# A2L Item 261

Goal: Recognize a lack of information

Source: CT151.2S02-24

Consider the situations at right. Let m < M. Which spring has
the largest spring constant?

1. A
2. B
3. C
4. A and B are equal
5. A and C are equal
6. B and C are equal
7. All of them have the same spring constant
8. Cannot be determined

### Commentary:

(8) The objective of this question is to reveal what students are
should be thoroughly discussed.

# A2L Item 254

Goal: Reasoning regarding inductors

Source: 283-750 LR equivalent at time = infinity

Consider the following circuit.

The switch is closed at t=0. Which circuit is equivalent to this circuit
as t approaches infinity?

### Commentary:

(3) Some students misunderstand the statement that inductors behave as a
short circuit after a long time and select #1 or #2.

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 253

Goal: Reason regarding inductors

Source: 283-755 RL equivalent circuit at t small

Consider the following circuit.

The switch is closed at t=0. Which circuit is equivalent to this circuit
for the instant immediately after the switch is closed?

### Commentary:

(2) Some students misunderstand the statement that inductors behave
initially as an open circuit and select #1 or #3.

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 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 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 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 241

Goal: Reason regarding circuits

Source: 283 compare dissipated energy

Consider the following circuits. Two identical batteries are connected
to two identical capacitors in series with different resistors. The
capacitors are initially uncharged. Which statement is true regarding
the energy supplied by the batteries to charge the capacitor?

1. The battery in A does more work.
2. The battery in B does more work.
3. Both batteries do the same work.
4. Cannot be determined

### Commentary:

(3) The energy dissipated in the resistor is independent of the
resistance. Consider a time when the capacitor contains some charge Q.
If an additional charge dq is added, the battery does work dqV and the
increment of stored energy in the capacitor is (Q/C)dq. By conservation
of energy, the difference must have been dissipated in the resistor. The
difference, [V-(Q/C)]dq is independent of resistance.

# A2L Item 240

Goal: Reason regarding power in a circuit

Source: 283 circuit powers

Consider the circuit below. Which resistor has the greatest power
consumption?

1. The 50Ω resistor
2. The 10Ω resistor
3. The 1000Ω resistor
4. The 50Ω and 10Ω resistors
5. The 50Ω and 1000Ω resistors
6. The 10Ω and 1000Ω resistors
7. All have the same power.

### Commentary:

(1) The potential drop over the 10Ω and 1000Ω resistors is the same.
Since power goes as V^2^/R, more power is consumed in the 10Ω resistor
than the 1000Ω resistor. Further, since power also goes as I^2^R and only
a fraction of the current through the 50Ω resistor flows through the 10Ω
resistor, the 50Ω resistor must dissipate the most energy.

# A2L Item 194

Goal: Reasoning with thermodynamics

Source: UMPERG-ctqpe212

The
two curves shown are isotherms. A system is taken from state A to state
B along the T2 isotherm. State C has the volume of state A
and the pressure of state B.

Which of the following is true:

1. QAB = 0
2. QAB = ΔEAB
3. QAB = -WAB
4. QAB = QCA-QCB
5. Not enough information

### Commentary:

(5) This is the only answer that is definitely correct. Students
will likely assume that the system is an ideal gas. Many will choose #3
and this should engender a discussion of the sign of work. Physicists
use the convention that positive work is that done BY the system.
Chemists frequently use the opposite convention.

The one choice giving students the most reasoning difficulty is #4. A
reasoning path that eliminates that choice is as follows. Q(AB) is
positive: gas does positive work on surroundings, so heat has to be
added to keep energy the same. Q(CA) is positive: no work is done, so
heat has to be added to raise the temperature. Q (CB) is positive: heat
must be added to expand the gas and still maintain constant pressure. So
Q(CB) [constant pressure] > Q(CA) [constant volume]; Q(CA) – Q(CB) < 0
cannot equal Q(AB) > 0