Calculator · Electrical Engineering
RLC Transient Response Calculator
A series RLC circuit switched onto a DC source Vs at t = 0, starting from an explicit capacitor voltage Vc(0) and loop current i(0). The damping ratio ζ decides whether the response rings (underdamped), settles fastest without overshoot (critical) or creeps (overdamped). Vs = 0 gives the natural response.
Inputs
Results
Damping
Capacitor voltage Vc(t)
Current i(t)
| Neper frequency α = R/(2L) | 2 1/s |
|---|---|
| Undamped natural frequency ω0 | 10 rad/s |
| Damping ratio ζ = α/ω0 | 200 m |
| Damped frequency ωd | 9.798 rad/s |
| Initial conditions | Vc(0) = 0 V · i(0) = 0 A |
| Response type | Step response |
Explore in the Lab
Same circuit and initial conditions; the inspected time is t.
Technical reference
L·C·Vc'' + R·C·Vc' + Vc = Vs
α = R/(2L), ω0 = 1/√(LC), ζ = α/ω0
ζ < 1: Vc = Vs + e^(−αt)(A cos ωd t + B sin ωd t), ωd = √(ω0² − α²)
ζ = 1: Vc = Vs + (A + Bt)e^(−αt); ζ > 1: Vc = Vs + A1e^(s1 t) + A2e^(s2 t)
i = C·dVc/dt; A, B fixed by Vc(0) and i(0)
- R
- series resistance (≥ 0)[Ω]
- L
- inductance (> 0)[H]
- C
- capacitance (> 0)[F]
- Vs
- DC step applied at t = 0[V]
- t
- time since the step (≥ 0)[s]
Reference: L = 1 H, C = 10 mF → ω0 = 10 rad/s; R = 20 Ω is critically damped.
R = 0 is the lossless LC oscillation (ζ = 0).