Download Lab 1

Experiment # 1
ENGN/PHYS 207—Fall 2014
Fundamentals of DC circuits and Measurement Techniques
Foreword
The goal of this lab is for you to become (re)acquainted with basic circuit construction and measurement principles and techniques. The techniques you will (re)master in this lab can be applied
more generally to just about any circuit you will ever build and measure! This lab begins with a
quick intro to some new equipment. Then the lab proceeds in 3 parts. The first 2 should be short
and sweet. For your open-ended design, you will have the opportunity to design an angle measurement system that might be used in robotics, prosthetics, biomechanics, or other angle measurement
systems. Away we go!...
The Multimeter
A multi-meter can be used to measure voltage, current, resistance, capacitance, etc. You will make
extensive use of it in this lab, so it’s important to know how to use it properly. Here are a few
helpful hints/reminders:
Figure 1: Meet your new friend in Circuit lab: the Fluke multi-meter.
1. Measuring Voltage: The voltmeter measures the potential across two points:
Vmeter = V+ − V−
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You must take care to properly place the probes of the voltmeter when making a measurement.
By convention, the reference probe (V− ) is the one colored black and labeled COM. Take care
that the other probe (V+ ), typically red in color, is plugged into the proper port. Finally,
make sure that the function dial is set to make a DC voltage measurement (the V with the
straight bars above it).
2. Measuring Resistance: Your meter can immediately tell you the value of a resistor—
or combination of resistors. You will find this feature to be incredibly useful (money back
guarantee!). Firstly, make sure your circuit is powered down before attempting to
make any resistance measurement (else you can damage the meter). Now, set the
dial to the Ω symbol. Connect the red and black probes across any resistor, or combination
of resistors. The polarity of the probes does not matter. The display reads out the resistance
value. Be sure to carefully note the units on the right-hand side of the meter. Voila, you are
done!
3. Measuring Current: To measure DC current, set the dial to the proper setting (A with
the straight bars above it). Make sure the red probe is plugged into the port at lower left
labeled “A”. The meter measures current running through it. Thus, you have to insert the
meter into the circuit.
The Potentiometer (aka “Pot”)
A potentiometer is just a variable resistor. Take a look at Fig. 2. You’ll see there are 3 terminals
with labels A, B, and W. Terminals A and B are essentially just two terminals of a normal resistor.
The magic happens at the wiper (W). As you turn the dial, the resistance between terminals A
and W (or B and W) changes. Pretty much anywhere you see a rotating knob changing the output
of electronics equipment (stereo, guitar pedal, etc.), rest assured it’s just a pot.
Figure 2: Potentiometer aka ”Pot”. Left: What you’ll find in lab. Center: what’s inside/theory of
operation. Right: circuit component schematic. The magic really happens at the wiper terminal ,
labeled W.
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KVL and KCL: Bumpin’ Stereo System:
Recall
P that KVL says that the sum of voltage gains and drops around any closed loop is equal to
0:
that the total current flowing into a node has to equal the total
k ∆Vk = 0. Also, KCL saysP
current flowing out of the node: k ik = 0.
Now, check out the sweet car stereo in Fig. 1. In order to properly build and design such a
system, one must properly apply KVL and KCL. The voltage source Vs and resistor R1 model the
stereo amplifier output. The volume is proportional to the magnitude of Vs . Resistors R2 and R3
model two speakers plugged into the system — just like in class. Amazing coincidence. Let’s build
this model system in order to understand, by analogy, the car stereo system.
R1
Vs
+
−
(a)
R2
R3
(b)
R1
Vs
+
−
R2
R3
R4
R5
(c)
Figure 3: (a) Ridiculously awesome car stereo system. Image credit: http://www.movingparts.
info/building-your-own-car-audio-system/. Let’s hope the playlist has been chosen wisely.
(b) Simple electrical model of car stereo amplifier plus two speakers. (c) Car stereo system with
four speakers.
1. Build the series circuit (Fig. 3(b)). (Don’t worry, we’ll plug in more speakers in a few
minutes!)Use nominal values of Vs = 5V, R1 ≈ 100 Ω, R2 ≈ 450 Ω, R3 ≈ 450 Ω.
