Electric Circuits and Networks, Ist Edition by Pearson

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,

d

d

d

d

CC

CS

2

2

11

vt

t

R

L

vt

tLC

vt

LC

vt

() ()

() ().++=

it C

vt

t

vt

()

()

()

=

−+

d

d

(By element equ ...