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Transcript
Physics 15b PSI Week 1: Introduction to Circuits and Equipment
An extremely important part of experimental physics is the equipment used to acquire data. This
introductory session is designed to familiarize you with some of the equipment that will be used
in 15b labs. Questions that must be answered are shown in green. For this lab, the manuals for the
scope and signal generator are available online.
Notes on the organization of all of the lab instructions:
We recommend that you do NOT print out the lab instructions for this lab or any future lab.
They will be available on the computer associated with each apparatus. The lab exercises are
divided into sections, each of which has a theme. The major headings are shown in blue. The
minor headings are shown in bold. The same outline and goals are also in the lab instructions
where they are the page following the prelab question. The apparatus assembly and measurement
instructions are shown in red. If you prefer meet the objective of the exercise without following
the apparatus instructions, go for it. The questions that must be answered are shown in green.
Pre-lab Questions: None for this week.
Goals:
1. Introduce basic concepts of circuits
2. Provide experience using an oscilloscope to acquire and display data
3. Provide experience using different types of standard electrical connectors (BNC, banana,
alligator clips, micrograbbers)
4. Introduce breadboards as quick, reliable tools for creating temporary electrical circuits
Outline
A. Oscilloscope Use
1. Setup the scope to monitor the voltage output of the signal generator
2. Demonstrate the that the scope probe does divide the input voltage by 10
3. Explore the triggering mechanism for this scope
B. Breadboard Use
1. Setup the scope to monitor the voltage output of the signal generator
C. LoggerPro Use
1. Use LoggerPro to acquire and display the voltage output of the signal generator.
D. Circuit Challenge
1. Design and build a circuit that will allow you to turn a light bulb on or off by toggling
either of two switches
Introduction to Circuits and Equipment
The supplemental information contains four sections. The first three sections provide
photographs and detailed discussion of the following lab equipment : 1. electrical
connectors (BNC, banana plugs, alligator clips, micrograbbers and hybrids); 2.
oscilloscopes 3. breadboards. Please look at those sections if you are having trouble
understanding how the equipment works. The fourth section covers electrical safety.
A. Oscilloscope Use:
Goals: Provide an introduction controlling the display of data on an oscilloscope.
Introduce signal generators. Introduce different kinds of electrical connectors.
One of the most important pieces of laboratory equipment is the oscilloscope. It presents
a graph of voltage as a function of time, so the y axis is voltage and the x axis is time. In
this exercise, the voltage to be displayed is generated by a signal generator, which is a
device that produces a controllable voltage as a function of time.
Materials: 1 four-channel oscilloscope; 1 signal generator; 1 Vernier voltage probe to
connect with the LabPro Mini input; 1 computer running LoggerPro; 2 sets of
micrograbbers with BNC jacks; 1 BNC-to-banana connector with wires clamped in the
banana posts; 2 BNC cables; 1 oscilloscope probe; BNC T
1. Setup the scope to monitor the voltage output of the signal generator
Recall that absolute electrical potential (like absolute potential energy) has no meaning;
only potential difference (a.k.a. “voltage”) has physical significance. As a matter of
notation, we will generally use V to refer to a voltage (potential difference). Every
apparatus used to measure voltage must really measure the difference between two
potentials. Typically, a circuit contains a reference point designated as V = 0; we call this
point ground. So when we speak of the “voltage” of a single wire, we mean relative to
ground. The voltage-measuring devices we will use today (the oscilloscope and the
Vernier voltage probe) both measure voltage relative to this absolute ground (which is
shared by the signal generator, the oscilloscope, the computer, the LabPro Mini, and
indeed anything else plugged into the electrical socked in the bench).
The signal generators are set so that their voltage output as function of time oscillates
sinusoidally according to
V ( t ) = Vmax sin ( 2! ft )
where Vmax is the amplitude of the oscillation and f is the frequency.
The object of this exercise is to display this voltage signal on an oscilloscope
(“scope”), so that the amplitude is 3 boxes and 3 periods of the sine wave are shown
on the scope.
Apparatus Assembly and Measurement Directions
a. Connect the micrograbber to the two wires attached to the banana post on
the output of the signal generator
i.
The unconnected version is shown on the left above
ii.
