Resistors in Series
Simple Explanation
When resistors are connected in series (one after another, forming a single path for current), their resistances simply add together to give the total (equivalent) resistance β the total is always greater than any individual resistor in the combination.
Why Do We Need It?
Series combinations are one of the two fundamental ways to combine resistors, and understanding when to add resistances directly (as opposed to using the parallel formula) is essential for circuit analysis.
Formula
Resistors in Series
Rβ = Rβ + Rβ + Rβ + ...
When resistors are connected in series (end to end, one path for current), their resistances simply add together to give the total (equivalent) resistance.
- Rβ
- β Total (equivalent) resistance of the series combination, in ohms
- Rβ, Rβ, Rβ...
- β Resistance of each individual resistor, in ohms
When to use it: Use to find the total resistance of resistors connected end-to-end along a single current path.
Worked Example
Finding total series resistance
Three resistors of 4 Ξ©, 6 Ξ©, and 10 Ξ© are connected in series. Find the total resistance.
Why Does This Work?
In a series circuit, the same current must flow through every resistor one after another β each resistor adds its own opposition to that single current path, so the total opposition (resistance) is simply the sum of each individual opposition, exactly like walking through several doorways of different widths one after another slows you down by the sum of each individual delay.
Real-Life Example
Old-style string Christmas lights
Older strings of Christmas lights sometimes go completely dark if just one bulb burns out.
These lights are wired in series β since series components share a single current path, a broken bulb (infinite resistance) completely interrupts the entire path, stopping current everywhere in the string.
Practice
Two resistors of 15 Ξ© and 25 Ξ© are connected in series. Find the total resistance.
MediumCommon mistake
Applying the series formula to resistors that are actually connected in parallel β always check the circuit topology (single path vs. multiple paths) before choosing the series or parallel formula.
Quick Review
- Rβ = Rβ + Rβ + Rβ + ... for resistors in series.
- Series total resistance is always greater than any individual resistor.
- Series components share a single current path β one break interrupts the whole circuit.