The Glenelg School of Abu Dhabi
Answer Key Practice Sheets #5-Semester 1
Unit/Topic:
Student’s
Name:
HS Physics
Subject:
Ch 24: Capacitance, Dielectric,
and Electric Energy Storage
Grade
Level:
11
Date:
Semester 1
NOTE
The questions in the Practice Sheets are intended to help you
practice solve problems and build up Problem-Solving strategies.
The questions are not necessarily selected to be given in your tests
or final exams.
Ch24: Capacitance
Key Formulas
Capacitance
𝐶=
𝑄
𝐴
= ɛ0
𝑉
𝑑
Stored Energy of a Capacitor
𝑄2
𝑈 = ½𝑄𝑉 = ½𝐶𝑉 =
2𝐶
Equivalent Capacitance of Two
Capacitors in Series
1
1
1
= +
𝐶𝑡 𝐶1 𝐶2
Equivalent Capacitance of Two
Capacitors in Parallel
𝐶𝑡 = 𝐶1 + 𝐶2
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Multiple - Choice Questions
Part A
Directions: Each of the sets of lettered choices below refers to the questions and/or statements
that follow. Select the lettered choice that is the best answer to each question and fill in the
corresponding oval on the answer sheet. In each set, each choice may be used once, more than
once, or not at all.
A
B
D
C
E
1. During the charging of a capacitor, which of the graphs above best represents the charge on
the capacitor as time passes? The correct answer is (A).
2. During the charging of a capacitor, which of the graphs above best represents the voltage
across the capacitor as time passes? The correct answer is (A).
3. During the discharging of a capacitor, which of the graphs above best represents the charge
on the capacitor as time passes? The correct answer is (B).
4. During the charging of a capacitor, which of the graphs above best represents the voltage
across the capacitor as time passes? The correct answer is (B).
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Part B
Directions: Each question or statement below is followed by five possible answers. In each case,
select the best possible answer and fill in the corresponding oval on the answer sheet.
5. The unit of capacitance, the farad, is dimensionally equivalent to which of the following?
(A) V/C
(B) C/V
(C) VC
(D) V/J
(E) J/V
The correct answer is (B).
6. Two parallel-plate capacitors are identical in every respect except that one has twice the
plate area of the other. If the smaller capacitor has capacitance C, the larger one has
capacitance
(A) C/2
(B) C
(C) 2C
(D) 4C
(E) 8C
The correct answer is (C).
7. A parallel-plate capacitor has a capacitance of C. If the area of the plates is doubled and the
distance between the plates is halved, what is the new capacitance?
(A) C/4
(B) C/2
(C) 2C
(D) 4C
(E) 8C
The correct answer is (D).
8. The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as
they are pulled apart. During this process, the amount of charge on the plates must
(A) increase.
(B) decrease.
(C) remain constant.
(D) either increase or decrease. There is no way to tell from the information given.
(E) None of the above
The correct answer is (B)
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9. Which of the graphs above best represents the charge on the capacitor as time passes while
charging?
(A) Graph A
(B) Graph B
(C) Graph C
(D) Graph D
(E) Graph E
The correct answer is (A).
10. During the charging of a capacitor, what does graph D show?
(A) The value of the current in the circuit as time passes.
(B) The value of the voltage across the terminals as time passes.
(C) The total value of the resistance as time passes.
(D) The total value of the capacitance as time passes.
(E) None of the above.
The correct answer is (A).
11. The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as
they are pulled apart. What happens to the strength of the electric field during this process?
(A) It increases.
(B) It decreases.
(C) It remains constant.
(D) cannot be determined from the information given
(E) either increase or decrease.
The correct answer is (B).
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12. Capacitance of a capacitor depends on
(A) Size of plate
(B) Distance between plates
(C)Nature of the dielectric between the plates
(D) All of the above
(E) None of the above
The correct answer is (D).
13. S.I unit of permittivity of free space is
(A) Farad
(B) Weber
(C) C2/N.m2
(D) C2/N.m
(E) N/ C2.m
The correct answer is (C).
14. A parallel-plate capacitor is connected to a 100 V battery until it is fully charged. The
distance between the plates is d and the space between the plates is filled with air (k=1.0).
Then, the battery is disconnected. If the distance between the plates is increased to 3d, the
voltage of the capacitor will be closest to …
(A) 33 V
(B) 100 V
(C) 300 V
(D) 600 V
(E) 900 V
The correct answer is (C).
15. In the previous problem: if, instead of changing the distance d between the plates, a dielectric
with k=3.0 is inserted between the plates such that it fully fills the space between the plates,
the voltage of the capacitor will be closest to …
(A) 33 V
(B) 100 V
(C) 300 V
(D) 600 V
(E) 900 V
The correct answer is (A).
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16. The area of the plates of a 1 farad capacitor separated by 8.85 mm and placed in the air is
(A)109 m2
(B) 05 m2
(C) 10-9 m2
(D) 10-15 m2
(E) 1015 m2
The correct answer is (A).
17. A capacitor may be considered as a device for
(A) Storing energy
(B) Increasing resistance
(C) Decreasing resistance
(D) None of the above
(E) All of the above
The correct answer is (A).
