Voltage Divider Output
Output of a two-resistor divider.
Formula
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Example
Scales voltage down
How it works
This formula tells you the voltage at the midpoint of two resistors connected in series across a source. It comes from the fact that the same current flows through both resistors, so the voltage across each one is proportional to its resistance; the output is the share of the input that appears across R_2. Because a larger R_2 takes a larger fraction of the total voltage, the output increases as R_2 grows relative to R_1.
When to use it
Use this when you need to find the node voltage in a simple resistor divider, such as reducing a sensor or supply voltage to a safer level for an input pin. It is also useful for quick circuit checks and choosing resistor values before building a prototype.
Worked example, step by step
Given: V_in = 12 V, R_1 = 3 kΩ, R_2 = 1 kΩ Step 1: Add the resistors: R_1 + R_2 = 3 kΩ + 1 kΩ = 4 kΩ Step 2: Compute the fraction: R_2 / (R_1 + R_2) = 1 kΩ / 4 kΩ = 0.25 Step 3: Multiply by the input voltage: V_out = 12 V × 0.25 = 3 V Final answer: V_out = 3 V
Common mistakes to avoid
- Swapping R_1 and R_2 in the fraction
- Using the formula for a loaded divider without accounting for the extra load resistance
- Forgetting that the resistors must be in series for this relation to apply
Did You Know?
A thermistor's resistance swings sharply with temperature, making it the sensor in most digital thermometers.
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