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C3-5.22s

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Problem 5.22 Determine (a) the amount of energy stored in each of the three
capacitors shown in Fig. P5.22, (b) the equivalent capacitance at terminals (a, b),
and (c) the amount of energy stored in the equivalent capacitor.
20 μF
a
10 kΩ
+
15 V _
υ1
+
_
+υ _
2
υ3
6 μF
+
_
5 μF
b
Figure P5.22
Solution: (a) Under dc conditions, the capacitors behave like open circuits. Hence,
no currents flow anywhere in the circuit, and no voltage drop exists across the resistor.
Hence, υab = 15 V.
For 6-µ F capacitor,
w1 =
1
1
2
Cυab
= × 6 × 10−6 × 152 = 0.675
2
2
(mJ).
For the 20-µ F and 5-µ F capacitors, from Eq. (5.47) for two capacitors in series,
20µυ2 = 5µυ3
or
υ2 =
υ3
.
4
(1)
Also,
υ2 + υ3 = 15.
(2)
Solution of Eqs. (1) and (2) gives:
υ2 = 3 V,
υ3 = 12 V.
1
× 20 × 10−6 × 32 = 0.09
2
1
w3 = × 5 × 10−6 × 122 = 0.36
2
w2 =
(mJ)
(mJ)
(b)
Ceq = 6 µ F +
!
20µ × 5µ
20µ + 5µ
"
F = 10 µ F
(c)
1
1
Ceq 152 = × 10 × 10−6 × 152 = 1.125
2
2
w1 + w2 + w3 = (0.675 + 0.09 + 0.36) mJ = 1.125
weq =
(mJ)
(mJ),
as expected.
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