18. A 32-µF capacitor holds plus and minus charges of 16×10-6 C. What is the voltage across the
capacitor?
(A) 2 V
(B) 0.5 V
(C) 5×10-7 V
(D) 2×106 V
(E) 2×103 V
The correct answer is (B).
19. The potential difference between two short sections of parallel wire in air is 120 V. They carry
equal and opposite charge of magnitude 240 pC. What is the capacitance of the two wires?
(A) 2 pF
(B) 2 F
(C) 5×1011 F
(D) 0.5 F
(E) 29 nF
The correct answer is (A).
20. How much charge flows from each terminal of a 12.0-V battery when it is connected to a
2.00 µF capacitor?
(A) 6.00 C
(B) 24.0 C
(C) 2.40×10-5 C
(D) 6.00×106 C
(E) 24.0×105 C
The correct answer is (C).
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21. A parallel-plate capacitor has plates of area 0.20 m2 separated by a distance of 1.0 mm.
What is the strength of the electric field between these plates when this capacitor is
connected to a 6.0-V battery?
(A) 1200 N/C
(B) 3000 N/C
(C) 6000 N/C
(D) 1500 N/C
(E) 2500 N/C
The correct answer is (C).
22. A parallel-plate capacitor has a plate separation of 5.0 cm. If the potential difference
between the plates is 2000 V, with the top plate at the higher potential, what is the electric
field between the plates?
(A) 100 N/C upward
(B) 100 N/C downward
(C) 40000 N/C upward
(D) 40000 N/C downward
(E) 20000 N/C downward
The correct answer is (D).
23. Doubling the capacitance of a capacitor holding a constant charge causes the energy stored
in that capacitor to
(A) quadruple.
(B) double.
(C) decrease to one half.
(D) decrease to one fourth.
(E) no change.
The correct answer is (C).
24. Doubling the voltage across a given capacitor causes the energy stored in that capacitor to
(A) quadruple.
(B) double.
(C) reduce to one half.
(D) reduce to one fourth.
(E) no change.
The correct answer is (A).
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25. A charge of 60 mC is placed on a 15 mF capacitor. How much energy is stored in the capacitor?
(A) 4.0 J
(B) 120 J
(C) 240 J
(D) 120 mJ
(E) 240 mJ
The correct answer is (D).
26. 20 V is applied across a 15 μF capacitor. What is the energy stored in the capacitor?
(A) 3.0 mJ
(B) 6.0 mJ
(C) 150 μJ
(D) 300 μJ
(E) 450 µJ
The correct answer is (A).
27. A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V
battery. How much work was done in charging this capacitor?
(A) 12.0 μJ
(B) 24.0 μJ
(C) 144 μJ
(D) 576 J
(E) 12.0 J
The correct answer is (A).
28. If a 10-μF capacitor is charged so that it stores 2.0 mJ of energy, what is the voltage across
it?
(A) 5.0 V
(B) 10 V
(C) 15 V
(D) 20 V
(E) 25 V
The correct answer is (D).
29. Two identical capacitors are arranged in a circuit. What is the ratio of the equivalent
capacitance of the circuit when the capacitors are in series to that when they are in parallel?
(A) 1/4
(B) 1/2
(C) 1
(D) 2
(E) 4
The correct answer is (A).
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30. Find the total capacitance for three capacitors in parallel with each other. The value of the
capacitors is 10 μF , 15 μF , and 35 μF .
(A) 60 μF
(B) 50 μF
(C) 20 μF
(D) 10 μF
(E) 5 μF
The correct answer is (A).
31. Find the total capacitance for three capacitors in series with each other. The value of the
capacitors is 10 μF , 15 μF , and 35 μF .
(A) 60 μF
(B) 50 μF
(C) 20 μF
(D) 10 μF
(E) 5 μF
The correct answer is (E).
32. The equivalent capacitance of the configuration (C=100 µF) between terminals a and b is …
(A) 25 μF
(B) 67 μF
(C) 133 μF
(D) 300 μF
(E) 150 μF
The correct answer is (B).
33. When capacitors are connected in parallel the net capacitance will
(A) Increase
(B) Decrease
(C) Remain constant
(D) None of the above
(E) All of the above
The correct answer is (A).
34. Materials called dielectrics are placed between the plates of capacitors to
(A) speed the current flow.
(B) slow the current flow.
(C) reduce charge leakage from the capacitor.
(D) increase the capacitance of the capacitor.
(E) decrease the capacitance of the capacitor.
The correct answer is (D).
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35. A potential difference of 𝜟𝑽exists between two plates of a parallel-plate capacitor with
capacitance C. A dielectric with a dielectric constant of 𝒌 is then placed between the plates of
the capacitor. What is the energy stored in the capacitor?
1 𝐶
(A) 2 (𝑘 )(𝛥𝑉)2
1 𝑘
(B) 2 (𝐶)(𝛥𝑉)2
1
(C) 2 𝑘𝐶(𝛥𝑉)2
1
(D) 2 𝑘𝐶𝛥𝑉
1 𝐶
(E) 2 (𝑘 ) 𝛥𝑉
The correct answer is (C).
36. Inserting a dielectric material between two charged parallel conducting plates, originally separated
by air and disconnected from a battery, will produce what effect on the capacitor?
(A) increase charge
(B) decrease capacitance
(C) increase capacitance
(D) increase voltage
(E) none of the above
The correct answer is (C).
37. A dielectric is inserted into a capacitor while the charge on it is kept constant. What happens
to the potential difference and the stored energy?
(A) The potential difference decreases and the stored energy increases
(B) Both the potential difference and the stored energy increase
(C) The potential difference increases and the stored energy decreases
(D) Both the potential difference and the stored energy decrease
(E) Both the potential difference and the stored energy remain the same
The correct answer is (D).
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Free-Response Questions
38. A 9500-pF capacitor holds plus and minus charges of 16.5×10-8 C. What is the voltage across
the capacitor?
Answer
Q  CV  V 
Q
C

