Series Circuit
A series circuit is an electrical circuit in which all components are connected end-to-end along a single path, so the same current flows through each component. The total resistance equals the sum of individual resistances, and the supply voltage is divided among the components. If any component in a series circuit fails (open circuit), current through the entire circuit ceases.
Key Formula
R_total = R1 + R2 + R3 + ... + Rn
LaTeX: R_{\text{total}} = R_1 + R_2 + R_3 + \ldots + R_n
| Symbol | Meaning | Unit |
|---|---|---|
| R_total | Total equivalent resistance | Ohm (Ω) |
| R₁, R₂, R₃ | Individual resistances | Ohm (Ω) |
Worked Example
Problem
Three resistors of 10 Ω, 20 Ω, and 30 Ω are connected in series to a 12 V battery. Find the total resistance, total current, and voltage across each resistor.
Solution
Step 1: R_total = 10 + 20 + 30 = 60 Ω. Step 2: I = V / R_total = 12 / 60 = 0.2 A (same through all). Step 3: V₁ = 0.2 × 10 = 2 V; V₂ = 0.2 × 20 = 4 V; V₃ = 0.2 × 30 = 6 V. Check: 2 + 4 + 6 = 12 V ✓
Answer
R_total = 60 Ω; I = 0.2 A; V₁ = 2 V, V₂ = 4 V, V₃ = 6 V
Key Properties of Series vs Parallel Circuits
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same through all components | Divides among branches |
| Voltage | Divides across components | Same across all branches |
| Total resistance | R_total = R₁ + R₂ + ... | 1/R_total = 1/R₁ + 1/R₂ + ... |
| Effect of one failure | Whole circuit breaks | Other branches unaffected |
| Example use | Old Christmas lights | Household wiring |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Parallel Circuit
A parallel circuit is an electrical circuit in which components are connected across the same two nodes, providing multiple independent current paths each sharing the same voltage. The total resistance of a parallel combination is always less than the smallest individual resistance. Parallel wiring is used in household electrical systems so that each appliance receives the full supply voltage independently.
Electrical Resistance
Electrical resistance is the opposition that a material offers to the flow of electric current, quantifying how much a conductor restricts charge flow for a given applied voltage. It depends on the material's resistivity, its length, and its cross-sectional area, and increases with temperature in most metals. Resistance is central to controlling current in circuits and forms the basis of Ohm's Law.
Ohm's Law
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across those points, provided temperature and other physical conditions remain constant. It is one of the most fundamental relationships in electrical engineering and circuit analysis. The law applies to ohmic (linear) materials and is used to calculate unknown voltages, currents, or resistances in simple circuits.
From Latin "series" meaning "a row" or "chain" — aptly describing the single-path arrangement. The term entered electrical engineering in the late 19th century as circuit theory was formalised by scientists such as Gustav Kirchhoff.