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Be sure to record the actual values of components used. Complete Table 1. You have two
options for measuring current. One involved directly measuring the current with an ammeter.
In most practical situations this turns out to kind of a pain, and you often risk destroying the
circuits. The second is an indirect technique, but still perfectly valid — if you trust Ohm’s
Law. I = V /R, right? It’s much easier to measure V and then derive I...so do it this way!
Interpret your results. Do your results pass the sanity check? As a rule of thumb in Circuits:
differences between theory and experiment ≤ 5% are “acceptable.”
Table 1: Data Table for Series Circuit
Component
R1 =
R2 =
R3 =
V (pred.)
V (meas.)
% diff.
Sanity check
I (pred.)
I (meas.)
% diff.
Sanity check
Please answer the following questions:
(a) According to your results above, does KVL appear to be valid (to within some reasonable
experimental uncertainty)? Briefly justify.
(b) According to your results above, does KCL appear to be valid (to within some reasonable
experimental uncertainty)? Briefly justify.
(c) What would the voltages and currents change if the volume were doubled, i.e., you set
Vs = 10 V. Provide a brief intuitive explanation to justify your answer.
2. A two speaker system is nice, but even better is a 4 speaker system, such as the one modeled
in Fig 3(c). Your sound system now incorporates an additional pair of speakers, R4 and R5 .
These are a different model of speaker, so their resistance (impedance, actually...we’ll talk
about that in a few weeks) is different than the other pair already plugged in. Augment your
previous circuit using nominal values of Vs = 5V, R1 ≈ 100 Ω, R2 ≈ 450 Ω, R3 ≈ 450 Ω.
R4 ≈ 900 Ω. R5 ≈ 900 Ω.
Be sure to record the actual values of components used. Complete Table 2. Interpret your
results. Do they pass the sanity check?
Table 2: Data Table for Parallel Circuit
Component
R1 =
R2 =
R3 =
R4 =
R5 =
V (pred.)
V (meas.)
% diff.
Sanity check
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I (pred.)
I (meas.)
% diff.
Sanity check
(a) According to your results above, does KVL appear to be valid (to within some reasonable
experimental uncertainty)?
(b) How do your results for current through and voltage across R2 and R3 differ from the
previous 2-speaker system. Provide an intuitive explanation for the observed differences.
(c) Through which set of “speakers” does more current flow? Provide a brief intuitive
explanation explaining your observation. (It might be helpful to invoke any appropriate
analogies to fluid flow, gravity, etc.)
(d) If you were to replace the speakers with a single equivalent resistor, Req , what value
would you use? Justify/show your calculation.
(e) What is the value of the equivalent resistance taking into account all 5 resistors?
(f) Which set of speakers do you expect to dissipate more power — justify your answer wiht
a breif, intuitive explanation. Now compute how much power each “speaker” dissipates?
Does this match your prediction — if not, try to re-reason why this should be the case.
(g) How much power is dissipated in within the stereo itself — i.e., in R1 ?
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Feel the Heat: Power Dissipation in Resistors
You already know that energy is dissipated in resistors as heat. For some applications (toaster,
space heater) this is desirable. For many other applications it is not — you certainly don’t want
your laptop, stereo, or house to burn down (see Fig. 2. This next experiment is a quick one
that will cut to the heart of this matter and demonstrate a very important safety principle in
circuits design. READ ALL OF THESE DIRECTIONS BEFORE YOU PROCEDE TO
BUILD. YOU WILL NEED TO BE PREPARED TO QUICKLY CYCLE POWER
TO YOUR CIRCUIT IN ORDER TO AVOID FRYING YOUR EQUIPMENT!
(a)
(b)
Figure 4: (a) Fried resistors in a stereo system. The charred appearance is the tell-tale sign that
the amount of power these resistors were dissipating far exceeded their power rating. Also note:
fried resistors are not as tasty as fried chicken. (b) Home destroyed by electrical fire. A hot burner
is great (especially for hot chocolate in winter!), but can spell disaster elsewhere.
1. Turn the power supply OFF.
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2. Build a “light bulb circuit” — one battery and one resistor in series — connecting the +5V
power supply in series with a ≈ 10 Ω resistor. Do NOT power up your circuit just yet.
