Series and Parallel Circuits: Why the Difference Matters
Every electrical circuit falls into one of two basic configurations — series or parallel — or a combination of both. Understanding how each type behaves is critical for accurate circuit analysis, safe wiring, and correct component selection.
Series Circuits (直列回路)
In a series circuit, all components are connected end-to-end in a single path. Current has only one route to travel.
Key Rules for Series Circuits
- Current is the same through every component: Itotal = I1 = I2 = I3
- Voltage divides across each component: Vtotal = V1 + V2 + V3
- Total resistance adds up: Rtotal = R1 + R2 + R3
Series Circuit Example
Three resistors — 4 Ω, 6 Ω, and 10 Ω — are connected in series to a 40 V supply.
- Rtotal = 4 + 6 + 10 = 20 Ω
- I = V ÷ R = 40 ÷ 20 = 2 A (same everywhere)
- V across 4 Ω = 2 × 4 = 8 V
- V across 6 Ω = 2 × 6 = 12 V
- V across 10 Ω = 2 × 10 = 20 V
Parallel Circuits (並列回路)
In a parallel circuit, components are connected across common nodes, giving current multiple paths to flow through.
Key Rules for Parallel Circuits
- Voltage is the same across every branch: Vtotal = V1 = V2 = V3
- Current divides among branches: Itotal = I1 + I2 + I3
- Total resistance is less than the smallest branch: 1/Rtotal = 1/R1 + 1/R2 + 1/R3
Parallel Circuit Example
Three resistors — 10 Ω, 20 Ω, and 20 Ω — are connected in parallel to a 20 V supply.
- 1/Rtotal = 1/10 + 1/20 + 1/20 = 0.1 + 0.05 + 0.05 = 0.2
- Rtotal = 1 ÷ 0.2 = 5 Ω
- Itotal = 20 ÷ 5 = 4 A
- I through 10 Ω = 20 ÷ 10 = 2 A
- I through each 20 Ω = 20 ÷ 20 = 1 A each
Comparison Table
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same everywhere | Splits between branches |
| Voltage | Splits across components | Same across each branch |
| Total Resistance | Sum of all resistors | Less than smallest resistor |
| Failure effect | One break stops all | Other branches still work |
Real-World Applications
Series circuits are used in fuses and simple control loops — a break anywhere interrupts the whole circuit (a safety feature). Parallel circuits are used in household wiring so that turning off one appliance doesn't affect others. Most real-world circuits are combinations of both.
Tips for Mixed Circuit Analysis
- Identify all purely series and purely parallel groups first.
- Simplify each group to a single equivalent resistance.
- Redraw the simplified circuit and repeat until one resistance remains.
- Work back through the steps to find individual currents and voltages.