The connected version is shown on the right above
i. Connect red to red and black to black
b. Connect the BNC connector on the micrograbber to the BNC jack
corresponding to the input of Channel 1 on the scope
c. Turn on the scope
d. Adjust the voltage scale to 1V/box
e. Adjust the time scale so that 3 periods of the sine wave are shown
f. Adjust the vertical position on the scope so that only the top half of the
sine wave is visible
g. Adjust the horizontal position on the scope so that the signal moves over
by half a period
h. Return the vertical position offset on the scope to zero
i. Change the signal generator output to a triangle wave
j. Change the signal generator output to a square wave
k. Return the signal generator output to a sine wave
l. Check that your signal is displaying on the scope
m. Reverse the micrograbber connections
i.
Connect the black micrograbber to the wire from the red banana
jack and the red micrograbber to the wire from the black banana
jack
What happens to your signal when the leads are reversed? Explain this
result.
n. Return the micrograbbers to their correct connections on the wires from
the banana jack
o. Verify that the sine wave is displaying correctly on the scope
p. Open the computer window to the oscilloscope by opening a browser and
clocking on the link to TDS 3014B Home.
q. Right click inside the scope image. Choose Copy Image to copy the image
to the clipboard.
Paste the image into your solution template.
2. Demonstrate the that the scope probe does divide the input voltage
by 10
Inside the scope probe is a voltage divider; however, the scope senses when the probe is
connected to its input and compensates so that the signal displayed on the scope
corresponds to the true input voltage on the probe.
The object of this exercise is to show that the scope probe divides the incoming
voltage by 10, but the scope recognizes the probe and displays the correct input
voltage
Apparatus Assembly and Measurement Directions
a. Leave all of the connections that you made in the previous sections
b. Connect the scope probe inputs to the two wires in the banana plug on the
output of the signal generator
c. Connect the BNC on the scope probe to the jack on the input to channel 2
on the oscilloscope.
d. Adjust to scope so that it displays the inputs to both channel 1 and channel
2
Can you verify that the scope displays the input voltage correctly? If so,
how?
Demonstrate that the scope probe output really is 1/10 the input and
explain how you did it.
3. Explore the triggering mechanism for this scope
The object of this exercise is to determine the limits on the triggering voltage.
Apparatus Assembly and Measurement Directions
a. Leave all of the connections that you made in the previous sections
b. Lower the input voltage slowly and watch the display on the scope
What happens when the trigger voltage exceeds the amplitude of the input
voltage?
B. Breadboard Use:
Goals: Familiarize you with using a breadboard to make quick, reliable, temporary
electronic connections.
Materials: 1 signal generator; breadboard; light bulb; connection wires; 2 sets of
micrograbbers with BNC jacks; 1 BNC-to-banana connector with wires clamped in the
banana posts; 2 BNC cables
Below is a picture of the electrical connections on the back of the breadboard. There
should be a real one available in lab for you to examine.
The object of this exercise is to use the breadboard to connect a circuit that uses the
voltage output of the signal generator to make a light bulb light.
Apparatus Assembly and Measurement Directions
a.
b.
c.
d.
Change the amplitude of the signal generator output to 6V
Display it on the scope so the signal so its amplitude is 3 boxes
Change the frequency of the signal generator to 10 Hz
Display it on the scope so two periods are shown
What is the mathematical expression for this time dependent voltage?
e. Wire up a light bulb circuit on your breadboard as shown in the diagram
on the left above. Use jumper wires from your box to make the
connections. NB: do not attempt to stick the micrograbber leads directly
into the breadboard holes.
f. Connect the voltage output of the signal generator to the breadboard
i. connect the micrograbber as shown in the picture above
ii. connect a BNC cable between the micrograbber BNC jack and the
output jack on the signal generator
g. Verify that the light bulb is lit
h. Lower the frequency to 1 Hz
i. Verify that the light bulb is flashing
How many times does the bulb flash in one second? Explain your result.
j. Increase the frequency until you can no longer see the light bulb flash
How does this frequency compare with the normal video camera
acquisition rate of 30 frames/second?
C. Logger Pro Use:
Goals: Acquire, Display, and manipulate data using a computer
In modern research, almost all experiments are controlled by computers. Any data
generated is sent to the computer. Once the data is on the computer, it can be manipulated
using software. A complex experiment at CERN can require hundreds of people to write
code for years in order to get the data acquisition and analysis to work. Low energy
experiments usually have code written by a few undergraduate or graduate students.
