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428 ⏐⏐⏐ CAPACITORS
1 2
E 80 V C
iC 10 pF
100 k�
+
–
i C
+ 40 V –
R 1
C = 2000 mF
+ vC –
FIG. 10.85
Problem 23.
FIG. 10.86
Problem 24.
vC R2 FIG. 10.87
Problems 25 and 29.
R 1
4.7 k�
– vR +
R
2.2 k�
i C
390 k�
E 10 V C 10 �F � 3 V
vC 40 V
R 1
10 k�
C = 1000 µF µ
+ –
6 V
+
–
FIG. 10.88
Problem 26.
R 2
8.2 k�
FIG. 10.89
Problem 27.
–
+
+ vC –
iC C
–12 V
6.8 �F �
+ 12 V –
22. Repeat Problem 21 for a capacitance of 20 mF.
*23. For the network of Fig. 10.85:
a. Find the mathematical expression for the voltage
across the capacitor after the switch is thrown into
position 1.
b. Repeat part (a) for the current iC. c. Find the mathematical expressions for the voltage vC and current iC if the switch is thrown into position 2
at a time equal to five time constants of the charging
circuit.
d. Plot the waveforms of vC and iC for a period of time
extending from t � 0 to t � 30 ms.
24. The capacitor of Fig. 10.86 is initially charged to 40 V
before the switch is closed. Write the expressions for the
voltages v C and v R and the current i C for the decay phase.
25. The 1000-mF capacitor of Fig. 10.87 is charged to 6 V. To
discharge the capacitor before further use, a wire with a
resistance of 0.002 � is placed across the capacitor.
a. How long will it take to discharge the capacitor?
b. What is the peak value of the current?
c. Based on the answer to part (b), is a spark expected
when contact is made with both ends of the capacitor?
SECTION 10.9 Initial Values
26. The capacitor in Fig. 10.88 is initially charged to 3 V
with the polarity shown.
a. Find the mathematical expressions for the voltage vC and the current iC when the switch is closed.
b. Sketch the waveforms for vC and iC. *27. The capacitor of Fig. 10.89 is initially charged to 12 V
with the polarity shown.
a. Find the mathematical expressions for the voltage vC and the current iC when the switch is closed.
b. Sketch the waveforms for vC and iC. SECTION 10.10 Instantaneous Values
28. Given the expression vC � 8(1 � e �t/(20�10�6 )
):
a. Determine vC after five time constants.
b. Determine vC after 10 time constants.
c. Determine vC at t � 5 ms.