Circuits and conductors
Series–parallel resistance
- where
- total resistance (Ω)
- series resistance (Ω)
- parallel pair resistances (Ω)
Explain this equation
Works out the total resistance of one resistance in series with a parallel pair. A common pattern when reducing real circuits.
Rₜ is the total. R₁ carries the whole current. R₂ and R₃ are the parallel pair that share the current after R₁.
Reduce the parallel pair to one equivalent with product over sum, then add R₁ because it is in series with that equivalent.
Sense check: 10 Ω plus 20 Ω in parallel with 30 Ω gives 10 + 12 = 22 Ω. The total sits above R₁ but below R₁ + R₂ + R₃.
Watch out: do not just add all three. Check which parts actually share both ends before grouping them.
Reduce the parallel part to a single equivalent resistance before adding the series part. Work from the inside of the grouping outward.
R₁ carries total current. After it, current splits between R₂ and R₃ and recombines on return.
Enter your values to see the result.
Common mistake
Adding all three resistances although two are parallel.
Limits
R₁ in series with the parallel pair R₂ and R₃.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.