Biomedical Engineering Reference
In-Depth Information
For 0 t 2
Z
t
1
C
v
ð
t
Þ¼
idt
þ
v
ð
0
Þ
0
and with
v
(0)
¼
0
,
we have
Z
t
t
0
¼
t
2
2
2
4
V
1
2
1
2
l
v
ð
t
Þ¼
l
d
l ¼
0
The voltage at
t
¼
2 needed for the initial condition in the next part is
t
¼2
¼
Þ¼
t
2
4
1V
v
ð
2
For t > 2
Z
t
Z
t
1
C
1
2
v
ð
t
Þ¼
idt
þ
v
ð
2
Þ¼
0
dt
þ
v
ð
2
Þ¼
1V
2
2
9.10 A GENERAL APPROACH TO SOLVING CIRCUITS INVOLVING
RESISTORS, CAPACITORS, AND INDUCTORS
Sometimes a circuit consisting of resistors, inductors, and capacitors cannot be simplified
by bringing together like elements in series and parallel combinations. Consider the circuit
shown in Figure 9.27. In this case, the absence of parallel or series combinations of resistors,
inductors, or capacitors prevents us from simplifying the circuit for ease in solution. In this
section, the node-voltage method is applied to write equations involving integrals and dif-
ferentials using element relationships for resistors, inductors, and capacitors. From these
equations, any unknown currents and voltages of interest can be solved using the standard
differential equation approach.
5 H
1 F
3
Ω
2 H
3 F
2
Ω
4 F
FIGURE 9.27
A circuit that cannot be simplified.
