Transient in RLC

Physical background

The physical background of the parallel RLC circuit may be started from the energy conservation law, where the original energy from a power source, stored in the capacitor, is stored alternatively in the capacitor electric field and inductor magnetic field and the rest is transformed into the heat.

The scheme of the circuit is in Figure 1. Is is a substitute scheme of the conductor consist of the paralel capacity and resistor R, and the substitute scheme of the inductor consist of the inductance L (in serie) and resistance RL The resistors R1D a R2D present the variable resistance.

Obr. 1 a) Scheme of the circuit b) Substitute scheme for better understanding

The measured circuit we can show by reduce scheme in the Figure 1b), where

R1=R1D+RL , R2=R2D (1)

and this circuit is possible to describe by a system of the equations

If we use the II. Kirchhoff law, we will obtain the corresponding differential equation for the voltage on the circuit (u =uC)

where

Its solution (subject to the condition ω0 > b) is

The value b is the damping and the damping factor has the value

The value e-b determine the relativelly reducing of the ampltude in the time.

Figure 2 The damping of the signal

References

[1] SCHAUER, F., KREMPASKÝ, J.: Fyzika I a II, Zlín : Univerzita T. Bati, 2004. 611 s.