AP Physics Whiteboards
Capacitance
1. The potential difference between the two metal plates in the illustration
to the right is 40 V.
a. Which plate is at the higher potential?
b. How much work must be done to carry a 3.0 µC charge from
plate B to A?
c. If the plate separation is 5.0 mm, what is the magnitude of E?
2. In the illustration shown for question 1, a source of 120 V is applied to
plate A with respect to plate B. The distance between the plates (d) is
2.0 cm.
a. What is E between the plates?
b. What is the force an electron experiences when placed between the plates?
c. What is the potential energy lost by an electron as it moves from plate B to
plate A?
d. If an electron is released from plate B, what is its speed just before it
collides with plate A?
3. The series combination of two capacitors shown below is connected across
1000 V. Calculate the following:
a. the equivalent capacitance of the
combination
b. the magnitudes of the charges on the
capacitors
c. the potential differences across the capacitors
d. the energy stored in the capacitors
4. The parallel capacitor combination shown to the right is
connected across a 120 V source. Determine the
following:
a. the equivalent capacitance of the combination
b. the charge on each capacitor
c. the charge on the combination
5. Cletus is down in his basement building a capacitor that consists of two parallel
conducting plates, each with an area of 200 cm2, separated by a 0.40 cm air gap.
He fires it up with a 500 V source applied across the plates. Calculate the
following:
a. the capacitance.
b. the charge on it
c. the energy stored in it
d. the value of E between the plates
ap_wb_09.doc -- froehlich
6. Earth* can be considered a capacitor with the charged layer of the atmosphere, the
ionosphere, as a spherical capacitor with two plates, the surface of Earth being the
negative plate. The ionosphere is at a level of about 70 km and the potential
difference between the earth and the ionosphere is about 350,000 V. Calculate the
following:
a. the capacitance of this system
b. the total charge on the capacitor
c. the energy stored in this system
7. An air capacitor is made by using two flat plates, each with
area A, separated by a distance d. A metal slab having
thickness a (less than d) and the same shape and size as the
plates is inserted between them, parallel to the plates and not
touching either plate.
a. What is the capacitance of this arrangement?
b. Express the capacitance as a multiple of the
capacitance C0 when the metal slab is not present.
c. Discuss what happens to the capacitance in the limits
a  0 and a  d.
8. In one type of computer keyboard, each key holds a small metal plate that serves
as one plate of a parallel plate, air filled capacitor. When the key is depressed, the
plate separation decreases and the capacitance changes. Electronic circuitry
detects the change in capacitance and thus detects that the key has been pressed.
In one particular keyboard, the area of each metal plate is 42.0 mm2, and the
separation between the plates is 0.700 mm before the key is depressed.
a. Calculate the capacitance before the key is pressed.
b. If the circuitry can detect a change in capacitance of 0.250 pF, how far
must the key be depressed before the circuit detects it?
9. The charge center of a thundercloud, drifting 3.0 km above Earth’s surface*,
contains 20 C of negative charge. Assuming the charge center has a radius of
1.0 km, and modeling the charge center and Earth’s surface as parallel plates,
calculate the following:
a. the capacitance of the system
b. the potential difference between charge center and ground
c. the average strength of the electric field between the cloud and ground
d. the electrical energy stored in the system
* The radius of Earth is 6.38 x 106 m.
ap_wb_09.doc -- froehlich
AP Physics Whiteboards
Capacitance II
Some things to remember:
Energy stored in the field of a capacitor: U = 12 CV 2
In a parallel configuration, voltage is the same across each capacitor.
In a series configuration, charge is the same in each capacitor.
€
1. Calculate the capacitance of the concentric shielded
assembly shown to the right. The outside conductor is a
cylinder of radius b, and the inside is a solid conductor
of radius a. Let the length of the assembly be L, and
ignore any fringing effects at the edges.
2. A 100 pF capacitor and a 400 pF capacitor are charged to 2.00 kV. They are then
connected to each other, positive plate to negative plate, and negative plate to
positive plate. Find the resulting potential difference across each capacitor.
3. Calculate the plate area necessary for a 1.0 F parallel plate
capacitor with an air dielectric. The plate separation is 1.0 mm.
If the plates were to be thin circular disks, what would be the
diameter of the disks? (illustration not to scale)
4. A spherical capacitor is to be constructed by using a metal sphere of radius b as
one plate and a concentric spherical metal shell as the other plate. The inner
radius of the shell is a > b. Derive the expression for the capacitance of this
structure in terms of a, b, and the usual collection of constants. Show the process
– don’t just copy the stuff out of the textbook.
5. You have two identical capacitors and a fixed external potential source.
a. Compare the total energy stored in the capacitors when they are connected
to the applied potential in series and in parallel.
b. Compare the maximum amount of charge stored in each case.
c. Energy storage in a capacitor can be limited by the maximum electric field
between the plates. What is the ratio of the electric field for the series and
parallel combinations?
ap_wb_10.doc -- froehlich
6. Find the equivalent capacitance of the combination shown in the
illustration to the right. Find the charge on the 4 µF capacitor.
7. The illustration to the right displays a 12 V battery and
three uncharged capacitors. The switch is thrown to the
left side connecting the 4 µF capacitor to the 12 V battery
until it is fully charged. Then the switch is thrown to the
right.
a. What is the final charge on each capacitor?
b. What is the potential difference across each
capacitor?
c. Find the energy in the capacitors when the switch
is initially to the left, and when it is finally to the
right. Is this what you expected?
8. Electronic flash units for cameras have a capacitor for storing the energy used to
produce the flash. In one such unit, the flash lasts for 1.48 ms with an average
light output of 2.70 x 105 W.
a. If the conversion of electrical energy to light energy is 95% efficient, how
much energy must be stored in the capacitor for one flash?
b. If 125 V is available to charge the capacitor, what is the required
capacitance to achieve the flash described above?
9. A solid conducting sphere of radius R carries a charge Q.
a. Calculate the electric field energy density at a point a distance r from the
center of the sphere for r < R and r > R.
b. Calculate the total electric field energy associated with the charged sphere.
(hint: Consider a spherical shell of radius r and thickness dr that has a
volume dV = 4 π r 2 dr , and find the energy stored in this volume. Then
integrate from r = 0 to r = ∞.)
c. Explain why the result of part (b) above can be interpreted as the amount
of work required to assemble the charge Q on the sphere.
d.€Calculate the capacitance of the sphere.
ap_wb_10.doc -- froehlich