Question

What is the time constant of an RLC circuit?

Answer 1

The time constant of an RLC circuit (Resistor-Inductor-Capacitor circuit) depends on the circuit configuration. There are three possible configurations:

RC Circuit (Resistor-Capacitor):
In an RC circuit, the time constant (denoted as τ) is equal to the product of the resistance (R) and the capacitance (C):
τ = R * C

RL Circuit (Resistor-Inductor):
In an RL circuit, the time constant (τ) is equal to the ratio of the inductance (L) and the resistance (R):
τ = L / R

RLC Circuit (Resistor-Inductor-Capacitor):
In an RLC circuit, the time constant (τ) is determined by the reciprocal of the damping factor (ζ) and the natural frequency (ωn) of the circuit. The damping factor and the natural frequency depend on the values of resistance, inductance, and capacitance in the circuit.

For an underdamped RLC circuit (ζ < 1), the time constant is given by:
τ = 1 / (ζ * ωn)

For a critically damped RLC circuit (ζ = 1), the time constant is:
τ = 1 / ωn

For an overdamped RLC circuit (ζ > 1), the time constant is:
τ = 1 / (ζ * ωn)

To calculate the damping factor (ζ) and the natural frequency (ωn) for an RLC circuit, you need to know the values of resistance (R), inductance (L), and capacitance (C) in the circuit.