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AP Physics 2
Capacitors & Capacitance HW:
due______________
Read Sections 21.7, 21.8, & 21.9
Conceptual Questions
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It would be unwise to unplug an old CRT television set, take off the back, and reach inside. The reason for the
danger is that if you happen to touch the terminals of a high-voltage capacitor you could receive a large
electrical shock—even though the set is unplugged. Why?
A capacitor is connected to a battery and fully charged. What becomes of the charge on the capacitor when it is
disconnected from the battery? What becomes of the charge when the two terminals of the capacitor are
connected to one another?
We say that a capacitor stores charge, yet the total charge in a capacitor is zero; that is, Q + (Q) = 0. In what
sense does a capacitor store charge if the net charge within it is zero?
The plates of a parallel-plate capacitor have constant charges of Q and Q. Do the following quantities
increase, decrease, or remain the same as the separation of the plates is increased? (a) Electric field between the
plates; (b) potential difference between the plates; (c) capacitance; (d) energy stored in the capacitor.
A parallel-plate capacitor is connected to a battery that maintains a constant potential difference V between the
plates. If the plates of the capacitor are pulled farther apart, do the following quantities increase, decrease, or
remain the same? (a) Electric field between the plates; (b) charge on the plates; (c) capacitance; (d) energy
stored in the capacitor.
On which of the following quantities does the capacitance of a capacitor depend: (a) the charge on the plates; (b)
the separation of the plates; (c) the voltage difference between the plates; (d) the electric field between the
plates; or (e) the area of the plates?
The plates of a particular parallel-plate capacitor are uncharged. Is the capacitance of this capacitor zero?
Explain.
The plates of a parallel-plate capacitor have constant charges of Q and Q. Do the following quantities
increase, decrease, or remain the same as a dielectric is inserted between the plates? (a) Electric field between
the plates; (b) potential difference between the plates; (c) capacitance; (d) energy stored in the capacitor.
A parallel-plate capacitor is connected to a battery that maintains a constant potential difference V between the
plates. If a dielectric is inserted between the plates of the capacitor, do the following quantities increase,
decrease, or remain the same? (a) Electric field between the plates; (b) charge on the plates; (c) capacitance; (d)
energy stored in the capacitor.
Problems
Capacitors and Dielectrics
1. It is desired that 4.8 C of charge be stored on each plate of a 32
. - F capacitor. What potential difference is
required between the plates?
2. To operate a given flash lamp requires a charge of 32 C. What capacitance is needed to store this much
charge in a capacitor with a potential difference between its plates of 3.0 V?
3. A parallel-plate capacitor is made from two aluminum-foil sheets, each 4.0 cm wide and 5.0 m long. Between
the sheets is a Teflon strip of the same width and length that is 0.025 mm thick. What is the capacitance of this
capacitor? (The dielectric constant of Teflon is 2.1.)
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4. A parallel-plate capacitor has plates with an area of 0.012 m and a separation of 0.88 mm. The space between
the plates is filled with a dielectric whose dielectric constant is 2.0. (a) What is the potential difference between
the plates when the charge on the capacitor plates is 4.7 C ? (b) Will your answer to part (a) increase,
decrease, or stay the same if the dielectric constant is increased? Explain. (c) Calculate the potential difference
for the case where the dielectric constant is 4.0.
5. A parallel-plate capacitor has plates of area 345
.  104 m2 . What plate separation is required if the capacitance
is to be 1330 pF? Assume that the space between the plates is filled with (a) air or (b) paper.
(From a table of constants, I, Mr. Jones, looked up: air = 1.00059, paper = 3.7)
6. Suppose that after walking across a carpeted floor you reach for a doorknob, and just before you touch it a spark
jumps 0.50 cm from your finger to the knob. Find the minimum voltage needed between your finger and the
doorknob to generate this spark. (hint: look up the “break-down” electric field for typical air.)
As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at
an altitude of 550 m to be the other plate. Assume the surface area of the cloud to be the same as the area of a
square that is 0.50 km on a side. (a) What is the capacitance of this capacitor? (b) How much charge can the
cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?
(hint: use the “break-down” electric field for typical air again.)
Electrical Energy Storage
8. Calculate the work done by a 3.0-V battery as it charges a 8.0 - F capacitor in the flash unit of a camera.
9. The membrane of a living cell can be approximated by a parallel-plate capacitor with plates of area
4.75  10 9 m 2 , a plate separation of 8.5  10 9 m, and a dielectric with a dielectric constant of 4.5. (a) What is
the energy stored in such a cell membrane if the potential difference across it is 0.0725 V? (b) Would your
answer to part (a) increase, decrease, or stay the same if the thickness of the cell membrane is increased?
Explain.
10. An electronic flash unit for a camera contains a capacitor with a capacitance of 850 F. When the unit is fully
charged and ready for operation the potential difference between the capacitor plates is 330 V. (a) What is the
magnitude of the charge on each plate of the fully charged capacitor? (b) Find the energy stored in the
“charged-up” flash unit.
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Answers
V = 1.5 V
C = 11 F
C = 0.15 F
(a) V = 19 kV
(b) The answer to part (a) will decrease because V is inversely proportional to .
(c) V = 9.7 kV
5. (a) d = 2.30 x 106 m
(b) d = 8.5 x 106 m
6. V = 15 kV
7. (a) C = 4.0 nF
(b) Q = 6.6 C
8. W = 36 J
9. (a) U = 5.8 x 1014 J
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(b) Since U  , the answer to part (a) would decrease if the thickness of the cell membrane is increased.
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10. (a) Q = 0.28 C
(b) U = 46 J
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