Capacitor Supplies Current to Bulb
Part A
Immediately after time
, what happens to the charge on the capacitor plates?
a.
Individual charges flow through the circui
t from the positive to the negative side
of the capacitor.
b.
Individual charges flow through the circuit from the negative to the positive side
of the capacitor.
c.
The positive and negative charges attract each other, so they stay in the capacitor.
d.
Current
flows clockwise through the circuit.
e.
Current flows counterclockwise through the circuit.
List the letters corresponding to the correct statements in alphabetical order. Do not use
commas. For instance, if you think that only statements a and c are correc
t, write ac.
bd
Correct
Part B
At any given instant after
, what is the relationship between the current flowing
through the
two ammeters,
and
, and the current through the bulb,
?
Correct
This is a fundamental result that reflects conservation of charge. In a circuit where
elements
are arranged in series, the voltage changes as current flows through the circuit,
but the current is constant. Otherwise, charge would accumulate in the circuit.
In a circuit where elements are arranged in parallel, the opposite is true; all parallel
branc
hes have the same voltage, although the current may be different in different
branches. This result is formalized in Kirchoff's junction law

the algebraic sum of
currents entering any junction must be zero. (In this law, a current leaving a junction is
considered negative).
Part C
What is the relationship between current and charge? If you are given the charge on the
positive plate of the capacitor as a function of time,
, what is
?
=
Correct
Part D
Light bulbs are often assumed to obey Ohm's law, but this is not strictly true, because
their resistance increases as the filament heats up at higher voltages. A typical flashlight
bul
b at full brilliance draws a current of approximately 0.5 A while attached to a 3 V
source. For this problem, assume that the changing resistance causes the current to be 0.5
A for any voltage between 2 V and 3 V.
Suppose this flashlight bulb is attached t
o a capacitor as shown in the circuit from the
problem introduction. If the capacitor has a capacitance of 3 F (an unusually large but not
unrealistic value) and is initially charged to 3 V, how long will it take for the voltage
across the flashlight bulb
to drop to 2 V (where the bulb will be orange and dim)? Call
this time
.
Express
numerically, in seconds, to the nearest integer.
=
6.00
seconds
Correct
Electrical Safety
Part A
What is the current flow through the body?
Express your answer numerically to two significant figures.
=
3.70×10
−2
A
Correct
The following are the effects of current on humans:
1 mA =
A or less: barely noticeable;
1 to 8 mA: strong surprise;
8 to 15 mA: unpleasant, victims able to detach from source;
15 to 75mA: painful, dangerous;
75
mA or more: fatal.
These values vary according to sex, age, and weight.
Resistance of a Heater
Part A
What current will flow through the heating coil when the heater is plugged in?
Express your answer for the current numerically, to three signific
ant figures.
=
12.50
A
Correct
Note t
hat watts/volts has the correct units: Since
and
,
then
.
Part B
What is
, the resistance of the heater?
Express your answer numerically, to three significant figures.
=
9.60
ohms
Correct
Part C
How long does it take to rai
se the temperature of the air in a good

sized living room
by
? Note that the heat capacity of air is 1006
and the density of air is
.
Express your answer numerically in minutes, to three significan
t figures.
=
16.10
minutes
Correct
Ac
tually, the heat capacity of the walls and other material in the room will generally
exceed that of the air by several times, so an hour is a more reasonable time to heat the
room by this much.
Power in DC Circuits
Part A
Focus on a single charge,
, passing through the resistor. Find the work
done on the
charge by the electric f
ield in the resistor.
Express the work
done on the charge in terms of
,
, and/or
.
=
q*V
Correct
In general, doing work on an object causes the kinetic energy of the object to increase.
You
might wonder if the kinetic energy of the charge increases in this case. If the charge
were free, the electric force
would
cause it to accelerate (this is how ion guns work), and
the charge would come out the far end of the resistor with increased velocity
, that is, with
increased kinetic energy. In fact, the speed of the charge is not substantially increased in
a resistor; instead the charge repeatedly bumps into the resistor, transferring its excess
kinetic energy to the resistor. The energy added to the
charge therefore appears as the
heat of the whole resistor.
Part B
When thinking about an electric circuit, you usually focus not on the motion of individual
charges, but rather on the continuous current (charge per unit time) flowing through the
circuit.
Thus, rather than considering the work done on a particular charge, it is useful to
compute the work done per unit time on the charge flowing through the circuit, or in
other words, the power.
Find the electrical power
delivered to the resistor via the work done on the individual
charges passing through it. (Again, this power ultimately appears in the form of heat).
Express
in terms of quantities given in the problem introduction.
=
V*I
Correct
Some textbooks use the variable
for power, to help you remember that it is measured
in
units of watts. Using
for power and reserving the symbol
to represent work
emphasizes the relationship to the underlying classical mechanics.
Power in Resistive Electric Circuits
Part A
What is the ammeter reading
?
Express your an
swer in terms of
,
, and
.
=
EMF/(R+r_int)
Correct
Note that the resistances of
the ammeter and voltmeter do not appear in the answer. That
is because these two circuit elements are "ideal." The voltmeter has infinite resistance, so
no current flows through it (imagine that there is a short circuit inside the voltmeter). The
ammeter
has zero resistance, so there is no voltage drop as current flows through it.
Part B
What is the voltmeter reading
?
Express your answer in terms of
,
, and
.
=
EMF/(R+r_int)*R
Correct
In the following parts, you will express the power dissipated in the resistor of resistance
using three different sets of variables.
Part C
What is the
power
dissipated in the resistor?
Express your answer in terms of
and
.
=
I*V
Correct
Part
D
Again, what is the power
dissipated in the resistor?
This time, express your answer in terms of one or more of the following variables:
,
,
and
.
=
I^2*R
Correct
Part E
For the third time, what is the power
dissipated in the resistor?
Express your answer in terms of one or more of the following variables:
,
, and
.
=
EMF^2*R/(R+r_int)^2
Correct
Part F
If the EMF and internal resistance of the battery are fixed, what value of resistance
would maximize the power dissipated in the resistor?
Express your answer in terms of
.
=
r_int
Correct
Part G
How much power
is dissipated in the battery?
Express your answer in terms of one or more of the following variables:
,
, and
.
=
(EMF/(R+r_int))^2*r_int
Correct
Part H
Wha
t is the power dissipated in the part of the circuit between points 1 and 2?
Correct
Part I
What is the power
dissipated in the entire circuit?
Express your answer in terms of one or more of the following variables:
,
, and
.
=
EMF^2/(r_int+R)
Correct
Part J
What is the total power
dissipated in the entire circuit, in terms
of the emf of the
battery and the current in the circuit?
Express your answer in terms of
and the ammeter current
.
=
EMF*I
Correct
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