Resistors in Series
Total resistance of resistors in series.
Formula
Variables
Example
Resistors of 2 Ω and 3 Ω in series total 5 Ω.
How it works
When resistors are connected end-to-end in a single path, the same current must pass through each one. Each resistor causes a voltage drop, so the source has to overcome all of those drops, which makes the total opposition to current equal to the sum of the individual resistances. This is why series resistances add directly.
When to use it
Use this formula for any circuit where components are connected in one continuous chain with no branching paths. It is especially useful when combining fixed resistors or checking the total resistance seen by a battery or power supply.
Worked example, step by step
A circuit has three resistors in series: 4 Ω, 6 Ω, and 10 Ω. Step 1: Write the series formula: R_eq = R_1 + R_2 + R_3 Step 2: Substitute the values: R_eq = 4 + 6 + 10 Step 3: Add them: R_eq = 20 Ω Final answer: The equivalent resistance is 20 Ω.
Common mistakes to avoid
- Adding resistors in series using the reciprocal formula, which is only for parallel circuits
- Forgetting to include every resistor in the single current path
- Mixing units, such as combining ohms with kilohms without converting first
Did You Know?
Resistors in series simply add up — the current has only one path through them all.
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