16.5  108 C
9.5  109 F
 17.4 V
39. The potential difference between two short sections of parallel wire in air is 120 V. They
carry equal and opposite charge of magnitude 95 pC. What is the capacitance of the two
wires?
Answer
Q  CV  C 
Q
V

95  1012 C
120 V
 7.9  1013 F
40. How much charge flows from each terminal of a 12.0-V battery when it is connected to a
7.00-F capacitor?
Answer


Q  CV  7.00  106 F 12.0 V   8.4  105 C
41. A parallel-plate capacitor has plates of area 0.50 m2 separated by a distance of 2.0 mm.
What is this capacitor's capacitance?
Answer
𝑐 = 𝜖0
𝐴
𝑑
𝑐 = 8.85 × 10−12
0.50
= 2.2 × 10−9 𝐹
2.0 × 10−3
42. A parallel-plate capacitor is filled with air, and the plates are separated by 0.050 mm. If the
capacitance is 17.3 pF, what is the plate area?
Answer
𝐴=
𝑐𝑑
𝜖0
𝐴=
17.3 × 10−12 × 0.050 × 10−3
≈ 9.8 × 10−5 𝑚2
8.85 × 10−12
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43. A 0.20-F capacitor is desired. What area must the plates have if they are to be separated by
a 2.2-mm air gap?
Answer
C
0 A
 A
d
Cd
0

 0.20 F   2.2  103 m 
8.85 10
12
C Nm
2
2

 5.0  107 m 2
44. An electric field of 8.50 105 V m is desired between two parallel plates, each of area 35.0 cm2
and separated by 2.45 mm of air.
a) What is the voltage across the capacitor?
b) What is the capacitance of the capacitor?
b) What charge must be on each plate?
Answer
a) 𝑉 = 𝐸𝑑 = (8.50 × 105 )(2.45 × 10−3 ) = 2082.5 𝑉 ≈ 2080 𝑉
35.0×10−4
𝐴
b) 𝐶 = ɛ0 𝑑 = 8.85 × 10−12 × 2.45×10−3 = 1.26 × 10−11 F
c) 𝑄 = 𝐶𝑉 = (1.26 × 10−11 )(2082.5) = 2.63 × 10−8 C
45. If a capacitor has opposite 5.2 C charges on the plates, and an electric field of 2.0 kV/mm is
desired between the plates, what must each plate’s area be?
Answer
Q  CV 
 0 AV
d
  0 AE 
 5.2 10 C 
A

