Series Resonance

Sweep a series RLC circuit through resonance. Inductive and capacitive reactance cancel, maximizing current and the resistor voltage. L1 is 10 mH and C1 is approximately 2.533 µF, setting the resonant frequency to 1 kHz. R1 = 10 Ω represents series loss and makes the resonance finite.

Resonance condition

$$\begin{aligned} f_0&=\frac{1}{2\pi\sqrt{LC}}=1\,\mathrm{kHz}\\ X_L(f_0)&=|X_C(f_0)|\approx62.83\,\Omega \end{aligned}$$

The same current passes through L1, C1 and R1. Their reactive voltage drops cancel at resonance, leaving only the resistor in the total impedance.

$$\begin{aligned} Z&=R+j\left(\omega L-\frac{1}{\omega C}\right)\\ I(f_0)&=\frac{1\,\mathrm V}{10\,\Omega}=100\,\mathrm{mA}\\ V_R(f_0)&=1\,\mathrm V\\ Q&=\frac{\omega_0L}{R}\approx6.28 \end{aligned}$$

Read the circuit and response

V1 supplies AC analysis magnitude = 1 V. The green VR probe reads the grounded resistor voltage, and the blue I probe measures series current.

The example opens in AC sweep, from 100 Hz to 10 kHz, with 100 points per decade and a logarithmic frequency axis. The chart shows magnitude and phase. Magnitude in dB is $20\log_{10}(|V|/1\,\mathrm V)$ for voltage or $20\log_{10}(|I|/1\,\mathrm A)$ for current; a 1 V voltage peak is 0 dB. These current dB values are referenced to one ampere, not voltage gain. Open Table to inspect numeric frequency samples, including 1 kHz.

At resonance VR is 1 V and I is 100 mA. Their phases are zero relative to the source. Below resonance the circuit is capacitive; above resonance it is inductive. AC sweep uses the source’s AC analysis magnitude/phase fields. The transient waveform Frequency and Phase fields do not control this sweep.

Try two changes

1. Double C1 → Capacitance to approximately 5.066 µF (5.0661 µF). Resonance moves down to $f_0/\sqrt{2}\approx707.1\,\mathrm{Hz}$. Restore C1 to 2.533 µF.
2. Double R1 → Resistance to 20 Ω. The peak current halves to 50 mA, Q halves and the response broadens. The VR peak remains 1 V at resonance. Restore R1 to 10 Ω afterward.

Model assumptions

This is small-signal sinusoidal steady-state analysis of ideal linear L and C with explicit resistance. It does not show switch-on ringing, saturation, breakdown, winding/ESR frequency dependence or parasitic resonances. Series resonance minimizes driving-point impedance.