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?
Goal: Hone the concept of average velocity
Source: CTtil2;12;02
While traveling from Boston to Hartford, Person A drives at a constant
speed of 55 mph for the entire trip. Person B drives at 65 mph for half
the trip and then drives 45 mph for the second half of the trip. When
would B arrive in Hartford relative to A?
(3) Many students are inclined to average the speeds and conclude that
they arrive at the same time. It is often useful to compare this
situation to the one in which time is halved.
Goal: Interrelate representations of kinematical quantities
Source: CT151.2-8
An object’s motion is described by the graph above. The position of the
object at t = 9 seconds is most nearly…
(6) This problem is primarily to determine if students appreciate the
information available from a graph. Many students will determine the
displacement forgetting that the initial position is unknown.
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?
(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.
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?
(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.
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?
(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.
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: Reason regarding RL circuits.
Source: 283 – energy dissipated in inductor
Consider the following circuit. The switch S is closed at t = 0.
The total energy dissipated in the resistor before the current reaches
its maximum value is:
(5) The total work done by the battery is QV where Q is a function of
time which is not limited. The total energy stored in the inductor is
finite. The difference must be the energy dissipated in the resistor.
Since it takes an infinite amount of time for the current to reach its
maximum value, the total amount of energy dissipated is also maximum.
A good follow up question is: Is there a time when the dissipated energy
is equal to the stored energy? If so, what is that time?
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.
Commentary:
Answer
(8) The objective of this question is to reveal what students are
assuming about the springs. The reasoning behind any incorrect answer
should be thoroughly discussed.