Even biology is becoming increasingly computerized with the advent of complex
microscopes that are run through computer interfaces.
In this exercise you are not required to manipulate the data, but you are required to
display it in two different ways. In one case the voltage is shown on a linear scale, and in
the second case the same data is shown on a semi-log scale where the x-axis is linear and
the y axis is logarithmic. This sort of display is very important for data which scales as an
exponential or a power law.
Materials: 1 signal generator; 1 Vernier voltage probe to connect with the LabPro Mini;
1 computer running LoggerPro; 2 sets of micrograbbers with BNC jacks; 1 BNC-tobanana connector with wires clamped in the banana posts; 2 BNC cables.
The object of this exercise is to display the time dependent output of the signal
generator on a linear scale and a semi-log scale
Apparatus Assembly and Measurement Directions
a. Set the signal generator frequency to 100 Hz
b. Change the amplitude on the signal generator to 1V.
c. Connect the output of the signal generator to the micrograbbers on the
vernier voltage probe. (Note: connect red to red and black to black)
d. Open Logger Pro
e. If the menu bar is not visible, click the button in the right hand corner
f. Click on the Data Collection Icon to get the input parameters
g. Display the output in one window of LoggerPro where the amplitude of
the voltage occupies the full screen and four periods of the signal are
shown.
h. Insert a second graph below the first, and then rearrange the window so
that each graph occupies half of the vertical space. Group the x-axes of the
graphs together.
i. Display the same output in the second window but use on a semi-log scale
where the time axis is linear and the voltage axis is logarithmic
j. Copy that data to the clipboard by pressing the control key, the command
key, and shift 4 simultaneously. If you left click on the mouse, you can
then outline the part of the screen that is taken in the screenshot. This
allows you to paste the screen shot into a lab report.
Paste the screenshot here:
Are all data points shown in the second graph? Explain
D. Circuit Challenge
Goals: Practice creative problem-solving using circuits
In many homes or buildings, there are situations where you want to be able to control a
single device using either of two switches. A simple example is a staircase light, which
can be turned on or off by toggling either a switch at the top of the stairs or a switch at
the bottom. However, the design of such a switching circuit is non-trivial.
Materials: breadboard; light bulb; connection wires; DC power supply; banana plugs
with alligator clip attachments; switches.
The object of this exercise is to design and build a circuit that will allow you to turn
a light bulb on or off by toggling either of two switches.
Apparatus Assembly and Measurement Directions
a. Take the red and black leads from the DC power supply (pictured, above
left) and use them to supply power to your breadboard.
From here, you’re on your own; we won’t give you specific connection instructions
(unless you get really stuck and ask for help). You’ll be using switches. Here’s how these
switches work: there are three pins, or terminals, on the switch. When the slide switch is
in the left position (as in the figure above), the left pin and middle pin are connected to
each other (and the right pin isn’t connected to anything). When you slide the switch to
the right, the right pin and middle pin are connected, and the left one is not.
b. As an easy first step, try to make the light bulb light steadily using the DC
power supply and the breadboard.
c. Now redesign your circuit to include one switch so that you can control
the light with the switch.
d. Now come up with a design to use two switches so that toggling either
switch toggles the light. When you get this working, show it to an
instructor. If you get really stuck, ask for help. It’s a challenging problem,
but the goal is not ultimately to frustrate you.
e. Bonus: How would you extend this circuit to three switches? Talk to an
instructor if this question interests you, or if you are presenting this
challenge next week.
The End
Supplemental Information
1 . Electronic Connectors
a. BNC connectors
The voltage output of the signal generator is delivered to a BNC jack, such as the one
labeled b in the image on the left above. Similarly, the voltage input to the scope is a
BNC jack. The connector was named after its bayonet mount locking mechanism and its
two inventors, Paul Neill of Bell Labs (inventor of the N connector) and Amphenol
engineer Carl Concelman (inventor of the C connector). Thus BNC stand for Bayonet
Neill Concelman. BNC connectors are linked by BNC cables. BNC cables are coaxial
cables. http://en.wikipedia.org/wiki/Coaxial_cable They consist of a central conductor
that is surrounded by an insulator, which is in turn surrounded by a second outer
conducting layer that shares the same axis as the central conductor as shown below. The
voltage at the input or output of a BNC connection is the potential difference between the
inner conductor and the outer conductor, where the outer conductor is usually grounded.
