2010 AP Notes Chapter 27
DC Circuits

Chapter 27
1.
What is emf? How is it defined?
2.
What happens if batteries are in series? Positive plates facing? Opposite plates
facing?
A battery or batteries connected to two parallel plates produce the equipotential lines
between t
he plates shown above.
3.
Which of the following configurations is most likely to produce these
equipotential lines?
2010 AP Notes Chapter 27
4.
What if a battery is not ideal?
5.
The emf of a battery is 12 volts. When the battery delivers a current of 0.5 ampere
to a load, the p
otential difference between the terminals of the battery is 10 volts.
The internal resistance of the battery is
a.
1
b.
2
c.
4
d.
20
e.
24
6.
A 12

volt storage battery, with an internal resistance of 2
, is being charged by a
current o
f 2 amperes as shown in the diagram above. Under these circumstances,
a voltmeter connected across the terminals of the battery will read
a.
4 V
b.
8 V
c.
10 V
d.
12 V
e.
16 V
7.
What happens when resistors are in series? Parallel? (think ab
out what resistance
of a resistor depends on)
2010 AP Notes Chapter 27
8.
The circuit in the figure above contains two iden
tical lightbulbs in series with a
battery. At first both bulbs glow with equal brightness. When switch S is closed,
which of the following occurs
to the bulbs?
Bulb I
Bulb 2
a.
Goes out
Gets brighter
b. Gets brighter
Goes out
c. Gets brighter
Gets slightly dimmer
d. Gets slightly dimmer
Gets brighter
e. Nothing
Goes out
9.
Which of the following combinations of 4
res
is
tors would dissipate 24 W when
connected to a 12 Volt battery?
10.
Fill in the chart
Ammeter
Voltmeter
Measures
Placed in series
or parallel?
Resistance?
2010 AP Notes Chapter 27
The batteries in each of the circuits shown a
bove are identical and the wires have
negligible resistance.
11.
In which circuit is the current furnished by the battery the
greatest
?
(A)
(B)
(C)
(D)
(E)
12.
In which circuit is the equivalent resistance connected to the battery the
greatest
?
(A)
(B)
(C)
(D)
(
E)
13.
Which circuit dissipates the
least
power?
(A)
(B)
(C)
(D)
(E)
14.
Kirchhoff’s loop rule
15.
Reminders
a.
If you go through a loop and your pencil travels away from the positive
side of battery does it add voltage or subtract voltage?
b.
If you go through
a resistor in the direction of the current does it add
voltage or subtract voltage?
16.
A circuit has three resistors in series with the battery. Write the loop rule.
2010 AP Notes Chapter 27
17.
A 30

ohm resistor and a 60

ohm resistor are connected as shown above to a
batt
ery of emf 20 volts and internal resistance r. The current in the circuit is 0.8
ampere. What is the value of r ?
a.
0.22
b.
4.5
c.
5
d.
16
e.
70
18.
Junction Rule
19.
A circuit has three resistors in parallel with the bat
tery. The battery is 20 V, the
first resistor is 10 ohms, the second 20 ohms and the third 30 ohms. Find the
current through each loop.
Equations
Rewritten Equations
Matrix
Answers
2010 AP Notes Chapter 27
20.
In the circuit shown above, what is the r
esistance R ?
a.
3
b.
4
c.
6
d.
12
e.
18
In the circuit above, the emf's and the resistances have the values shown. The current I in
the circuit is 2 amperes.
21.
The resistance R is
a.
1
b.
2
c.
3
d.
4
e.
6
22.
T
he potential difference between points X and Y is
a.
1.2 V
b.
6.0 V
c.
8.4 V
d.
10.8 V
e.
12.2 V
23.
How much energy is dissipated by the 1.5

ohm resistor in 60 seconds?
a.
6 J
b.
180 J
c.
360 J
d.
720 J
e.
1,440 J
2010 AP Notes Chapter 27
24.
In the circuit be
low for what value of R will the ideal battery transfer energy to
the resistors
a.
At a rate of 60.0W
b.
At the maximum possible rate
c.
At the minimum possible rate?
d.
What are those rates?
2010 AP Notes Chapter 27
25.
Draw a RC Circuit
a.
Write a Loo
p rule for the above circuit.
b.
Put this equation in terms of time by substituting for current.
c.
Rewrite and integrate both sides from the moment when the switch is
closed to an arbitrary later instant:
Charging capacitor
Object falling against air
resistance
d.
Write the expression for the charge on a capacitor as a function of time
while the capacitor is charging.
e.
Write the expression for the current in a RC circuit while the capacitor is
charging.
2010 AP Notes Chapter 27
f.
Draw a graph of charge versus t
ime as a capacitor is charging. Current
versus time.
g.
What is a time constant?
26.
In an RC series circuit the battery has a voltage of 12 V, resistor is 1.4 M
Ω, and
capacitor is 1.8µF.
a.
Calculate the time constant
b.
Find the maximum charge that will appear on the capacitor during
charging.
c.
How long does it take for the charge to build up to 16.0µC?
2010 AP Notes Chapter 27
27.
Write the loop rule for a capacitor disc
harging.
a.
substitute in for current in terms of time.
b.
Integrate this expression from the moment the switch is closed to a later
instant.
Capactor discharging
Object rising with air resistance
c.
Write the expression for charge o
n a capacitor as a function of time while
discharging.
d.
Find current as a function of time as a capacitor discharges.
2010 AP Notes Chapter 27
e.
Draw a graph of charge versus time while discharging and current versus
time.
28.
A resistor R and a capacitor C are connecte
d in series to a battery of terminal
voltage V
0
. Which of the following equations relating the current I in the circuit
and the charge Q on the capacitor describes this circuit?
a.
V
0
+ QC