 0.29 m
2000 V 
 E

8.85 10 C N  m   10 m 
6
Q
12
0
2
2
2
3
46. How strong is the electric field between the plates of a 0.80-F air-gap capacitor if they are
2.0 mm apart and each has a charge of 72 C?
Answer
The voltage across the capacitor is the magnitude of the electric field times the separation distance of
the plates.
Q  CV  CEd 
 72 10 C 
E


Cd  0.80  10 F  2.0  10 m 
6
Q
6
3
4.5  10 4 V m
47. What is the capacitance of two square parallel plates 5.5 cm on a side that are separated by
1.8 mm of paraffin?
Answer
C  K 0
A
d

  2.2  8.85  1012 C 2 N  m 2
Ch24- Practice Sheets #5
 5.5 10 m 
 1.8 10 m


2
3
2
 3.3  10 11 F
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48. What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 3.2
mm of mica?
Answer
C  K 0
A
d

  7  8.85  10
12
C Nm
2
2

  5.0  102 m 
 3.2 10 m 
3
2
 1.5  1010 F
49. 650 V is applied to a 2200-pF capacitor. How much energy is stored?
Answer
PE  12 CV 2 
1
2
 2.2 10 F  650 V 
9
2
 4.6 104 J
50. A cardiac defibrillator is used to shock a heart that is beating erratically. A capacitor in this
device is charged to 5.0 kV and stores 1200 J of energy. What is its capacitance?
Answer
The capacitance can be found from the stored energy using the eq.
PE  12 CV 2  C 
2  PE 
V
2

2 1200 J 
 5.0 10 V 
3
2
 9.6  10 5 F
51.
a) What is the capacitance of two square plates, 8.0 cm on a side, separated by a 1.5-mm air
gap? The charges on the plates are equal and opposite and of magnitude 420 C.
b) How much energy is stored by the electric field between the two square plates?
Answer
𝐴
8.0 × 10−2 × 8.0 × 10−2
−12
𝑎) 𝑐 = ɛ0 = 8.85 × 10
×
= 3.78 × 10−11 F
𝑑
1.5 × 10−3
b) 𝑃𝐸 = ½
𝑄2
𝐶
=½
(420×10−6 )2
3.78×10−11
= 2.3 × 103 J
52. A homemade capacitor is assembled by placing two 9-in. pie pans 5 cm apart and connecting
them to the opposite terminals of a 9-V battery. Estimate
(a) the capacitance,
(b) the charge on each plate,
(c) the electric field halfway between the plates,
(d) the work done by the battery to charge the plates.
(e) Which of the above values change if a dielectric is inserted?
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Answer
0 A
8.85 10

12

C2 N  m 2   4.5in  .0254 m in 
2
 7.265  1012 F  7  1012 F
(a)
C
(b)
Q  CV  7.265  1012 F  9 V   6.54 10 11 C  7 10 11 C
(c)
E
(d)
By energy conservation, the work done by the battery to charge the plates is the potential energy
stored in the capacitor, given by the eq.
d

V
d

(e)


