Basic ConceptsDC CircuitsElectric Circuit AnalysisElectrical DesignElectrical Formulas & Equations

Time Constant τ “Tau” Formulas for RC, RL & RLC Circuits

Time Constant τ “Tau” Equations for RC, RL and RLC Circuits

Time constant also known as tau represented by the symbol of “τ” is a constant parameter of any capacitive or inductive circuit. It differs from circuit to circuit and also used in different equations. The time constant for some of these circuits are given below:

Time Constant τ “Tau” Equations for RC, RL and RLC Circuits

τ for RC Circuit:

In this circuit, resistor having resistance “R” is connected in series with the capacitor having capacitance C, whose  τ “time constant” is given by:

τ = RC

τ = RC = 1/2πfC

Where

  • τ = RC = is the time constant in seconds
  • R is the resistance in series in ohms (Ω)
  • C is the capacitance of the capacitor in farads
  • fC = cutoff frequency in hertz

τ for RL Circuit:

Inductor of inductance “L” connected in series with resistance “R”, whose time constant “τ” in seconds is given by:

τ = L/R

Where

  • R is the resistance in series
  • L is the Inductance of the Inductor

Universal time Constant “τ” Formula

Change = Final – Start (1 – 1/et/τ)

Where:

  • Final = Value of calculated variable after infinite time (Ultimate value)
  • Start = Initial value of calculated variable
  • e = Euler’s number (≈2.7182818)
  • t = Time in seconds
  • τ = Time constant for circuits in seconds

Related Post: Analysis of a Simple RL Circuit with AC and DC Supply

τ for RLC Circuit:

In RLC circuit, we have both RL and RC time constant combined, which makes a problem calculating the time constant. So we calculate what we call the Q-Factor (quality factor).

τ for Series RLC Circuit:

Q factor Series RLC Circuit

τ for Parallel RLC Circuit:

Q factor parallel RLC Circuit

Where

  • R is the resistance in series
  • L is the Inductance of the Inductor
  • C is the capacitance of the capacitor

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