# A2L Item 251

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? ### Commentary:

(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.

# A2L Item 252

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? ### Commentary:

(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.

# A2L Item 249

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:

1. V^2^/R
2. CV^2^/2
3. QV
4. V/RC
5. none of the above

### Commentary:

(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.

# A2L Item 247

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:

1. V^2^/R
2. CE^2^/2
3. QV/2
4. V/RC
5. none of the above

### Commentary:

(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.

# A2L Item 245

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?

1. C, E, and U only
2. ΔV and U only
3. C and U only
4. E and U only
5. C, ΔV, and U only
6. ΔV and E only
7. C and ΔV only
8. None of the above

### Commentary:

(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?

# A2L Item 246

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?

1. C, E, and U only
2. Q and U only
3. C and U only
4. E and U only
5. Q, ΔV, and U only
6. ΔV and E only
7. C and Q only
8. None of the above

### Commentary:

(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?

# A2L Item 219

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? 1. Charge on C1 decreases.
2. Total charge on C1 and C2 is the same as the original Q.
3. The total energy stored in both capacitors is the same as the
original U stored in C1.
4. The potential (Voltage) across C1 decreases.
5. All of the above.
6. Only 1, 2, and 3 are true.
7. Only 1, 2, and 4 are true.

### Commentary:

(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.

# A2L Item 217

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? 1. V stays same, Q increases, U increases
2. V stays same, Q decreases, U stays same
3. V increases, Q decreases, U increases
4. V decreases, Q stays same, U decreases
5. None of the above
6. Cannot be determined

### Commentary:

(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.

# A2L Item 218

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? 1. V same, Q increases, U increases
2. V same, Q decreases, U same
3. V increases, Q decreases, U increases
4. V decreases, Q same, U decreases
5. None of the above
6. Cannot be determined