Try these "busters" to exercise your brain ... they should help you grasp the concepts underlying capacitance, etc. To gain the maximum effect you should attempt to answer them before looking at the answers!
[1] A capacitor is made of two parallel plates separated by a distance d. The top plate has a charge +Q, the bottom plate has a charge -Q. A slab of metal of thickness l (< d) is inserted between the plates but not connected to either one. What happens to the potential difference between the two plates when the slab is inserted?
[2] A parallel plate capacitor is charged by a battery. Tha battery is then disconnected but the charge remains on the plates. Explain whether each of the following increases, decreases or remains the same as the distance between the plates is increased:
[3] A dielectric is inserted between the plates of a capacitor and the system is charged using a battery. If the battery is disconnected and the dielectric removed, what happens to the energy stored in the capacitor?
[4] A parallel plate capacitor is attached to a battery that maintains a constant potential difference between the plates. While the battery is still connected a glass slab is inserted so as to just fill the space between the plates. What happens to the stored energy?
[5] You have four identical capacitors, each of value C. You have to connect all four capacitors together in such a way that their equivalent capacitance is C. How many ways can you find to do it?
[6] Two identical parallel plate capacitors, X and Y, are connected across a battery as shown below.
If a sheet of paper is inserted between the plates of capacitor Y, how does the charge, the potential difference and the stored energy of Y now compare with X? That is, do these quantities increase, stay the same or decrease?
[7] Imagine you have a capacitor whose plate spacing is a, like that shown below, with a slab of metal of thickness b between the plates, that can move vertically between the plates.
Explain what happens to the capacitance of the system as the slab moves downwards, from being in contact with the upper plate to being in contact with the lower plate.
[8] There is something distinctly unusual - perhaps, amusing or surprising - about these four circuits. Can you figure out what it is?
[9] A capacitor is made of N parallel plates each of area A and spaced a distance d apart. A second set of N identical plates is positioned midway between the first set, as shown below. What is the total capacitance of the whole system?
[10] We determined that the energy stored in a charged capacitor is
How or in what way is this energy stored.?
[11] The figure below shows a parallel plate capacitor in which the plates have undergone a lateral shift so that they only partially "overlap".
Can you figure out what the approximate capacitance is?
[12] (This brain "buster" deals with a comparison of a "real" battery" with a capacitor as a source of energy.) According to the published data sheets a typical (Duracell) AA alkaline battery (1.5V) has an energy capacity of 3W.h (watt.hour) when new. What capacitance should a capacitor have in order to store a comparable amount of energy at 1.5V? Before you start trying to solve the problem ... do you think it will be a large or a small capacitance?
[13] You and a friend are standing as close as you can together without actually touching each other.
If you are both holding a conducting wire in one hand, can you figure out what the approximate capacitance is?
[14] Four capacitors, each with capacitance C are arranged as shown below.
What is the equivalent capacitance across A-B?
If another capacitor, of capacitance C, is connected across X-Y, what is the "new" equivalent capacitance?
The idea of brain "busters" was suggested to me by Ms. Lilian Jordan of Palm Beach Community College. The problems have been collected from a number of sources over the years, including myself(!) and inspired from ideas in texts such as "Conceptual Physics" by Paul Hewitt, "Peer Instruction" by Eric Mazur, "Physics for Scientists and Engineers" By Paul Tipler, "University Physics" by Hugh Young and Roger Freedman, "Physics" by John Cutnell and Kenneth Johnson, and "The Flying Circus of Physics" by Jearl Walker. I have adapted them to suit my courses.