Resistors and Capacitors in Series and Parallel Circuits
Definition
Series Circuit
A circuit where components are connected one after another in a single loop, so current flows through each component in turn.
Definition
Parallel Circuit
A circuit where the electrical path splits into branches, so current divides and only part flows through each branch.
Resistors in Series and Parallel
Definition
Resistor
An electronic component that limits or controls the flow of electric current in a circuit.
| Configuration | Rule | Example Calculation |
|---|---|---|
| Series | Total Resistance (Rₜ) = R₁ + R₂ + R₃… | Rₜ = 10 + 20 = 30 Ω |
| Parallel | 1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃… | 1/Rₜ = 1/10 + 1/20 → Rₜ = 6.67 Ω |
Example
- If you have three resistors with values of 2Ω, 3Ω, and 5Ω in series, the total resistance is 10Ω.
- For two resistors of 4Ω and 6Ω in parallel, the total resistance is 2.4Ω.
Tip
- Use series to increase resistance.
- Use parallel to reduce resistance and allow more current flow.
Capacitors in Series and Parallel
Definition
Capacitor
An electronic component that stores and releases electrical energy by holding an electric charge between two conductive plates.
| Configuration | Rule | Example Calculation |
|---|---|---|
| Series | 1/Cₜ = 1/C₁ + 1/C₂ + 1/C₃… | 1/Cₜ = 1/4 + 1/4 → Cₜ = 2 µF |
| Parallel | Total Capacitance (Cₜ) = C₁ + C₂ + C₃… | Cₜ = 4 + 4 = 8 µF |
Example
- If you have two capacitors of 4μF and 6μF in series, the total capacitance is 2.4μF.
- For three capacitors of 2μF, 3μF, and 5μF in parallel, the total capacitance is 10μF.
Tip
- Use parallel to increase storage capacity (e.g., energy backup).
- Use series for higher voltage applications.
Why This Matters
- Series resistors: Useful for limiting current (e.g., LED protection).
- Parallel resistors: Useful for maintaining current across multiple branches.
- Parallel capacitors: Store more charge => good for power supply smoothing.
- Series capacitors: Handle higher voltages=> used in filtering and timing.
Exam technique
Use correct units:
- Resistance (Ω)
- Capacitance (µF or farads)
