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29. For the situation of Problem 25, determine when the discharge
current is one-half its maximum value if contact is
made at t � 0 s.
30. For the network of Fig. 10.90, VL must be 8 V before the
system is activated. If the switch is closed at t � 0 s, how
long will it take for the system to be activated?
E
12 V
(t = 0 s)
R 33 k�
C 20 mF
FIG. 10.90
Problem 30.
System
R = ∞ � V +
L
–
*31. Design the network of Fig. 10.91 such that the system
will turn on 10 s after the switch is closed.
32. For the circuit of Fig. 10.92:
a. Find the time required for vC to reach 60 V following
the closing of the switch.
b. Calculate the current iC at the instant vC � 60 V.
c. Determine the power delivered by the source at the
instant t � 2t.
*33. For the network of Fig. 10.93:
a. Calculate v C, i C, and v R1 at 0.5 s and 1 s after the
switch makes contact with position 1.
b. The network sits in position 1 10 min before the
switch is moved to position 2. How long after making
contact with position 2 will it take for the current i C to
drop to 8 mA? How much longer will it take for v C to
drop to 10 V?
34. For the system of Fig. 10.94, using a DMM with a
10-M� internal resistance in the voltmeter mode:
a. Determine the voltmeter reading one time constant
after the switch is closed.
b. Find the current i C two time constants after the switch
is closed.
c. Calculate the time that must pass after the closing of
the switch for the voltage v C to be 50 V.
E
20 V
(t = 0 s)
R
C 200 mF
FIG. 10.91
Problem 31.
12 k�
R 1
8 k�
PROBLEMS ⏐⏐⏐ 429
V L = 12 V to turn on
System
R = ∞ �
E 80 V C 6 mF vC –
R2 E
E
FIG. 10.92
Problem 32.
+ v R1 –
R1 1
1 M�
2
60 V C
R2 4 M�
60 V
i C
FIG. 10.93
Problem 33.
+ v C –
C
0.2 mF
FIG. 10.94
Problem 34.
i C
i C
0.2 mF
+
+
v C
–
DMM
+ –