Series Circuits

Part of Basic Electrical Circuits

How series circuits behave, where they are and are not appropriate, and the calculations needed to design and troubleshoot them.

Why This Matters

Series circuits—where components connect end-to-end along a single current path—are the simplest circuit topology. They appear in every battery string, every current-limiting resistor, every fuse, and every voltage divider. Despite being the simplest configuration, series circuits have important and often counterintuitive properties that cause problems for those who don’t understand them.

The most common error in series circuits: connecting multiple batteries in series without understanding that the weakest battery limits the whole string, or adding a second lamp in series with an existing one expecting to add more light, only to find both lamps dim. Understanding series circuit behavior prevents these mistakes and enables deliberate use of series connections—stacking battery voltages, creating voltage dividers, controlling current with series resistors.

Series and parallel circuits are the two fundamental building blocks of all more complex circuit configurations. Series circuit mastery is prerequisite to everything that follows.

The Defining Properties

In a series circuit, there is only one path for current. Therefore:

1. Current is identical through every component: I₁ = I₂ = I₃ = I_total
2. Voltage divides between components proportionally to their resistance: V_total = V₁ + V₂ + V₃ + …
3. Total resistance is the sum of all individual resistances: R_total = R₁ + R₂ + R₃ + …

Property 1 follows directly from the single path: every electron that passes through one component must pass through all others. There is nowhere else to go.

Property 2 is a statement of Kirchhoff’s Voltage Law: the total voltage rise from the source must equal the total voltage drop across all loads.

Property 3 follows from Properties 1 and 2 combined with Ohm’s Law.

Calculating Series Circuit Behavior

Basic procedure:

1. Sum all resistances: R_total = R₁ + R₂ + … + R_n
2. Calculate total current: I = V_supply / R_total
3. Calculate voltage across each component: V_n = I × R_n

The same current I flows through every component.

Example: A 24V battery (internal resistance 0.5Ω) powers three series loads:

• R₁ = 4Ω (a lamp)
• R₂ = 8Ω (a heater element)
• R₃ = 3.5Ω (a motor winding)

R_total = 0.5 + 4 + 8 + 3.5 = 16Ω I = 24V / 16Ω = 1.5A (same through all components)

Voltage drops:

• Across internal resistance: 1.5A × 0.5Ω = 0.75V (energy wasted in battery)
• Across lamp: 1.5A × 4Ω = 6V
• Across heater: 1.5A × 8Ω = 12V
• Across motor: 1.5A × 3.5Ω = 5.25V

Check: 0.75 + 6 + 12 + 5.25 = 24V ✓

Power dissipated in each component:

• Lamp: 1.5A × 6V = 9W
• Heater: 1.5A × 12V = 18W
• Motor: 1.5A × 5.25V = 7.875W
• Battery internal: 1.5A × 0.75V = 1.125W (waste)

Voltage Dividers

A voltage divider uses two series resistors to create an intermediate voltage from a supply:

V_out = V_in × R₂ / (R₁ + R₂)

Where V_out is measured across R₂ (the lower resistor, connected from the output to ground).

Applications:

• Create a 5V reference from a 12V supply for a control circuit
• Create a low-voltage test signal from a high-voltage source
• Reduce the voltage to a sensor whose range is lower than the supply

Important limitation: A voltage divider only works as a voltage source for loads that draw very little current compared to the divider current. If the load draws significant current, it appears in parallel with R₂, reducing the effective resistance and lowering V_out.

Rule of thumb: for a voltage divider to be stable, the load resistance should be at least 10× larger than R₂. If the load resistance is lower, use a different approach (a separate winding on a transformer, or a different supply).

Series Battery Connections

Connecting batteries in series adds their voltages:

• Three 6V batteries in series = 18V
• Four 1.5V cells in series = 6V

The current capacity remains limited by the weakest battery or the lowest-rated cell.

Series battery hazards:

Cell reversal: If one cell discharges completely and others continue to drive current through it, the dead cell is driven in reverse—its polarity reverses. This damages most battery chemistries permanently and can cause venting or rupture in sealed cells.

Unmatched capacities: If cells have different capacities (due to age or damage), the weakest cell reaches full discharge first and is subsequently driven into reversal. Always use matched batteries in series strings.

Charging series batteries: Each cell must be charged to the same voltage. In a series string, the charger applies total voltage to all cells equally only if all cells have identical internal resistance. Mismatched cells may overcharge or undercharge individually. For important applications, charge cells individually before assembling the series string.

Series Lamps: A Common Mistake

Christmas lights and early wiring designs connected lamps in series. The problems:

• All lamps must carry the same current—if lamps are rated for different currents, mismatched brightness
• One lamp fails open: all go out (the “one failed, all fail” problem)
• Adding another lamp in series reduces current and dims all lamps

For lighting distribution, parallel connection is almost always correct.

Where series lamps are used deliberately:

• Series-parallel strings where a set number of low-voltage lamps share a higher supply voltage
• Current-limited circuits where the series resistance of additional lamps prevents excessive current

Series vs. Parallel: Decision Guide

Situation	Series	Parallel
Increasing voltage from batteries	Yes	No
Increasing capacity from batteries	No	Yes
Distributing loads in a building	No	Yes
Limiting current to a load	Yes (series resistor)	No
Fault tolerance required	No (one open = all fail)	Yes
Current control required	Yes	No
Stacking voltages	Yes	No

Series Circuit Fault Diagnosis

Open circuit in one component: All current stops. The full supply voltage appears across the open component (and zero across all others). Measure voltage across each component to find which one shows full supply voltage—that is the open circuit.

Short circuit across one component: Remaining components share the full supply voltage, with the shorted component showing zero volts. Current increases through all remaining components (R_total decreases, current = V/R_total). Remaining components may overheat due to higher current.

High resistance in one component: Voltage across that component increases; voltage across all others decreases. Current throughout the circuit decreases. This is the behavior of a corroded connection, partially damaged wire, or resistive component that has drifted high.

Systematic diagnosis: Measure voltage across each component in the series chain. The ratios should equal the ratios of their resistances. Any component with unexpectedly high or low voltage indicates a fault at that location.