Electric Circuits and Networks

11.6 THE SERIES RLC CIRCUIT — ZERO-INPUT RESPONSE

Let us begin the study of RLC circuits with series RLC circuit in this section. Figure 11.6-1 shows a series RLC circuit with voltage excitation with all instantaneous variables identified.

We choose to develop the differential equation governing the circuit in terms of the voltage across the capacitor v_C(t), i.e., we select v_C(t) as the describing variable for the circuit. We obtain all other variables in terms of this variable once the solution is obtained.

 

 

Substituting for i(t) in terms of v_C(t) and rearranging terms,

 

 

 

Fig. 11.6-1 Series RLC Circuit with Voltage Source Excitation ...