University, Electromagnetism Round 1/6 Score 0

〰️ RLC Tuner

Tune damping, resonance and quality factor in a series RLC circuit.

Transient response

Natural frequency 0 Hz
Critical resistance 0 Ω
Quality factor Q 0
Damping regime Critical
R XL − XC Z = R + j(XL − XC) XL = ωL XC = 1/(ωC)
At resonance, inductive and capacitive reactances cancel.

Tune the resistance

Step response

Frequency response

The physics

Series RLC: L d²q/dt² + R dq/dt + q/C = Vsource.

Natural angular frequency: ω₀ = 1/√(LC) (rad/s).

Critical damping: Rcrit = 2√(L/C) (Ω).

R below Rcrit: underdamped; R equal to Rcrit: critically damped; R above Rcrit: overdamped.

Resonance: f₀ = 1/(2π√(LC)) (Hz).

Quality factor: Q = (1/R)√(L/C), dimensionless.

Steady-state current: |I| = Vac/√(R² + (ωL − 1/(ωC))²).

At the −3 dB points, current amplitude is peak amplitude divided by √2. For a series circuit, bandwidth Δf = R/(2πL), and Q = f₀/Δf.