How it works
Resistors in series carry the same current, so their voltage drops add and their resistances add. Resistors in parallel share the same voltage, so their conductances (1/R) add and the total is the reciprocal of that sum, always less than the smallest resistor.
A voltage divider is two resistors in series: the output taken across the second resistor is the source voltage times R₂ divided by the total. It assumes nothing else loads the output.
Worked example
Resistors of 1 kΩ and 2 kΩ on a 12 V source:
- Series = 1,000 + 2,000 = 3,000 Ω
- Parallel = 1 ÷ (1/1,000 + 1/2,000) = 666.667 Ω
- Divider = 12 V × 2,000 ÷ (1,000 + 2,000) = 8 V
- Series current = 12 ÷ 3,000 = 0.004 A; power = 12² ÷ 3,000 = 0.048 W
| Input | Value |
|---|---|
| Resistor 1 | 1000 Ω |
| Resistor 2 | 2000 Ω |
| Third resistor | Not used |
| Resistor 3 (if used) | 3000 Ω |
| Source voltage | 12 V |
| Result | Value |
|---|---|
| Total in series | 3 kΩ |
| Total in parallel | 666.667 Ω |
| Divider output across R₂ (R₁ over R₂) | 8 V |
| Current in the series circuit | 4 mA |
| Power in the series circuit | 48 mW |
Assumptions and limits
- Ideal resistors; tolerances, temperature coefficients, and power ratings are not modeled.
- The divider output is unloaded. A load on Vout lowers it, since the load is in parallel with R₂.
- The series current and power are for all resistors connected in one loop across the source.
Common questions
How do I find the total resistance in parallel?
Add the reciprocals of the resistances and take the reciprocal of the sum. For two resistors this is R₁R₂ ÷ (R₁ + R₂).
Why is parallel resistance always smaller?
Each added path gives the current another way through, so the total opposition falls below the smallest single resistor.
How does a voltage divider work?
Two series resistors split the source voltage in proportion to their resistances; the output across R₂ is Vin × R₂ ÷ (R₁ + R₂).
Does it account for loading?
No. Put the load’s resistance in parallel with R₂ and use the parallel result as the lower resistor.
Sources
- Series and parallel resistance and the voltage-divider rule, from standard circuit theory (Kirchhoff’s laws with Ohm’s law).
Updated 2026-09-30