Serie RLC-circuit zonder bron

A source-free RLC circuit a composed of a resistor, an inductor, and a capacitor in series without an external energy source.

Here, the initial energy stored in the capacitor and inductor stimulates the circuit.

This circuit can be represented by a second-order differential equation.

The resistor dissipates energy, favoring an exponential solution for the equation.

Substituting this solution results in a quadratic equation.

The two roots of this characteristic equation give the circuit's natural frequencies, associated with the natural response of the circuit.

These roots, expressed in terms of the damping factor and resonant frequency, indicate two possible solutions.

So, the natural response of the series RLC circuit is a linear combination of these two distinct solutions.

The damping factor and the resonant frequency determine the circuit's behavior.

If the damping factor exceeds the resonant frequency, the response is overdamped with distinct real roots.

When the damping factor equals the resonant frequency, the response is critically damped with equal roots.

If the damping factor is less than the resonant frequency, the response is underdamped with complex roots.