AC Circuit Cheat Sheet (R, L, C)
1. Basic Quantities
- Angular frequency: ω = 2πf
- Inductive reactance: XL = ωL
- Capacitive reactance: XC = 1 / (ωC)
2. Pure Components
Pure Resistor (R)
- Impedance: Z = R
- Phase angle: φ = 0°
- Voltage and current are in phase
Pure Inductor (L)
- Impedance: Z = jωL
- Phase angle: φ = +90°
- Current lags voltage
Pure Capacitor (C)
- Impedance: Z = 1 / (jωC)
- Phase angle: φ = −90°
- Current leads voltage
3. RL Circuit (Series)
- Impedance: Z = √(R² + (ωL)²)
- Phase angle: φ = tan⁻¹(ωL / R)
- Current lags voltage
Special Cases
- ωL >> R → behaves like inductor (φ ≈ 90°)
- R >> ωL → behaves like resistor (φ ≈ 0°)
4. RC Circuit (Series)
- Impedance: Z = √(R² + (1/ωC)²)
- Phase angle: φ = tan⁻¹(−1 / (ωCR))
- Current leads voltage
Special Cases
- 1/ωC >> R → behaves like capacitor (φ ≈ −90°)
- R >> 1/ωC → behaves like resistor (φ ≈ 0°)
5. RLC Circuit (Series)
- Impedance: Z = √[R² + (XL − XC)²]
- Phase angle: φ = tan⁻¹((XL − XC)/R)
6. Key Conditions in RLC
Inductive Case
- XL > XC
- φ > 0
- Current lags
Capacitive Case
- XC > XL
- φ < 0
- Current leads
Resonance Condition
- XL = XC → ωL = 1/ωC
- Frequency: f₀ = 1 / (2Ï€√(LC))
- Z = R (minimum)
- φ = 0°
- Current is maximum
7. Power Factor
Power factor = cosφ
| Condition | Power Factor |
|---|---|
| Pure Resistor | 1 |
| Inductive | Lagging |
| Capacitive | Leading |
| Resonance | 1 |
8. Current Amplitude
I₀ = V₀ / Z
Summary
- L → Lag (Inductor)
- C → Lead (Capacitor)
- Resonance → Maximum current
- High impedance → Low current