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RLC Series Circuit Transient Response MicroSim

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Run the RLC Circuit MicroSim in fullscreen

Description

This MicroSim visualizes the second-order transient response of a series RLC circuit. When the switch closes, a DC source charges a capacitor through a resistor and inductor. Depending on the resistance, the response can be underdamped (oscillating), critically damped (fastest non-oscillating), or overdamped (sluggish, exponential).

Key Parameters:

Parameter Formula Description
Neper frequency \(\alpha = \frac{R}{2L}\) Controls envelope decay rate
Natural frequency \(\omega_0 = \frac{1}{\sqrt{LC}}\) Undamped oscillation frequency
Damped frequency \(\omega_d = \sqrt{\omega_0^2 - \alpha^2}\) Actual oscillation frequency
Critical resistance \(R_{crit} = 2\sqrt{L/C}\) Boundary between damped/underdamped

Damping Conditions:

Condition Response
\(R < R_{crit}\) (α < ω₀) Underdamped — Vc overshoots and oscillates
\(R = R_{crit}\) (α = ω₀) Critically damped — fastest rise without overshoot
\(R > R_{crit}\) (α > ω₀) Overdamped — slow exponential rise, no oscillation

Interactive Features:

  • Resistance Slider: Sweep from 0Ω through critical damping to overdamped
  • Inductance & Capacitance Sliders: Change natural frequency ω₀
  • Damping Info Box: Live display of α, ω₀, ωd, R_crit, and damping type
  • Animated Electrons: Flow speed proportional to current magnitude
  • Capacitor Fill: Visual charge level indicator
  • Inductor Glow: Blue glow proportional to stored magnetic energy

How to Use

  1. Click Start — switch closes, circuit starts charging with default R=20Ω (underdamped)
  2. Observe Vc overshoot above Vs and IL oscillations in the graphs
  3. Reset, then drag the R slider to R_crit (shown in the info box) — see critically damped response
  4. Keep increasing R past R_crit — observe overdamped, sluggish response
  5. Change L and C to shift the natural frequency ω₀

Technical Notes

The simulation uses numerical integration (Euler method with 20 sub-steps per frame):

\[ \frac{dI_L}{dt} = \frac{V_s - RI_L - V_C}{L} \]
\[ \frac{dV_C}{dt} = \frac{I_L}{C} \]

Animation speed scales with the natural period \(T_0 = 2\pi/\omega_0\), so one natural period takes approximately one real second regardless of component values.

References