In the image on the left above the foil has been bent back and the braid metal braid has
been separated to show that it consists of many very small flexible wires that are
collected into strands and then braided. A BNC jack is shown in the images in the center
of the figure above, and the BNC connectors at the ends of cables are shown on the right.
The connections between the cables and the connectors are illustrated in the schematic.
The connector is attached to the jack by pressing them together, rotating the connector
clockwise until the connector slips over the jack, then rotating clockwise by another
quarter turn to lock the connector in place. To undo a BNC connection, gently press in
and rotate ! turn counterclockwise, then pull back to separate the connectors.
b. Banana Jacks and Plugs
Banana Jack
Banana plugs
Banana plugs are shown in the image above. They are used to make rapid temporary
connections. The connection is made by simply inserting the plug into the jack. The
banana jakcs also have internal holes that are revealed by unscrewing the cylindrical
piece. Once the cylinder is unscrewed, a wire can be placed in the hole and the cylinder
can be screwed back until it is making firm contact with the wire. This provides an
electrical contact between the wire and both ends of the banana jack. Banana plugs are
often used in audio systems.
c. Alligator Clips
Alligator Clips
Alligator clips are shown in the image at left above. The rubber insulation is pulled back
from the black wire to show the complete alligator clip. Jumper wires with "alligator"
style spring clips at each end provide a safe and convenient method of quickly and
temporarily electrically joining components together. The connection is made by pressing
on the back of the clip to open the jaws, placing the jaws over the conductor to which the
connection is to be made, and then releasing the back of the clip to allow the jaws to
close. Note: to make a connection the alligator clips need to be connected directly to a
metallic surface, attaching the alligator clip to the rubber insulation on a wire will not
make a connection.
d. Micrograbbers
The images above show micrograbbers. The make temporary connections between wires,
just like alligator clips. They consist of a hook on a spring loaded plunger. When the
plunger is depressed, the hook is pushed out of the protective housing. Once the hook is
around the wire, the plunger is released. The spring pulls the hook back toward the
housing, trapping the wire between the hook and the housing that electrically connects
the hook to the wire.
f. Hybrids
Above is a BNC to banana connector, where the red banana post is connected to the
center of the BNC and the black banana post is connected to the outside of the BNC.
The image on the left above shows a standard scope probe. The end that attaches to the
oscilloscope has a BNC connector. There is a micrograbber on the end that connects to
the signal voltage, where the alligator clip on the same end is attached to the
corresponding reference ground. Thus, the BNC will measure the voltage difference
between the signal and the reference ground.
The image on the right shows a BNC jack attached to micrograbbers. The red connector
on the micrograbber is attached to the signal. The black connector is attached to the
ground reference. The center connection on the BNC jack is attached to the red
micrograbber and the outside connection on the BNC jack is attached to the black
micrograbber. This connector allows you to make connections between devices with a
BNC input (such as a scope) or a BNC output (such as a signal generator) and wires in a
circuit.
1. Signal Generator
Signal generators are used to create a tailored voltage as a function of time. They are
usually used to generate periodic signals. The signals can be sine waves, triangle waves,
or square waves. The generator allows you to control the amplitude and frequency of the
generated signal. Most signal generators also offer a DC offset, so the output is of the
form
V ( t ) = Vmax sin ( 2! ft ) + DC offset
where Vmax is the amplitude in volts, f is the frequency in Hz which is also cycles/sec, and
the DC offset is the time independent added voltage offset. It is also possible to generate
pulsed signals using the signal generator.
2. Oscilloscopes
Oscilloscopes are one of the most universally used pieces of test equipment in all of
physics. They present graphs of a voltage difference as a function of time. The vertical
axis that represents the voltage is typically divided into 8 units each of which is called a
division. The divisions are shown below as the grey lines that run across the screen in the
horizontal direction. The voltage sensitivity of the scope is expressed by the number of
volts represented by each unit, or the volts/division. The time axis is typically divided
into 10 divisions corresponding to a time given by the time/division. These divisions are
indicated by the gray vertical lines. A link to a You Tube video explaining oscilloscopes
is http://www.youtube.com/watch?v=rC8HBcsNm2g&feature=related.