3. Compute how much power you expect to be dissipated in the resistor.
4. Position a couple of fingers near the resistor in your circuit. Your other hand and/or lab
partner should be at the ready to control the power switch.
5. Turn the power supply ON. Qualitatively monitor the temperature of the resistor. You should
feel it get toasty warm in less than a few seconds. Once you sense a noticeable amount of heat
coming from the resistor, turn the power OFF immediately. If and when you smell burning
plastic, power down immediately!
6. At your own discretion, you can touch/grip the resistor. WARNING: It is possible that you
get a small burn. It’s nothing that will send you to the health center or hospital, but it may
sting.
7. Now, replace the 10 Ω resistor with a 100 kΩ resistor. Compute how much power you expect
to be dissipated in the 100 kΩ resistor.
8. Turn the power ON. Wait for a few seconds. Do you feel the resistor getting hot as before?
You can wait for a few minutes, if you like, to see if the resistor ever becomes noticeably
warm. (Hint: you can wait all day and all night, and you probably will never sense any heat.)
9. Explain your results: why does the 10 Ω resistor become hot very quickly, while the 100 kΩ
never does.
10. IMPORTANT SAFETY ANNOUNCEMENT: Now for the punchline. Every resistor
has a power rating . For instance, you may try to buy some resistors on digikey.com and
see that they are rated for 1/8 W or 1/4 W (typical of the small resistors we use in lab).
Translation: this is the maximum amount of power the resistor can safely dissipate without
heating up...and possibly causing catastrophic failure in your electronic device. Heed this
warning—electrical fires are nastier than the lyrics of a 2LiveCrew song.
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Design Project: Goniometer
A goniometer measures angular displacement(gonia is Greek for angle). Goniometers find a great
many practical uses in biomechanics and prosthetics (Figs. 5(a) and 5(b)), robotics (Fig. 5(c)),
gaming systems, etc. Anywhere you might want to measure an angle, you might want a goniometer.
You think to yourself, “Sure would be cool if I built one of these useful devices.” Well, today is
your lucky day—you’ll design, build, and test one! Your system will essentially convert an angular
displacement θ into a corresponding voltage V (θ). Hint: For your post-experiment analysis you
need to know the theoretical relation for voltage vs. angle. Therefore, you need to calibrate your
pot by gathering data for resistance as a function of theta. Most pots are expected to be linear in
resistance vs angle.
Here are the design objectives/constraints:
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(a) Biomechanical study of knee (b) Knee joint angle measurement
joint. The voltage output from the made with protractor.
goniometer records data used to
derive angular displacement.
(c) Happy, dancing robots
Figure 5: Two example uses of goniometers. The electrical read-out can be used obtain information
about the angle of the knee joint during walking, or of robots that party hard.
• Must be able to measure 0 to ≈180 degrees
• The V vs. θ relation must be as linear as possible. (It is impossible to make it exactly linear.)
For instance you don’t want the majority of the voltage change to happen only over a small
range of angles - specifically if turning your goniometer between 0 and 10 degrees causes a
change of 4 V, that’s no fun because there’s the other 170 degrees has only 1 V of operating
range.
• Maximize the 5V dynamic range. For instance, having your voltage signal vary between
approximately 0–5 V as θ goes from 0 to 180 is very good; whereas, having say a 0.2 V change
is too small and difficult to tell any substantial difference in measurement.
• You may use one power supply or one battery
• You may use any other circuits components you find in the lab
Acquire a sufficient number of data points to demonstrate the operation of your goniometer
system.
You’ll summarize the design and the operation thereof in a short report (probably about 1–2
pages). Here’s what it should include:
• Circuit diagram of your design. Be sure to specify all component values!
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• Paragraph of your design rational. To help get you started, some questions to answer are:
what’s the “main idea”? How did you choose the circuit component values? Where in the
circuit do you measure (“read out”) the voltage?
• Clearly state an equation for the measured voltage as a function of the angle, V (θ)
• Plot V vs. θ data points acquired during your experiment.
• On the SAME graph, plot the function you derived for the theoretical (expected) V (θ).
• A few sentences or paragraph assessing how will your system worked, and any other “User
manual” type comments. What features were nice? What features stand improvement?
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