📘 Introduction
Understanding how resistors combine in series and parallel circuits is essential for designing and analyzing electrical and electronic systems. This guide will break down the key formulas, provide easy-to-follow examples, and explain when and why each configuration is used.
🔗 Resistors in Series
When resistors are connected end-to-end, they form a series connection. The total resistance increases because the current must pass through each resistor in turn.
Formula:
Rtotal = R₁ + R₂ + R₃ + ... + Rn
Key Features:
- Same current flows through all resistors
- Voltage divides across resistors
- Total resistance is the sum of individual resistances
⚡ Resistors in Parallel
When resistors are connected across the same two nodes, they are in a parallel configuration. The total resistance decreases because the current splits and takes multiple paths.
Formula:
1 / Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rn
Key Features:
- Same voltage across all resistors
- Current splits among resistors
- Total resistance is always less than the smallest resistor
📏 Series and Parallel Resistance Formulas
| Configuration | Total Resistance Formula |
|---|---|
| Series | Rtotal = R₁ + R₂ + R₃ + ... |
| Parallel | 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ... |
🧮 Example Calculations
Series Example:
R₁ = 100Ω, R₂ = 220Ω, R₃ = 330Ω
Rtotal = 100 + 220 + 330 = 650Ω
Parallel Example:
R₁ = 100Ω, R₂ = 200Ω
1/Rtotal = 1/100 + 1/200 = 0.015 → Rtotal ≈ 66.67Ω
🔍 Real-World Applications
- Series: Used in LED strings to ensure equal current
- Parallel: Load sharing in power supplies, precise control of resistance
❓ FAQ
Q: Can I mix series and parallel resistors?
Yes! Complex circuits often use a combination. Use the formulas step by step for each section.
Q: What if one resistor fails?
In series, the whole circuit breaks. In parallel, current can still flow through other paths.
Q: Does temperature affect resistance?
Yes, most resistors have a temperature coefficient. High-temp use may require specific materials.
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Recommended Reading: Ultimate Guide to Resistors
