roofner (bar784) – Homework 8 – Weathers – (22202)
1
This printout should have 11 questions.
Multiplechoice questions may continue on
the next column or page – Fnd all choices
before answering.
001
(part 1 of 2) 10.0 points
Three capacitors of 3
.
2
μ
±, 1
.
6
μ
±, and
16
.
8
μ
± are connected to the terminals of
a 16
.
1 V battery.
How much energy does the battery supply
if the capacitors are connected in series?
Correct answer: 0
.
129992 mJ.
Explanation:
The equivalent capacitance when the three
capacitors are connected in series is equal to
C
s
=
1
1
C
1
+
1
C
2
+
1
C
3
=
1
1
3
.
2
μ
±
+
1
1
.
6
μ
±
+
1
16
.
8
μ
±
= 1
.
00299
μ
±
.
The energy supplied by the battery is then
U
=
1
2
C
s
V
2
=
1
2
1
.
00299
μ
± (16
.
1 V)
2
=
0
.
129992 mJ
.
002
(part 2 of 2) 10.0 points
How much energy does the battery supply if
the capacitors are connected parallel?
Correct answer: 2
.
79947 mJ.
Explanation:
The equivalent capacitance when the three
capacitors are connected parallel is
C
p
=
C
1
+
C
2
+
C
3
= 3
.
2
μ
± + 1
.
6
μ
± + 16
.
8
μ
±
= 21
.
6
μ
±
.
The energy supplied by the battery is
U
=
1
2
C
p
V
2
=
1
2
21
.
6
μ
± (16
.
1 V)
2
=
2
.
79947 mJ
.
003
(part 1 of 2) 10.0 points
A capacitor network is shown below.
64 V
34
μ
±
40
What is the e²ective capacitance of the
circuit?
Correct answer: 37
μ
±.
Explanation:
Let :
C
1
= 34
μ
±
,
C
2
= 40
μ
±
,
C
3
= 34
μ
±
,
C
4
= 40
μ
±
and
E
B
= 64 V
.
±or capacitors in series,
1
C
series
=
s
1
C
i
V
series
=
s
V
i
,
and the individual charges are the same.
±or parallel capacitors,
C
parallel
=
s
C
i
Q
parallel
=
s
Q
i
,
and the individual voltages are the same.
E
B
C
1
C
2
C
3
C
4
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2
Parallel connections:
C
parallel
=
C
1
+
C
2
+
C
3
+
· · ·
Series connections:
1
C
series
=
1
C
1
+
1
C
2
+
1
C
3
+
· · ·
C
1
and
C
2
are in parallel, so
C
12
=
C
1
+
C
2
= 34
μ
F + 40
μ
F
= 74
μ
F
C
3
and
C
4
are in parallel, so
C
34
=
C
3
+
C
4
= 34
μ
F + 40
μ
F
= 74
μ
F
.
E
B
C
12
C
34
C
12
and
C
34
are in series with the battery,
so
C
1234
=
p
1
C
12
+
1
C
34
P
−
1
=
p
C
12
+
C
34
C
12
C
34
P
−
1
=
C
12
C
34
C
12
+
C
34
=
(74
μ
F) (74
μ
F)
74
μ
F + 74
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 Fall '00
 Littler
 Capacitance, Magnetism, Energy, Work, Correct Answer, Vab, μF

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