Voltage Divider
Output voltage from two series resistors.
Formula
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How it works
A voltage divider uses two resistors in series to split an input voltage into a smaller output voltage across one of the resistors. Because the same current flows through both resistors in a series circuit, the voltage across each resistor is proportional to its resistance, so the output across R_2 is the input voltage multiplied by the fraction R_2 / (R_1 + R_2). This comes directly from Ohm’s law and the fact that series resistances add.
When to use it
Use this when you need to create a lower reference voltage from a higher supply, such as feeding an analog input, setting a bias voltage, or scaling a signal for a sensor or microcontroller. It is also useful any time two resistors are used in series and you want the voltage at their midpoint.
Worked example, step by step
Given: V_in = 12 V, R_1 = 3 kΩ, R_2 = 9 kΩ Step 1: Add the resistors in series: R_1 + R_2 = 3 kΩ + 9 kΩ = 12 kΩ Step 2: Substitute into the formula: V_out = V_in × R_2 / (R_1 + R_2) Step 3: V_out = 12 × 9 / 12 Step 4: V_out = 9 V Final answer: The output voltage across R_2 is 9 V.
Common mistakes to avoid
- Using the wrong resistor in the numerator, which gives the voltage across the other resistor instead
- Forgetting that the resistors must be in series for this formula to apply
- Ignoring load current on the output, which can change the divider voltage in real circuits
Did You Know?
The humble voltage divider, just two resistors, is one of the most-used circuits in all of electronics.
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More in Electronics & Circuits
View allOhm's Law
BasicVoltage equals current times resistance.
Electrical Power (VI)
BasicPower dissipated by a component.
Power (I²R)
BasicPower lost as heat in a resistor.
Power (V²/R)
BasicPower from voltage and resistance.
Resistors in Series
BasicSeries resistances add directly.
Resistors in Parallel
IntermediateReciprocals of parallel resistances add.