LivePhoto Physics Activity 28
Name: ___________________________
Date: ____________________________
Resistance and OhmàLaw
When designing or using electronic devices, we
often need to know how changing the voltage
across the device will affect the current flowing
through it.
For example, what will happen to the current
flowing through a circuit element, such as a bulb
that is part of a circuit, if we increase the voltage
across it? Alternatively, what will happen to the
current passing through a carbon resistor as
voltage increases? To answer these questions,
letàstart with two definitions:
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Figure 1:
The two
multimeters in
this circuit are
wired to
record the
current
passing
through a
bulb and the
voltage drop
across it.
2.49
Definition 1:We define the resistance, R, of an electrical device as the ratio of the potential difference or
voltage drop, V, across it to the current passing through it.
(definition of Resistance).
Definition 2: We say that a device obeys OhmàLaw if the current passing through it is always directly
proportional to the voltage drop across it, independent of the value of the voltage drop, so that the value of
its resistance doesn change even if we apply a different voltage across it.
In this assignment you will compare the behavior of a flashlight bulb to that of a carbon resistor and
determine whether or not these devices obey OhmàLaw.
1. Preliminary Questions
Note: You will receive full credit for each prediction made in this preliminary section whether or not it
matches conclusions you reach in the next section. As part of the learning process it is important to
compare your predictions with your results. Do not change your predictions!
(a) Which of the two meters is wired to measure the current passing through the bulb shown in
Figure 1? The one of the left or the one on the right? Note: The )ght grey7ire in the bottom left in
the photo is an enhancement of a red wire in the movie frame. If you still have trouble interpreting the
wiring open the image entitled and use it instead of Figure 1.
Left Meter ______ Right Meter ______
(b) How many batteries are in the circuit in Figure 1?
Zero ______ One ______ Two ______ Three ______
(c) Draw a neat circuit diagram for Figure 1 using the following standard symbols:
A
V
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(d) Circle the only graph shown below that depicts a proportional relationship.
2. Activity-Based Questions
In this section, you will work with a Logger Pro file entitled in which you can enter
meter readings shown in two movies. The first movie shows what happens to the current passing through
a flashlight bulb when there are different voltage drops (or potential differences) across it when 0, 1, 2
and 3 batteries are hooked into the circuit. The second movie been created in a similar manner but the
bulb has been replaced with a carbon resistor. Note: Before taking data you may want to play the movies
and then enlarge them so you can see the numbers and the decimal points on the meters clearly! Take
data for the voltage across and the current through the bulb: In use frames 0, 26
or 27, 43 or 44, and 64 or higher for recording data and enter values in the table below.
(a) Take data for the voltage across and the current through the resistor: In
use frames 0, 28 or 29, 48 or 49, and 73 or higher and enter values in the table below.
i bulb
(mA)
V_bulb
(Volts)
i_resistor
(mA)
V_resistor
(Volts)
(b) Graph your results: Sketch your results for the two devices in the graph frames below.
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(c) Calculate the resistance for the flashlight bulb in ohms for each of your values of current and voltage
drop (except i = 0 A and V = 0 V). Report your results to two significant figures. Hint: Don forget
to change milliamps (mA) to amps (A).
R1 Bulb
R2 Bulb
R3 Bulb
(d) Does the flashlight bulb obey OhmàLaw over the range of voltages used in the circuit? Why or why
not? Cite evidence for your answer from both parts 2(b) and 2(c).
(e) Calculate the resistance for the carbon resistor in ohms for each of your values of current and voltage
drop (except i = 0 A and V = 0 V). Report your results to two significant figures. Hint: Don forget
to change milliamps (mA) to amps (A).
R1 Resistor
R2 Resistor
R3 Resistor
(f) Does the carbon resistor obey OhmàLaw over the range of voltages used in the circuit? Why or why
not? Cite evidence for your answer from both parts 2(b) and 2(e).
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3. Reflections on Your Findings
(a) If either or both of your circuit elements did not obey OhmàLaw, can you think of any reasons for
the non-ohmic behavior? In other words what might be happening to one or both of the elements as
the applied voltage drop increases?
Part 2
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LivePhoto Physics Activity 29
Parallel Plate Capacitor: Potential Difference vs. Spacing
In this assignment you will consider how a charged capacitor constructed from a fairly large pair of
parallel metal plates behaves when the spacing between the plates increases. In particular we want you to
explore how the voltage (a.k.a. potential difference) across the plates varies as the distance between the
charged plates increases.
Theoretical Review: [1] A capacitor is defined as
any two conductors, separated by an insulator
where each conductor carries a net excess charge
that is equal in magnitude and opposite in sign. Its
capacitance, C, is defined as
d
[Eq. 1]
where Q is the magnitude of the excess charge on
each conductor and V is the voltage (or potential
difference) across the plates. [2] We can use GaussŒaw to analyze a parallel plate capacitor if we
assume that most of the electric field lines is
perpendicular to the plates. According to Gauss, if
air is the insulator, the capacitance, C, is related to
the area of the plates, A, and the spacing between
them, d, by the equation
.