A time dependent sinusoidal voltage with an amplitude of 1.5 volts and a period of
8 ms is given by 1.5 sin(2pi t /0.008 ) where t is the time in seconds is shown on the
virtual scope below in the upper left hand corner of the figure where the volts/div = 0.5 V
and the time/div= 1 ms. The same signal is shown in the upper right hand corner when
the volts/div=1 V and time/div= 1 ms. The signal in the lower left hand corner shows
the same when volts/div=0.5 V and time/div=2 ms.
The signal out is not uniquely determined by the voltage and time scales. The time at
which the signal starts also matters. The trigger level picks the signal voltage at which
the scope begins to display the voltage vs. time. The picture on the lower right has the
same settings as the upper left, except that the trigger level is changed to a higher voltage,
which corresponds to a later time. The images above are all made using
http://www.virtual-oscilloscope.com/simulation.html#. This is an excellent website that
offers an oscilloscope simulation where the controls are operated using the mouse. It
offers a great opportunity to play with an oscilloscope without owning one.
The image below shows an image of the virtual scope with two input channels, labeled I
and II. The knobs that control the voltage/div,time/div, and trigger are indicated along
with the horizontal position control and vertical position control that allow the image to
be moved around on the screen, but do not change the sensitivity or the trigger. The
trigger level control only works if the button above the trigger is set to normal. If the
button is set to automatic then the scope makes its own decision about when the trigger
and the trigger level knob has no effect. Below is the scope showing the sine wave used
in the examples above. The voltage inputs are the colored cables at the bottom left. The
connectors are called BNC connectors and in real life the cable is connected to the input
by pushing the cable end over the scope connector and turning the cable clockwise. On
the virtual scope, you just use the mouse to drag the cable to the input. If you turn the
power button on and connect the purple cable to the input of channel I, this is the image
that you will see. If you go to http://www.virtual-oscilloscope.com/simulation.html#.,
you can try out all of the controls shown above. You will notice that there actually many
more controls. We will not consider them here now, but you are more than welcome to
try them out. If you double click on a control, a pop-up window will provide an
explanation of what the control does. A tutorial that discusses oscilloscope controls in
general is available at
https://www.cs.tcd.ie/courses/baict/bac/jf/labs/scope/controls.html This is a part of a
larger and more general discussion of oscilloscopes http://oscilloscope-tutorials.com/
The scopes that you will be using in lab are actually nicer than the one shown on the
virtual oscilloscope. It actually has four input channels rather than two. The scope above
uses one set of three buttons to control the vertical scale, vertical position, and horizontal
position of channel I and a second set of three to control channel II. In order to avoid
having too many knobs, the scope you will use is designed so that there is only one set of
three knobs to control all four channels. To display the voltage that is input to a particular
channel, press the channel button corresponding to that signal (ch1,ch2,ch3,ch4). The
color of the button corresponds to the color of the signal on the display. To stop the
scope from displaying a channel, press the channel selection button corresponding to that
channel, and then hit the waveform off button. The knobs control Volts/div, horizontal
position, and vertical position. You choose the channel that is being controlled by
pressing one of the four buttons at left that are labeled ch1,ch2,ch3,and ch4. The color of
the voltage trace for each channel on the scope corresponds to the color of the button.
Once you have set the correct values for one channel you can choose a different channel
and set its values. Many functions are selected through menus. For example the choice to
trigger automatically or manually is made on the edge trigger menu. Similarly, the
coupling mode (AC,DC,ground) for the input of each channel is controlled by the menu
that comes up when a channel button is pressed and then the menu button below the
vertical scale knobs is pressed. The menus are controlled by the plain gray buttons at the
bottom and right edge of the screen. The scope has an autoset button in the far right
column. If the button is pressed, the scope decides all the settings for you. Sometimes it
makes good decisions, and sometimes not. If you are lost, it is worth trying the button.
The image below provides descriptions of the general functions of all of the controls on
the scope, many of which are not covered in the short discussion above. A full
description of all of the controls is available in the manuals posted on the course website.
The scope can be controlled remotely using a computer, and the information on the scope
can be transferred back to the computer using the protocols described below. They are
copied from the user manual, which is posted on the website.
