EL03 · Sem 3 · Network analysis

Series RLC: under-damped ringing

Aim: See the natural frequency and damping of a series RLC circuit.

🧪 Live simulation🧊 Real-time 3D bench⚠ Simulated values, not physical measurements

🔬 Virtual lab

Starting the lab…

📘 Theory

An RLC circuit exchanges energy between the inductor and capacitor. With a small resistance the response rings at about ω₀ = 1/√(LC) and decays with α = R/2L. The damping ratio ζ = (R/2)√(C/L) decides under-, critically- or over-damped behaviour.

f₀ = 1 / (2π√(LC)) · ζ = (R/2)·√(C/L) · R_crit = 2√(L/C)

🧰 Apparatus (virtual)

Step source
10 Ω
10 mH
1 µF
oscilloscope

📝 Procedure

Run the simulation and measure the ringing period on the scope
Compute 2π√(LC) and compare
Raise R with the knob until the ringing just disappears
Note that value as the critical resistance

Observations and result (kept on this device)

🎤 Viva questions

What resistance gives critical damping here

R = 2√(L/C) = 2√(0.01/1e-6) = 200 Ω.

Where is this used

Snubbers, filters, and in the tuning of control loops.

🛡️ Safety

Virtual lab at safe low voltages. On a real bench: switch off before rewiring, check capacitor polarity, and never touch mains wiring without supervision.