# 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 250

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:

1. V^2^/2R
2. LV^2^/2R2
3. LV
4. V/RL
5. none of the above

### Commentary:

(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?

# A2L Item 220

Goal: Reason regarding resistance

Source: 283-550 Resistance and geometry

Which object below has the lowest resistance? All three have length L
and are made out of the same material. 3. # 3

4. Both #1 and #3 have the same, and theirs is less than the resistance of
#2.

### Commentary:

(2) Students should be able to reason that the contribution to the total
resistance from a slice of material decreases as the area increases.

# A2L Item 170

Goal: Recognize macroscopic and microscopic quantities

Source: 283 Resistance variations with area. An
ohmic conductor is carrying a current. The cross-sectional area of the
wire changes from one end of the wire to the other. Which of the
following quantities vary along the wire?

1. The resistivity
2. The current
3. The current density
4. The electric field
1. A only
2. B only
3. C only
4. D only
5. A and B only
6. C and D only
7. A, B, C, and D
8. None of the above