9V
5.0  102 m
PE  12 QV 

5.0  102 m
1
2
 180 V m  200 V m
 6.54 10 C  9 V   2.94 10
11
10
J  3 1010 J
If a dielectric is inserted, the capacitance changes, and so the charge on the capacitor
and the energy stored also change. The electric field does not change because it only depends on
the battery voltage and the plate separation.
53. Given the three capacitors,𝑪1, 𝑪2, 𝑪3, and the 12.0 V power source:
(a) If capacitors 𝐶 1 and 𝐶 2 are placed in parallel with each other and their combination is connected
in series with 𝐶 3 and connected to the 12.0 V source, draw the diagram.
(b) Determine the total charge acquired by the capacitors in part (a).
(c) The capacitors are discharged and reconnected with 𝐶 1, now in series with the parallel
combination of 𝐶 2 and 𝐶 3. The entire arrangement is now reconnected with the 12.0 V power source.
Draw the diagram.
(d) Determine the total charge acquired by the capacitors in part (c).
Answer
(a)
(b) Using 𝑄 = 𝑉𝐶 and the fact that 𝐶 3 is in series with the parallel combination of 𝐶 1 and 𝐶 2:
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𝐶 1,2 = 0.200 µ𝐹 + 0.400 µ𝐹 = 0.600 µ𝐹
1/𝐶 1,2,3 = (1/𝐶 1,2) + (1/𝐶 3) = (1/0.600 µ𝐹) + (1/0.600 µ𝐹)
𝐶 1,2,3 = 0.300 µ𝐹
𝑄 = 𝑉𝐶 = (12.0 𝑉)(0.300 µ𝐹) = 3.6 µ𝐶
(c)
(d) Using 𝑄 = 𝑉𝐶 and the fact that 𝐶 1 is in series with the parallel combination of 𝐶 2 and 𝐶 3:
𝐶 2,3 = 0.400 µ𝐹 + 0.600 µ𝐹 = 1.00 µ𝐹
1/𝐶 1,2,3 = (1/𝐶 2,3) + (1/𝐶 1) = (1/1.00 µ𝐹) + (1/0.200 µ𝐹)
𝐶 1,2,3 = 0.167 µ𝐹
𝑄 = 𝑉𝐶 = (12.0 𝑉)(0.167 µ𝐹) = 2.0 µ𝐶
54. A 12.0 V storage battery is connected to three capacitors, C1 = 2.0 μF, C2 = 6.0 μF, and C3 =
4.0 μF respectively.
(a) Calculate the equivalent capacitance for the combination.
Answer
𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐 + 𝑪𝟑
𝑪𝒆𝒒 = 𝟐. 𝟎 𝝁𝑭 + 𝟔. 𝟎 𝝁𝑭 + 𝟒. 𝟎 𝝁𝑭
𝑪𝒆𝒒 = 𝟏𝟐 𝝁𝑭
(b) Determine the total charge Q that must leave the battery.
Answer
𝑸𝒆𝒒 = 𝑪𝒆𝒒 𝑽
𝑸𝒆𝒒 = (𝟏𝟐 𝝁𝑭)(𝟏𝟐. 𝟎 𝑽) = 𝟏𝟒𝟒 𝝁𝑪 ≈ 𝟏𝟒𝟎 𝝁𝑪
(c) Determine the charge on each capacitor.
Answer
𝑸𝟏 = 𝑪𝟏 𝑽
𝑸𝟏 = (𝟐. 𝟎 𝝁𝑭)(𝟏𝟐. 𝟎) = 𝟐𝟒 𝝁𝑪
𝑸𝟐 = 𝑪𝟐 𝑽
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𝑸𝟐 = (𝟔. 𝟎 𝝁𝑭)(𝟏𝟐. 𝟎) = 𝟕𝟐 𝝁𝑪
𝑸𝟑 = 𝑪𝟑 𝑽
𝑸𝟑 = (𝟒. 𝟎 𝝁𝑭)(𝟏𝟐. 𝟎) = 𝟒𝟖 𝝁𝑪
55. A 24.0 V storage battery is connected to three capacitors, C1 = 3.0 μF, C2 = 6.0 μF, and C3 =
8.0 μF respectively.
