A series circuit is an electrical path where components are connected end-to-end in a single continuous loop, forcing the exact same current to flow through every component. What this topology changes in a real installation is the voltage distribution: instead of every component receiving the full source voltage, the source voltage is divided among the components based on their resistance or impedance. This creates a highly predictable voltage scaling effect, but it also introduces a critical single point of failure—if one component opens, the entire circuit dies.
The Core Rule: Current is Constant, Voltage Divides
To understand a series circuit, forget about voltage for a moment and focus entirely on current. Because there is only one physical path for electrons to travel, the current (measured in Amperes) is identical at every single point in the loop. If you measure 50mA leaving the positive terminal of a battery, exactly 50mA is flowing through the first resistor, the second resistor, and back into the negative terminal.
Think of it like a single-lane road with three toll booths. The number of cars passing through each toll booth per minute (the current) must be exactly the same, because there are no on-ramps or off-ramps. However, each toll booth extracts a toll (voltage drop). The total toll collected across all three booths equals the total amount of money the drivers started with (source voltage). This principle is formalized in Kirchhoff’s Voltage Law (KVL), which states that the sum of all voltage drops in a closed loop must equal the applied source voltage. For a deeper mathematical proof of this behavior, the All About Circuits DC textbook provides an excellent breakdown of KVL in series networks.
Worked Numeric Example: 12V Battery and Three Resistors
Let’s move from theory to the bench. Suppose you have a 12.0V DC power supply and you wire three resistors in series: R1 = 100Ω, R2 = 220Ω, and R3 = 330Ω.
- Find Total Resistance (Rt): In series, resistances simply add up. Rt = 100 + 220 + 330 = 650Ω.
- Calculate Circuit Current (I): Using Ohm’s Law (I = V / R), I = 12.0V / 650Ω = 0.01846A (or 18.46mA). This 18.46mA flows through R1, R2, and R3 equally.
- Calculate Individual Voltage Drops: Now apply Ohm’s Law (V = I × R) to each component.
- V_R1 = 0.01846A × 100Ω = 1.85V
- V_R2 = 0.01846A × 220Ω = 4.06V
- V_R3 = 0.01846A × 330Ω = 6.09V
- Verify with KVL: 1.85V + 4.06V + 6.09V = 12.00V. The math checks out perfectly.
| Component | Resistance | Current | Voltage Drop | Power Dissipated |
|---|---|---|---|---|
| R1 | 100 Ω | 18.46 mA | 1.85 V | 34.1 mW |
| R2 | 220 Ω | 18.46 mA | 4.06 V | 75.0 mW |
| R3 | 330 Ω | 18.46 mA | 6.09 V | 112.4 mW |
| Total | 650 Ω | 18.46 mA | 12.00 V | 221.5 mW |
Notice how the largest resistor (R3) hogs the majority of the voltage and dissipates the most heat. This is a crucial design consideration when sizing components for series voltage dividers.
Where You Meet Series Circuits in Practice
Practical Applications: While we rarely wire entire rooms of AC loads in series, series topologies are everywhere in DC electronics and power systems.
- Battery Packs: Wiring 18650 lithium cells or LiFePO4 prismatic cells in series (e.g., a 3S or 4S configuration) adds their voltages together while keeping the Ah capacity identical to a single cell.
- LED Strips: Cuttable 12V LED strips use a series-parallel hybrid. Each cuttable segment contains three LEDs and one current-limiting resistor wired in series to drop the 12V down safely.
- Voltage Dividers: Two resistors in series are used to scale down a high voltage (like 24V) to a safe logic level (like 3.3V) for an ESP32 or Arduino ADC pin.
- Current Sensing: A low-value shunt resistor placed in series with a load allows a microcontroller to measure current by reading the millivolt drop across the shunt.
For more on how series resistance applies to complex impedance in AC circuits, Georgia State University's HyperPhysics resource is a standard academic reference.
Bench War Story: The 24V Relay Coil Mistake
Theory assumes perfect components; the workbench does not. Here is a real-world scenario walkthrough that demonstrates why you must be careful when wiring inductive loads in series.
The Setup: A junior technician needed to control two 12V DC Omron G2R-1-DC12 relay coils from a single 24V DC PLC output. To save a wire and a PLC output channel, he wired the two 12V relay coils in series across the 24V supply, assuming the voltage would split evenly (12V each).
The Numbers: The datasheet lists the nominal coil resistance at 155Ω. On paper, two 155Ω coils in series equal 310Ω. At 24V, the current is 77.4mA, and the voltage drop across each is exactly 12V. It looked perfect.
The Outcome: When the PLC output turned on, Relay B clicked loudly and pulled in. Relay A buzzed, chattered violently, and failed to latch. Within ten minutes, Relay B’s coil was too hot to touch and eventually burned out.
What Went Wrong: Manufacturing tolerances. Relay A actually measured 140Ω, and Relay B measured 170Ω. Because they were in series, the exact same 77.4mA flowed through both, but the voltage divided unevenly: Relay A got 10.8V, and Relay B got 13.2V. Relay B was overvolted (running hot), while Relay A was undervolted. Worse, relay coils are inductive. When Relay B pulled in first, its mechanical movement changed its inductance dynamically, causing a transient voltage spike that further starved Relay A of the voltage it needed to close its armature. Never wire relay coils or solenoid valves in series.
What People Commonly Confuse With Series Wiring
When discussing home wiring and DIY electronics, the term 'series' gets thrown around incorrectly. Here is what people commonly confuse it with:
- Daisy-Chained Receptacles: People assume that because outlets are wired sequentially from one to the next down a wall, they are in series. They are not. The hot, neutral, and ground wires are merely spliced at each box; the actual loads plugged into the outlets are wired in parallel. If they were in series, plugging in a vacuum cleaner would dim the lamp on the next outlet.
- 3-Way and 4-Way Switches: Multi-way light switches use series logic (the switches must form a continuous path to complete the circuit), but the switches themselves are not series loads. They are control devices routing a single parallel branch.
- Old Christmas Lights: Those old-school mini-lights where one bulb burns out and the whole string dies are true series circuits. Modern LED strings usually use parallel or series-parallel topologies with internal rectifiers.
FAQ: Series Circuit Edge Cases
Q: What happens to the total resistance if I add another resistor in series?
A: Total resistance always increases. Every component you add in series acts as an additional bottleneck, reducing the overall circuit current and increasing the total voltage drop required to maintain that current.
Q: Can I wire two different voltage batteries in series (e.g., a 12V and a 6V)?
A: Yes, their voltages will add up to 18V. However, you must ensure the Ah (Amp-hour) capacity and chemistry of both batteries are identical. If the 6V battery has a lower capacity, it will be driven into deep discharge and potentially reverse-charged by the larger 12V battery, causing severe damage or a fire hazard.
Q: Why does a break in a series circuit stop all current?
A: Because there is only one path for electron flow. An open circuit (a break, a blown fuse, or a burnt-out filament) introduces infinite resistance into that single path. According to Ohm's Law (I = V / ∞), the current drops to absolute zero everywhere in the loop simultaneously.
Q: Do capacitors add up the same way in series as resistors do?
A: No, capacitors behave inversely to resistors in series. The total capacitance of capacitors in series is calculated using the reciprocal formula (1/Ct = 1/C1 + 1/C2 + 1/C3), meaning the total capacitance is always less than the smallest individual capacitor in the string. However, their voltage ratings add together, which is why high-voltage power supplies often use series capacitor banks.
