MihsabaIn series, equivalent resistance is the sum of all resistors. In parallel, add the reciprocal of each resistance, then take the reciprocal of that total. With positive resistances, parallel equivalent resistance is below the smallest branch resistance.
Formula
Series: R = R1 + R2 + ...; Parallel: 1/R = 1/R1 + 1/R2 + ...; Two parallel resistors: R = R1×R2/(R1+R2).
How to calculate
- Identify whether resistors share one path or sit on parallel branches.
- For series, sum the resistances; for parallel, sum reciprocals.
- Check the result in ohms against the expected series/parallel bounds.
Worked examples
| Scenario | Calculation | Answer |
|---|---|---|
| 100 Ω and 200 Ω in series | 100 + 200 | 300 Ω |
| 100 Ω and 200 Ω in parallel | 100×200 / 300 | About 66.67 Ω |
| Two 100 Ω resistors in parallel | 100×100 / 200 | 50 Ω |
Important limitation
The examples assume ideal positive resistors. Mixed circuits require reducing one recognizable series or parallel subnetwork at a time; real components may have tolerances.
Common question
Is parallel equivalent resistance always smaller?
For positive ideal resistors, it is lower than the smallest individual branch resistance.
Try the calculator: Parallel & Series Resistor Calculator – Equivalent Resistance