Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

11.7 
proBLEms
[Circuits are initially relaxed unless specified otherwise]
1. What is the differential equation describing v
C
(t) for t 
≥
0
+
in the circuit in Fig. 11.7-1?
+
v
C
(
t
)
u
(
t
) – 
u
(
t
–1)
t
=2 s
R
1
C
R
2
–
+
–
Fig. 11.7-1 
2. A parallel RC circuit with non-zero initial energy is driven by a 1A DC current source from 
t 
= 
0. v
C
(t) is found to reach 75% of its steady-state value in one time constant. Express the initial 
voltage across capacitor as a percentage of its steady-state value.
3. A parallel RC circuit is driven by a 1A DC current source from t 
=
0. v
C
(t) is found to be 50% at 
t 
=
t
. Was there any initial voltage across C? If so, what is its magnitude and polarity?
4. Find and plot the v
C
(t) and voltage across the current source as functions of time in Fig. 11.7-2. Is 
there any exponential function in the expression for v
C
(t)? If not why? 
0.001 
u
(
t
) 
1 k
Ω
R
1 
µ
F
+
v
C
(
t
)
C
–
Fig. 11.7-2 

---

11.30


First-Order
RC
Circuits
5. Derive an expression for v
C
in an initially relaxed series RC circuit when it is driven by v
S
(t) 
=
t 
for 0
+
≤
t 
≤
t
and 0 for all other t, where 
t
=
RCt.
6. What is the time required for the energy stored in C in a series RC circuit with voltage source 
input to reach 99% of its steady-state value in step response?
7. v
C
in the circuit in Fig. 11.7-3 is –10 V at t 
=
0
-
. If v
C
(t) 
=
0 for t 
≥
0
+
, find C.
+
v
C
(
t
)
R
C
–
+
–
100 
Ω
0.01 (
t
)
δ
Fig. 11.7-3 
8. A parallel RC circuit is driven by a 1A DC current source from t 
= 
0. The resistor voltage is found 
to be (10 
-
5e
-
 t
) V for t 
≤
0
+
. What are the values of C, R and initial voltage?
9. v
C
in the circuit in Fig. 11.7-4 at t 
=
0
-
is –12 V. It is found that v
C
(t) 
=
0 for t 
≤
0
+
. What is the 
rise time of step response of the circuit?
+
v
C
(
t
)
R
C
–
+
–
0.01 (
t
)
100 
Ω
δ
Fig. 11.7-4 
10. A parallel RC circuit with non-zero initial energy is driven by a 1A DC current source from t 
=
0. 
The capacitor voltage is found to be 15 V for t 
≤
0
+
. What is the value of initial voltage and what 
is its polarity relative to the observed voltage? What is the value of R in the circuit?
11. A parallel RC circuit with non-zero initial energy is driven by a 1A DC current source from t 
=
0. 
The resistor current is found to be 12 mA under steady-state. What is the new steady-state value 
of this current if (i) the initial condition is doubled (ii) if 2u(t) is applied with no change in initial 
condition?
12. The capacitor voltage v
C
(t) 
=
0 for t 
≤
0
+
in the circuit in Fig. 11.7-5. Find the values of V
0
and I
S
. 
The circuit elements that produced initial energy storage in the capacitor are not shown.
+
–