I
2
R = 0
b.
V
0

Q/C

IR = 0
c.
V
0
2

Q
2
/2C

I
2
R = 0
d.
V
0

C(dQ/dt)

I
2
R = 0
e.
Q/C

IR = 0
Assume the capacitor C is initially uncharged. The following graphs may represent
different quantities related to the circuit as functions of time t after the switch S is closed
29.
Which graph best represe
nts the voltage versus time across the resistor R ?
(A)
(B)
(C)
(D)
(E)
30.
Which graph best represents the current versus time in the circuit?
(A)
(B)
(C)
(D)
(E)
31.
Which graph best represents the voltage across the capacitor versus time?
(A)
(B)
(C)
(D)
(E)
2010 AP Notes Chapter 27
32.
In the circuit shown above, the capacitor is initially uncharged. At time t = 0,
switch S is closed. The natural logarithmic base is e. Which of the following is
true at time t = RC?
a.
The current is
/eR .
b.
The current is
/R
c.
The voltage across the
capacitor is
.
d.
The voltage across the capacitor is
/e .
e.
The voltages across the capacitor and resistor are equal.
33.
In the circuit shown above, the capacitor C is first charged by throwing switch S
to the left, then discharged by throwing S to the r
ight. The time constant for
discharge could be increased by which of the following?
a.
Placing another capacitor in parallel with C
b.
Placing another capacitor in series with C
c.
Placing another resistor in parallel with the resistor R
d.
Increasing battery emf
e.
Decreasing battery emf
In the circuit shown above, the battery supplies a constant voltage V when the switch S is
closed. The value of the capacitance is C, and the value of the resistances are R
1
and R
2
.
34.
Immediately after the switch is closed, the
current supplied by the battery is
a.
V/(R
1
+ R
2
) b. V/R
1
c. V/R
2
d.
V(R
1
+ R
2
)/R
1
R
2
e. zero
35.
A long time after the switch has been closed, the current supplied by the battery is
a.
V/(R
1
+ R
2
)
b.
V/R
1
c.
V/R
2
d.
V(R
1
+ R
2
)/R
1
R
2
e.
zero
2010 AP Notes Chapter 27
36.
The series circuit shown above contains a resistance R = 2 x 10
6
ohms, a capacitor of
unknown
capacitance C, and a battery of unknown emf
E
and negligible internal resistance. Initially the
capacitor is uncharged and the
switch S is open. At time t = 0 the switch S is closed. For t > 0 the
current in the circuit is described by the equation:
i(t) = i
o
e

t/6
where i
o
= 10 microamperes and t is in seconds.
a.
Determine the emf of the battery.
b
. By evaluating an approp
riate integral, develop an expression for the charge on the
right

hand plate of the
capacitor as
a function of time for t > 0.
b.
On the axes below sketch a graph of the charge Q on the capacitor as a function
of time t
.
c.
Determine the capacitanc
e C
2010 AP Notes Chapter 27
37.
Your engineering firm has built the
RC
circuit shown above. The current is
measured for the time t after the switch is closed at t = 0 and the best

fit curve is
represented by the equation
I(t) = 5.20 e

t/10
, where I is in milliamperes and t is
in se
conds.
a.
Determine the value of the charging voltage V
o
predicted by the equation.
b.
Determine the value of the capacitance C predicted by the equation.
c. The charging voltage is measured in the laboratory and found to be greater than
predicte
d in part a.
i.
Give one possible explanation for
this finding.
ii.
Explain the implications that your answer to part i has for the
predicted value of the capacitance.
2010 AP Notes Chapter 27
38.
You have been hired to determine the internal resistance of 8.0
F capaci
tors for an electronic
component manufacturer. (Ideal capacitors have an infinite internal resistance

that is, the
material between their plates is a perfect insulator. In practice, however, the material has a very
small, but nonzero, conductivity.) You
cannot simply connect the capacitors to an ohmmeter,
because their resistance is too large for an ohmmeter to measure. Therefore you charge the
capacitor to a potential difference of 10 V with a battery, disconnect it from the battery and
measure the pote
ntial difference across the capacitor every 20 minutes with an ideal voltmeter,
obtaining the graph shown above.
a.
Determine the internal resistance of the capacitor.
b.
Determine the magnitude of the charge leaving the positive plate of
the capacitor in
the first 100 min.
2010 AP Notes Chapter 27
39.
Capacitors 1 and 2, of capacitance C
1
= 4
F and C
2
= 12
F, respectively, are connected in a circuit
as shown above with a resistor of resistance R = 100
and two switches. Capacitor 1 is initially
charged to a voltag
e V
o
= 50 V, and capacitor 2 is initially uncharged. Both of the switches S are then
closed at time t = 0.
a.
What are the final charges on the positive plate of each of the capacitors 1 and 2
after equilibrium has been reached?
b.
Write, but do not solv
e, an equation that, at any time after the switches are closed,
relates the charge on capacitor C
1
, its time derivative (which is the instantaneous
current in the circuit), and the parameters V
o
, R, C
1
, and C
2
.
The current in the resistor is given as a function of time by
I = I
o
e

t/
,
where I
o
= 0.5A
and
= 3 x 10

4
s.
c.
Determine the rate of energy dissipation in the resistor as an explicit function of
time.
d.
How much energy is dissipated in the resistor fro
m the instant the switch is closed
to when equilibrium is reached?
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