RLC Circuit Calculator Formula

Understand the math behind the rlc circuit calculator. Each variable explained with a worked example.

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Formulas Used

Resonant Frequency

resonant_freq = omega_0 / (2 * pi)

Damping Factor

damping = resistance / (2 * sqrt(l_h / c_f))

Quality Factor

q_factor = sqrt(l_h / c_f) / resistance

Variables

VariableDescriptionDefault
resistanceResistance(Ω)10
inductance_mhInductance(mH)10
capacitance_ufCapacitance(µF)10
l_hDerived value= inductance_mh / 1000calculated
c_fDerived value= capacitance_uf / 1000000calculated
omega_0Derived value= 1 / sqrt(l_h * c_f)calculated

How It Works

Series RLC Circuit

f_0 = 1 / (2pi x sqrt(LC))

Damping = R / (2 x sqrt(L/C))

Q = sqrt(L/C) / R

Damping < 1 is underdamped (oscillatory), = 1 is critically damped, > 1 is overdamped.

Worked Example

R=10 ohms, L=10 mH, C=10 uF.

resistance = 10inductance_mh = 10capacitance_uf = 10
  1. 01f_0 = 1 / (2pi x sqrt(0.01 x 0.00001)) = 503.3 Hz
  2. 02Damping = 10 / (2 x sqrt(0.01/0.00001)) = 10 / 63.25 = 0.158
  3. 03Q = 31.62 / 10 = 3.16 (underdamped)

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