Engineering Masterclass
Series vs Parallel Circuits — Differences, Formulas & Examples
Clear comparison of series and parallel circuits: current, voltage, resistance formulas, and when to use each. Links to free resistor calculators.
Calculate total R and branch current
Parallel Resistor CalculatorEquivalent R for parallel or series listsOpen calculator Current Divider CalculatorHow current splits across parallel branchesOpen calculator Series-Parallel Circuit SolverNested networks like 1k+(2.2k||4.7k)Open calculator
Full index: All resistor color code values
Series vs parallel at a glance
| Property | Series | Parallel |
|---|---|---|
| Current | Same through every part | Splits among branches |
| Voltage | Divides across parts | Same across every part |
| Total resistance | Sum (always larger) | Reciprocal sum (always smaller) |
| Open failure | Entire path opens | Other branches may still conduct |
Series circuits
Parts share one current path:
Rtotal = R1 + R2 + R3 + …
Use series when you need voltage division, higher total R, or to share voltage/power across packages.
Parallel circuits
Parts share the same two nodes:
1/Rtotal = 1/R1 + 1/R2 + …
For two resistors: Rtotal = (R1 × R2) / (R1 + R2)
Use parallel when you need lower Req, higher power handling, or independent branch currents.
Combination (series-parallel) networks
Real schematics often mix both. Simplify innermost groups first. Example: 1k + (2.2k ∥ 4.7k) ≈ 2.5 kΩ.
- Pure lists → Parallel Resistor Calculator
- Nested expressions → Series-Parallel Circuit Calculator
- Branch currents → Current Divider Calculator
Next reading
- Equivalent Resistance Guide — classroom method for Req
- Ohm's Law Calculator — V, I, R after you know the network