Series vs Parallel Resonance
How to Use
- L slider — set inductance (1–100 mH).
- C slider — set capacitance (1–100 µF).
- Q slider — set the quality factor, which controls bandwidth. (R is derived from Q and f₀.)
- f marker slider — move a cursor across both plots to read values at any frequency.
- Sweep f button — animates the frequency cursor automatically across both plots.
What to Observe
- Both circuits share the same resonant frequency f₀ = 1/(2π√LC).
- Series RLC at f₀: Impedance is minimum (= R); current is maximum. XL and XC cancel.
- Parallel RLC at f₀: Impedance is maximum (= Q²R); current from source is minimum.
- At frequencies above or below f₀, both circuits move away from their resonant extremes.
- Higher Q → sharper peak (series) or sharper notch (parallel) → better frequency selectivity.
- Series resonance is used as a bandpass filter (passes f₀, blocks others).
- Parallel resonance is used as a bandstop / tank circuit (blocks f₀, passes others).
Key Equations
Series RLC: [|Z_{series}| = \sqrt{R^2 + (X_L - X_C)^2} \quad \text{(minimum at } f_0\text{)}]
Parallel RLC: [|Z_{parallel}| = \frac{1}{\sqrt{(1/R)^2 + (\omega C - 1/(\omega L))^2}} \quad \text{(maximum at } f_0\text{)}]
Resonant frequency (same for both): [f_0 = \frac{1}{2\pi\sqrt{LC}}, \qquad Q = \frac{\omega_0 L}{R}]
| Property | Series at f₀ | Parallel at f₀ |
|---|---|---|
| Z | ||
| I_source | ||
| Application | Bandpass (select f₀) | Bandstop (reject f₀) |
| Q effect | Voltage magnification | Current magnification |
Key Concepts
- Series resonance: Reactive elements cancel; circuit "looks" purely resistive at f₀
- Parallel resonance: Large circulating current between L and C; source sees high impedance
- Tank circuit: Common name for a parallel LC resonant circuit
- Quality factor Q: Ratio of energy stored to energy dissipated per cycle; controls sharpness