3. Breadboards
Breadboards are used to quickly create model circuits without creating the mass of wires
that would be required to connect everything with alligator clips or micrograbbers. An
image of a breadboard is shown on the left in the image below. Breadboards consist of a
series of holes into which the leads from circuit elements can be inserted. Leads are the
wires that stick out of circuit elements and allow them to be connected. The holes are
connected on the back of the breadboard as shown in the diagram on the right below,
where the light blue regions indicate holes that are electrically connected. The holes
between the red and blue lines at the top and the bottom of the breadboard (called “rails”)
are connected horizontally. They are usually used to distribute the voltage from the power
supply to the circuit. The two central regions are electrically connected in columns.
They are used to connect circuit elements to each other. The photograph below shows
the back of the breadboard with part of the protective insulation peeled off. The metal
strips that connect the central columns and the edge rows are clearly visible. On some
breadboard models (such as the one in the photograph), there is a break in the rails in the
midpoint of the board. If you want the entire rail to be connected, you’ll need to manually
add a small jumper wire to bridge the gap.
4. LoggerPro
LoggerPro is software that controls data acquisition using a computer. It also allows the
acquired data to be mathematically manipulated using the computer. A screen shot of the
LoggerPro showing the data for this week is below. Screenshots are obtained by
simultaneously pressing Control, Command, Shift, and 4. If you left-click-and-drag on
the mouse, you can then outline the part of the screen that is taken in the screenshot.
To open LoggerPro, click on the graph icon in the bottom toolbar. If the data acquisition
menu does not show, click the button in the upper right hand corner. Use the Data
Acquisition icon to set the data acquisition parameters. The digitized data is displayed in
the left hand window in the form of a spreadsheet. The lower left hand corner shows the
current voltage input. To control the graph settings, right click with the mouse over the
graph. Left click on Graph Options. Choose the Axes options window, shown below.
The Y axis settings are set by the upper left box. In the scaling menu choose manual.
Then you can set the maximum and minimum values by typing them into the boxes
labeled Top and Bottom. You can make the axis logarithmic by checking the box next to
the word logarithmic. The x axis is set by the lower box.
5. Effects of Electricity on the Body
In the United States the voltage at a wall socket as a function of time is approximately
given by
. Unfortunately, the nerve impulses in the
human have a similar frequency, so they are strongly perturbed by the alternating current.
Below is a table of the current that would flow through a resistive object as a function of
the voltage across the object. The table is taken from a nice discussion of electrical shock
hazards that is presented at
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/shock.html#c3
The resistances shown correspond roughly to the resistance across a person with dry skin
(100,000 Ohms) or wet skin (1,000 Ohms).
Notice that the AC voltage coming from a wall outlet in the US is not too dangerous if
one makes a connection across it with dry skin, though this is certainly NOT a good idea.
A connection through wet skin is a serious hazard. The effect of the voltage also depends
its duration, with shorter exposure producing a smaller effect. This is why GFI plugs that
quickly cut-off the current make a significant contribution to electrical safety. Typically,
GFI outlets are required in wet areas such as kitchens, bathrooms, and outdoors. An
image of a typically GFI outlet is shown below, along with a wiring diagram. Notice that
the two vertical slots in the outlet have different lengths, as required for a polarized plug.
The longer slot corresponds to the neutral, and the shorter slot to the hot. In both the
image and the diagram black indicates hot, white indicates neutral, and green indicates
ground. These correspond to the colors of the insulation in household wiring, though the
ground is sometimes uninsulated. If too much current goes to ground without going
through the circuit, the GFI cuts off the voltage to all of the outlets connected to it. The
red reset button must be hit to restore voltage. Some outlets are GFI protected at the
breaker box without a visible test/reset switch at the outlet. The physics that underlie the
differential current sensing in the GFI outlet are not presented until Chapter 7 of Purcell.
The lab on chapter 7 will include GFI operation.
http://www.passandseymour.com/pdf/U013-U020.pdf
People who routinely work with high voltage often wear insulating shoes and keep one
hand in a pocket, so that even if they contact high voltage there will be no path to ground
through their chest. Connecting a finger across a few thousand volts will result in a burn,
but usually not a more serious injury though it is quite scary, as I can attest.