Let us begin the study of RLCcircuits with series RLCcircuit in this section.
Figure 11.6-1 shows a series RLCcircuit 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
()()
()().++=
itC
vt
t
vt
()
()
()
=
−+
d
d
(By element equ ...
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