Formula & Calculator
Voltage Divider Rule
Voltage across a resistor in a series chain.
Interpretation
Voltage divider rule: the voltage across a specific resistor in a series chain is the total voltage multiplied by that resistor divided by the total resistance.
It is widely used to obtain a lower voltage from a higher supply.
Example: V_in=10V, R₁=1kΩ, R₂=2kΩ (total 3k) → V₂ = 10 × (2/3) = 6.67V.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V_x | Output voltage | Volts |
| V_in | Input voltage | Volts |
| R_x | Resistor of interest | Ohms |
| R_T | Total resistance | Ohms |
What it means
The voltage divider rule applies to a series chain of resistors. The voltage across a specific resistor (or combination) is equal to the total voltage multiplied by the ratio of that resistor to the total series resistance. The formula for a single resistor Rx in a series chain with total resistance R_T is V_x = V_in * (R_x / R_T). This rule is widely used in electronic circuits to derive a lower voltage from a higher supply without using a regulator. For example, it is used in biasing transistors, setting reference voltages for comparators, and in analog signal conditioning. The rule assumes that the load current is negligible compared to the divider current; otherwise, loading effects must be considered. The voltage divider can be implemented with potentiometers to provide variable output. In power supplies, it can generate feedback voltages for regulation. The rule is derived directly from Ohm’s law and KVL. Understanding the voltage divider is essential for any electronics designer. Example: With V_in=10V, R1=1kΩ, and R2=2kΩ (total 3kΩ), the voltage across R2 is V2 = 10V * (2k/3k) = 10 * 2/3 = 6.67V.
Worked example
Voltage Divider – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Vin (max) | 12 V |
| Vx (max desired) | 3.3 V |
| RT = R₁ + R₂ | 10 kΩ |
| Formula | Vx = Vin · (R₂ / RT) |
Common mistakes
- R_x: The resistor across which you want the voltage – not the total resistance.
- R_T: Sum of all series resistors – do not forget to include R_x in the total.
- Loaded divider: If a load is connected, the formula changes – use Thevenin.
- Sign: The voltage is referenced to the bottom of the divider (ground).
- AC signals: Works for DC and AC (with impedances instead of resistances).
Applications
The voltage divider rule provides the voltage across a specific resistor in a series chain as the total voltage multiplied by that resistor divided by the total series resistance. This is one of the most widely used formulas in electronics, enabling the generation of reference voltages, signal scaling, and biasing. Engineers apply the voltage divider to create stable reference voltages for analog‑to‑digital converters, to bias transistors, and to set the gain of operational amplifier circuits. In power supplies, it is used for feedback networks to regulate output voltage. The rule is simple yet powerful, allowing quick calculation of intermediate voltages without solving full circuit equations. Mastering the voltage divider is essential for any electronics designer.
- Generating reference voltages for ADCs and comparators
- Biasing transistors and operational amplifiers
- Feedback networks for voltage regulators
- Attenuating signals for measurement and control
- Educational introduction to circuit analysis
Frequently Asked Questions
The voltage across a resistor R_x in a series chain is V_x = V_in × (R_x / R_T), where R_T is the total series resistance.
Voltage dividers are used in sensor circuits (thermistors, LDRs), biasing transistors, adjusting voltage levels, volume controls, generating reference voltages, and level shifting.
The voltage divider is affected by the load connected to it. Adding a load in parallel with the output resistor changes the division ratio and reduces voltage. Use buffer amplifiers for precision.
A loaded voltage divider has a load resistor in parallel with one of the divider resistors. This reduces the output voltage compared to the unloaded case. Consider both divider and load resistance.
Choose resistors whose ratio gives the desired output voltage. Consider the current through the divider (it should be at least 10× the load current for stability). Use standard resistor values.
Maximum power is transferred to the load when load resistance equals the Thevenin resistance of the voltage divider. However, this reduces efficiency to 50%.
A potentiometer is an adjustable voltage divider. By moving the wiper, you change the resistance ratio and thus the output voltage. Used as volume controls, sensor readouts, and position sensors.
The Thevenin equivalent is V_th = V_in × R2/(R1+R2) and R_th = R1||R2 (parallel combination). This simplifies analysis when a load is attached to the voltage divider.
The AC voltage divider uses impedance instead of resistance: V_x = V_in × (Z_x/Z_total). The output is a phasor with both magnitude and phase, so account for phase shifts.
Common errors include: 1) using the wrong total resistance, 2) forgetting to include the load resistance, 3) using the formula for parallel instead of series, 4) mixing up the resistor positions, and 5) applying it to non-linear circuits.