Figure 1: The spacing, d, between the surfaces of
two parallel metal plates is changed while the
voltage between the plates is measured.
[Eq. 2]
is known as the electric constant (or permittivity).
1. Preliminary Questions
Note: You will receive full credit for each prediction made in this preliminary section whether or not it
matches conclusions you reach in the next section. As part of the learning process it is important to
compare your predictions with your results. Do not change your predictions!
As you proceed with this assignment, you, be working with a short video clip entitled
. It shows the spacing between a pair of parallel plates increasing by a known
amount each time a knob is twisted by a half turn. The potential difference between the plates is measured
with both an electrometer and voltage probes connected to a computer (see Fig. 1) so data can be recorded
with the Logger software. Before proceeding, you should view the video clip.
(a) Use Equations 1 and 2 to derive an equation that describes how the voltage across a parallel plate
capacitor depends on the plate spacing, d, and area, A. Show your work.
(b) If the plate spacing increases by 1.25 mm for each full turn of a knob, by what amount does the
spacing change in millimeters (mm) when the knob goes through half a turn?
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(c) You should have noticed in frame 5 of the movie that only one plate of the capacitor is being charged
positively. The other plate is òounded. he right-hand plate and the left-hand plate are separated
by only one-half of a turn of the dial. How can we claim this set up is actually a capacitor and thus
has equal and opposite excess charges on both plates? Hint: What happens immediately after the first
plate is charged? Is induction possible?
(d) What do you expect will happen to the capacitor system as the spacing between the plates increases?
Hint: Refer to the equation you derived in section 1(a).
The potential difference will:
Increase
Decrease
Stay the same
The excess charge on each plate will:
Increase
Decrease
Stay the same
(e) When the potential difference is large the capacitor system is storing more energy than when it is
small. Where does the additional energy ïme from!s the plate spacing increases?
(f) If the two plates behave like an ideal capacitor, sketch the shape of a graph of voltage vs. spacing you
might expect to measure and explain your reasoning.
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2. Activity-Based Questions
In this section, you will start by working with the Logger Pro file that has the
movie inserted in it. The electrometer shown in the background has numbers
that are too small to read, but you can easily see the deflection of the needle. However, separate
Logger Pro voltage probe readings were recorded as the movie was made. In the < SensorDataSet.cmbl>
file the movie and the voltage readings have been synchronized. Although the capacitor plates look as if
they are in contact at first, they are actually separated by 0.625 mm or a !lf turn. fter a few seconds
the left capacitor plate is charged to about 13 volts relative to the right plate. Then the spacing between
the two plates is increased a half turn at a time. You can see this process by opening the Logger Pro file
and clicking on the Start button in the Replay window.
(a) Enter data into Logger Pro for voltage vs. plate spacing: In use the
Examine tool to find a typical value for the voltage between the plates at each spacing. Enter the
results in the Manual Entries table below. Also sketch the resulting graph of V vs. d. Note: We¥
assumed for you that when the plates are in contact at d = 0 mm the charges neutralize, so V = 0.0 v.
Table 1anual Entries
Rotations
(# of turns)
D
(mm)
V_readings
(volts)
0.0
0.5
1.0
1.5
2.0
(b) Is this an ideal capacitor? Close your original Logger Pro file and then open a second file entitled
. Enter the data from Table 1 into the designated columns manually. A graph of
V_readings vs. d will appear. Use the Curve Fit tool in the Logger Pro Analyze menu to determine
whether the graph seems to show a proportional relationship between V and d. Hint: Do not perform
a linear fit. Instead select Curve Fit from the Analyze menu and select a Proportional Fit (denoted
y = Ad). Does the capacitor act like an ideal capacitor? Explain.
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(c) Find the area of the plates in square millimeters. The faces of the capacitor plates are disks. Use
the video analysis tools to find the data needed to calculate the area, A, of each plate. Then calculate A
in mm2 to three significant figures. Show your calculations. Hints: (1) The yellow ruler at the bottom
of each frame is 20.0 cm long, and (2) The Enable Video Analysis (
), Set Scale ( ), and Photo
Distance ( ) tools will come in handy!
(d) Convert the area of the plates from mm2 to m2.
(e) Determine excess charge on the capacitor. When d = 1.25 mm, V is about 25 V. Rearrange the
equation you derived in Section 1(a) and calculate the magnitude of the excess charge on each plate in
Coulombs. Represent the plate area in m2, the plate spacing in meters and note that
. Show your calculations with detailed units so you can perform a units check
as you do your calculations. Express your answer using two significant figures. Hints: It can be
shown that 1 volt = 1 [N.m/C]. Your answer should be between 7 and 10 nC.
3. Reflections on Your Findings
Consider your analysis of the graph of V vs. d. The assignment forced you to look at the relationship as it
exists when there is a very small separation distance between the plates of a parallel plate capacitor and to
categorize it as being proportional. Do you see any evidence of deviations from ideal capacitor behavior
in the graph of these data as the spacing was increased more and
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