(a) Calculate the equivalent capacitance for the combination.
Answer
𝟏
𝟏
𝟏
𝟏
=
+
+
𝑪𝒆𝒒 𝑪𝟏 𝑪𝟐 𝑪𝟑
𝟏
𝟏
𝟏
𝟏
𝟓
=
+
+
=
𝑪𝒆𝒒 𝟑. 𝟎 𝟔. 𝟎 𝟖. 𝟎 𝟖. 𝟎
𝑪𝒆𝒒 =
𝟖. 𝟎
= 𝟏. 𝟔 𝝁𝑭
𝟓
(b) Determine the total charge Q that must leave the battery.
Answer
𝑸𝒆𝒒 = 𝑪𝒆𝒒 𝑽
𝑸𝒆𝒒 = (𝟏. 𝟔 𝝁𝑭)(𝟐𝟒. 𝟎 𝑽) = 𝟑𝟖. 𝟒 𝝁𝑪 ≈ 𝟑𝟖 𝝁𝑪
(c) Determine the voltage across each capacitor.
Answer
𝑽𝟏 =
𝑸 𝟑𝟖. 𝟒
=
= 𝟏𝟐. 𝟖 𝑽 ≈ 𝟏𝟑 𝑽
𝑪𝟏
𝟑. 𝟎
𝑽𝟐 =
𝑸 𝟑𝟖. 𝟒
=
= 𝟔. 𝟒 𝑽
𝑪𝟐
𝟔. 𝟎
𝑽𝟑 =
𝑸 𝟑𝟖. 𝟒
=
= 𝟒. 𝟖 𝑽
𝑪𝟑
𝟖. 𝟎
Ch24- Practice Sheets #5
The Glenelg School of Abu Dhabi: Page 16 of 18
The Glenelg School of Abu Dhabi
56. A 12.0 V storage battery is connected to four capacitors, C1 = 60. μF, C2 = 20. μF, C3 = 9.0 μF,
and C4 = 12 μF respectively.
(a) Calculate the equivalent capacitance for the combination.
Capacitors C1 and C2 are connected in series, so they are equivalent to a single capacitor, C12, having
the following capacitance
𝟏
𝟏
𝟏
=
+
𝑪𝟏𝟐 𝑪𝟏 𝑪𝟐
𝟏
𝟏
𝟏
=
+
𝑪𝟏𝟐 𝟔𝟎. 𝟐𝟎.
𝟏
𝟏
=
𝑪𝟏𝟐 𝟏𝟓
𝑪𝟏𝟐 = 𝟏𝟓 𝝁𝑭
C12 and C3 are connected in parallel, so they are equivalent to a single capacitor, C123, having the
following capacitance
𝑪𝟏𝟐𝟑 = 𝑪𝟏𝟐 + 𝑪𝟑
𝑪𝟏𝟐𝟑 = 𝟏𝟓 𝝁𝑭 + 𝟗. 𝟎 𝝁𝑭
𝑪𝟏𝟐𝟑 = 𝟐𝟒 𝝁𝑭
Capacitors C123 and C4 are connected in series, so the equivalent capacitance of the entire circuit,
Ceq, is given by
𝟏
𝟏
𝟏
=
+
𝑪𝒆𝒒 𝑪𝟏𝟐𝟑 𝑪𝟒
𝟏
𝟏
𝟏
=
+
𝑪𝒆𝒒 𝟐𝟒 𝟏𝟐
𝟏
𝟑
=
𝑪𝒆𝒒 𝟐𝟒
𝑪𝒆𝒒 = 𝟖. 𝟎 𝝁𝑭
(b) Determine the total charge Q that must leave the battery.
Ch24- Practice Sheets #5
The Glenelg School of Abu Dhabi: Page 17 of 18
The Glenelg School of Abu Dhabi
𝑸𝒆𝒒 = 𝑪𝒆𝒒 𝑽
𝑸𝒆𝒒 = (𝟖. 𝟎 𝝁𝑭)(𝟏𝟐. 𝟎 𝑽) = 𝟗𝟔 𝝁𝑪
(c) Determine the voltage across each capacitor.
- To find V4
The charge, Qeq = 96 𝜇𝐶 , that leaves the battery arrives at the negative plate of C4, SO
𝑄4 = 96 𝜇𝐶
𝑸𝟒 𝟗𝟔 𝝁𝑪
𝑽𝟒 =
=
= 𝟖. 𝟎 𝑽
𝑪𝟒
𝟏𝟐 𝝁𝑭
- To find V3
Capacitors C12 and C3 are connected in parallel, so the voltage across C12 and C3 is the same.
𝑽𝟏𝟐 = 𝑽𝟑 = 𝑽 − 𝑽𝟒
𝑽𝟏𝟐 = 𝑽𝟑 = 𝟏𝟐. 𝟎 − 𝟖. 𝟎 = 𝟒. 𝟎 𝑽
The voltage across V3 is
𝑽𝟑 = 𝟒. 𝟎 𝑽
To find V1 and V2
C1 and C2 are connected in series so the charge on each capacitor is the same.
𝑸𝟏𝟐 = 𝑪𝟏𝟐 𝑽𝟏𝟐
𝑸𝟏𝟐 = (𝟏𝟓 𝝁𝑭)(𝟒. 𝟎 𝑽) = 𝟔𝟎. 𝝁𝑭
𝑸𝟏𝟐 𝟔𝟎.
=
= 𝟏. 𝟎 𝑽
𝑪𝟏
𝟔𝟎.
𝑸𝟏𝟐 𝟔𝟎.
𝑽𝟐 =
=
= 𝟑. 𝟎 𝑽
𝑪𝟐
𝟐𝟎.
𝑽𝟏 =
Practice Makes Perfect
Ref. Giancoli
Physics for Scientists & Engineers
END of Chapter 24
Ch24- Practice Sheets #5
The Glenelg School of Abu Dhabi: Page 18 of 18