How to Calculate Series and Parallel Resistance
Resistors in a circuit can be connected in series (one after another) or in parallel (side by side). In a series circuit, current must flow through each resistor in turn and resistances simply add. In a parallel circuit, current splits across multiple paths, and the total resistance is always less than the smallest individual resistor. Mixed circuits are solved by combining groups using both rules.
Last updated: March 31, 2026
The Formula
Series: R_total = R1 + R2 + R3 + … Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 + … For two resistors in parallel (simplified): R_total = (R1 × R2) / (R1 + R2) Current divider (parallel): I1 = I_total × R2 / (R1 + R2) Voltage divider (series): V1 = V_total × R1 / (R1 + R2)
Variable Definitions
| Symbol | Name | Description |
|---|---|---|
| R_total | Total Resistance | The equivalent single resistance that produces the same effect as the resistor network |
| R1, R2 | Individual Resistors | The resistance values of each component, in ohms (Ω) |
| I | Current | Electrical current in amperes — same throughout a series circuit |
Step-by-Step Example
Find the total resistance of: R1 = 10Ω and R2 = 20Ω in series, then that combination in parallel with R3 = 15Ω.
Given
Solution
- 1Series combination of R1 and R2:
R12 = 10 + 20 = 30 Ω - 2R12 in parallel with R3:
1/R_total = 1/30 + 1/15 = 1/30 + 2/30 = 3/30 = 1/10 - 3Invert to find R_total:
R_total = 10 Ω
Total resistance = 10 Ω.
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Common Mistakes to Avoid
Adding parallel resistors instead of using the reciprocal formula — in parallel, use 1/R_total = Σ(1/Rn).
Forgetting to invert after summing the reciprocals — the formula gives 1/R_total, so you must take 1/(the result) to get R_total.
Assuming parallel resistance equals the average — it is always less than the smallest resistor in the parallel group.
Mixing up current and voltage rules — current is constant in series, voltage is constant in parallel.