is not a power supply: if you connect a load across the output, it draws current and changes the division. This loading effect is one of the most important practical limitations of a simple divider.
Intermediate How it behaves in a circuit
When a load R_L is connected across R₂, the effective lower resistance becomes R₂ || R_L, and V_out = V_in × (R₂ || R_L)/(R₁ + R₂ || R_L). This is always lower than the unloaded value. For a given load, a divider with smaller resistances is stiffer but draws more current and dissipates more power.
Advanced Limits, assumptions, engineering detail
Dividers are often used with a buffer amplifier to isolate the load, or replaced by a regulator when the load current varies. In high-voltage measurement, the divider must be designed with appropriate creepage, clearance and resistor voltage ratings, and the voltmeter’s input resistance is part of the divider. Capacitive dividers are used for AC and pulse measurements, where the ratio depends on capacitances instead of resistances.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | V | volt (V) |
| Resistance | R | ohm (Ω) |
| Current | I | ampere (A) |
| Power | P | watt (W) |
Worked examples
Output of an unloaded divider
Problem. A 12 V supply feeds R₁ = 10 kΩ in series with R₂ = 4.7 kΩ, with the output across R₂. Find V_out.
Solution. V_out = 12 × 4.7/(10 + 4.7) = 12 × 4.7/14.7 = 56.4/14.7 ≈ 3.84 V.
Effect of connecting a load
Problem. A 9.0 V supply feeds R₁ = 1.0 kΩ and R₂ = 2.0 kΩ. Find V_out unloaded and then with a 10 kΩ load across R₂.
Solution. Unloaded: V_out = 9.0 × 2.0/3.0 = 6.0 V. Loaded: R₂ || R_L = (2.0 × 10)/(2.0 + 10) = 20/12 ≈ 1.667 kΩ. V_out = 9.0 × 1.667/(1.0 + 1.667) = 9.0 × 1.667/2.667 ≈ 5.63 V.
Practical applications
- Sensor signal scaling
- Reference and bias voltages
- Battery voltage monitoring
- Adjustable feedback networks
Automotive applications
Voltage dividers appear in sensor circuits and module inputs: a thermistor or potentiometer forms one arm of a divider, and the module measures the resulting voltage. A damaged ground or an unexpected parallel path changes the divider ratio and produces a plausible but wrong sensor reading. Technicians compare the measured voltage with the expected divider value and check the reference and ground supplies before condemning the sensor.
Industrial applications
Industrial measurement uses dividers to scale high voltages into the input range of meters, PLC analogue inputs and data-acquisition systems. Signal conditioning often adds buffering and filtering, because a bare divider has a relatively high output impedance and is susceptible to noise and cable capacitance. For safety-related high-voltage measurement, the divider’s insulation and resistor ratings are part of the design.
Measurement procedure
- A voltmeter’s input resistance appears in parallel with the lower resistor and lowers the measured output.
- Use a high-impedance meter, or account for its resistance when the divider resistors are comparable in value.
- Measure the input voltage and the output voltage together, since the input may sag when loaded.
- Check both resistors and the ground connection; an open upper resistor gives zero output, while an open lower resistor gives the full input.
Common mistakes
- Ignoring the load and using the unloaded formula for a loaded output.
- Swapping R₁ and R₂ when the output is expected across the other resistor.
- Trying to power a load from a divider instead of using a regulator or buffer.
- Choosing resistor values so high that the meter or load resistance dominates the result.
Safety considerations
- A divider does not provide isolation from the input; the whole network may be at a hazardous potential.
- Check the voltage rating of the resistors, especially in high-voltage dividers.
- Allow for power dissipation in each resistor; an undersized resistor can overheat even in a low-current divider.