Goal: Reason regarding capacitors
Source: 283-585 RC equivalent circuit at early time
Consider the following circuit.
The capacitor is uncharged when the switch is closed at t=0. Which
circuit is equivalent to this circuit for the instant immediately after
the switch is closed?
Goal: Reason regarding capacitors
Source: 283-590 RC equivalent at t infinity
Consider the following circuit.
The capacitor is uncharged when the switch is closed at t=0. Which
circuit is equivalent to this circuit as t approaches infinity?
(2) Students often misunderstand the statement that capacitors behave
like an open circuit after a long time.
This item is best used in conjunction with the previous one. Both should
be asked before discussion of either to reveal whether students just
have the behaviors reversed or evidence a more serious problem.
Goal: Reason regarding RC circuits.
Source: 283 – energy dissipated in RC circuit
Consider the following circuit. The capacitor is uncharged when
switch S is closed at t = 0. During the charging process the total
energy dissipated in the resistor is:
(2) Students should recognize that if the capacitor ultimately is
charged to Q, the total work done by the battery is QV. Half of this is
stored in the capacitor and half is dissipated in the resistor.
Goal: Link energy with electrical quantities
Source: 283 – energy in capacitor
Consider the following circuit. The capacitor is uncharged when switch S
is closed at t = 0. After current stops flowing and the capacitor is
fully charged the energy stored in the capacitor is:
(3) The intent of this question is to provide students the opportunity
to distinguish a correct but uncommon form for the stored energy from a
number of other familiar forms.
Goal: Reason and link electrical quantities.
Source: 283-Del C, E, U, etc – cstQ
Two parallel conducting plates form a capacitor. It is isolated and a
charge Q is placed on it. A metal cylinder of length half the plate
separation is then inserted between the plates. Which of the quantities
C, ΔV, Q, E, and U change?
(8) Students who are formula bound find this a difficult question.
Obviously Q does not change. Depending on how students interpret the
question, they may conclude that E does or does not change. The value of
E in regions outside the cylinder does not change [Students taking this
interpretation may respond #5.], but inside the cylinder it is now zero.
Since E is now zero for half of the distance between the original
plates, both ΔV and U must change. That C also changes can be
appreciated in many different ways.
There are many good follow up questions, such as: Does it make a
difference where the cylinder is placed? How would the quantities change
if the cylinder was made of a dielectric material? Suppose a half
cylinder of length 2d were placed between the plates. How would
quantities change?
Goal: reason and link electrical quantities
Source: 283-Del C, E, U, etc. – cstV
Two
parallel conducting plates form a capacitor. With a metal cylinder of
length half the plate separation inserted between the plates, it is
connected to a battery with potential ΔV. The cylinder is now removed.
Which of the quantities C, ΔV, Q, E, and U change?
(8) Since ΔV does not change, E must because the distance between
plates doubles. If E changes, so must Q. If Q changes, so must C.
Finally, that U chages can be seen in a variety of ways.
There are many good follow up questions, such as: How would the
quantities change if the cylinder was made of a dielectric material?
Goal: Reason regarding capacitors
Source: 283-545 Adding capacitors in parallel
A capacitor having, C1, is connected to a battery until
charged, then disconnected from the battery. A second capacitor,
C2, is connected in parallel to the first capacitor. Which
statements below are true?
(7) Statement #3 is the hardest for students to reason about. This is
most easily decided as incorrect if the two capacitors are taken as
equal.
Goal: Reason regarding capacitors and dielectrics.
Source: 283-535 inserting a dielectric changes a capacitor
A capacitor with capacitance C is connected to a battery until charged,
then disconnected from the battery. A dielectric having constant
κ is inserted in the capacitor. What changes occur in the charge,
potential and stored energy of the capacitor after the dielectric is
inserted?
(4) It should be clear to students that the charge cannot change. Most
students recognize that capacitance increases when a dielectric is
inserted into a capacitor. The issue then becomes whether they
appreciate the relationships between C, Q, V and U.
Goal: Reason regarding capacitors
Source: 283-540 Adding capacitors in series
A capacitor, C1, is connected to a battery until charged, and
then disconnected from the battery. A second capacitor, C2,
is connected in series to the first capacitor. What changes occur in
capacitor C1 after C2 is connected as shown?
(5) All quantities remain the same. Some students may consider the
capacitors to be connected in parallel despite the figure.
Commentary:
Answer
(3) Some students misunderstand the statement that capacitors behave
initially as a short circuit and select #1 or #2.
This item is best used in conjunction with the next one. Both should be
asked before discussion of either to reveal whether students just have
the behaviors reversed or evidence a more serious problem.