ECE201 Lab 1

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The MULTIMETER and the BASIC LAWS OF
ELECTRICITY EEE202 - LAB 1 2.5 of final grade
Projects and Notes prepared by Dr. Gabriele
Formicone
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OUTLINE

• Introductory notes on the use of the multimeter
• and the breadboard.
• 2) How to connect multimeter to measure voltages
• and currents.
• Circuit 1 Voltage Divider and KVL.
• Circuit 2 Current Divider and KCL.
• Circuit 3 Series and Parallel Combination with
• voltage source.
• Circuit 4 Series and Parallel Combination with
• current source.

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WARNING
It is possible to damage the equipment by
exceeding certain voltage or current levels at
the various terminals. Usually, in well designed
equipment this results in blowing a fuse or
triggering a circuit breaker. The idea is that
we would rather replace a 10 cent fuse than a
thousand dollar instrument. Please remember
that we would really rather not replace anything
at all! ALSO, handling of some of the part we
use in the lab may result in burns! Power
dissipation in electrical elements generates
heat. Some of the parts we use can get very HOT.
Make sure you turn off the power supply
whenever you need to touch the circuit elements,
as required to either make changes to the
circuits or for certain measurements. Be
careful in handling electrical material!
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Sensors and transducers produce voltages and
currents. Today, we will learn how the
multimeter can be used to measure dc voltages
and currents. You will also verify that both
Kirchhoffs laws and Ohms law hold true.
Components needed A Breadboards A DC variable
power supply A Digital Multimeter (voltmeter,
ampermeter, ohmmeter) Assorted resistors from 10
ohms to 1 Mega-ohms, 5, 1/4 watt red/black
pairs of cables for power supply red/black pairs
of multimeter probes Connection wires
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Stimulus-Response Experiments
Resistance is an example of a parameter which
describes how something responds to an applied
stimulus. A wide variety of engineering
experiments fall into the STIMULUS-RESPONSE
EXPERIMENT category.
How does the multimeter measure resistance?
The multimeter generates a small test current
which it runs through the resistance being
measured. This current is the stimulus. The
multimeter then measures the voltage drop across
the resistance. This is the response. Ohms
Law is used to compute the resistance value,
which is then displayed.
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How to connect the multimeter?
Voltage Measurement Connect the multimeter in
parallel with the element across which you want
to measure the voltage drop. Set the multimeter
to V / W measurement. Current Measurement
Connect the multimeter in series with the
element across which you want to measure the
current flowing through, in the same branch of
the circuit. Set the multimeter to A
measurement.
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Breadboard
The breadboard has two halves separated by an
indentation. The holes in the breadboard are
connected on the bottom of the breadboard. See
the figure below. The outer two rows with 2
holes are for the power supply. The inner rows
with 5 holes each correspond to a node.
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Example of using a breadboard for a series and
parallel connection
Power Supply
Series Connection
Parallel Connection
Power Supply
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How to measure the voltage drop in a resistor for
a series connection
Power Supply
Series Connection
Voltmeter
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How to measure the current through a resistor for
a series connection
Power Supply
Series Connection
Ammeter
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How to measure the current through a resistor for
a parallel connection
Ammeter
Parallel Connection
Power Supply
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How to measure the voltage drop in a resistor for
a parallel connection
Voltmeter
Parallel Connection
Power Supply
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Putting things in/out of board
Make sure that the pins or wires are straight and
that they line up well with the holes you intend
to use. Extract things slowly and carefully.
Slide something (a wire or screw driver blade )
under the item you are extracting and gently
raise it.
Check your understanding of breadboard use. Have
each member of your team connect a simple
circuit with two resistors together on a
breadboard and then use the lab instruments to
verify either voltage division for a series
connection or current division for a parallel
connection.
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Circuit 1 Voltage Divider and KVL
Connect two resistors and a voltage supply in
series in a circuit.
Use the multimeter to measure the voltages VR1
and VR2, and the current I flowing in your
circuit. Compute the power dissipated across the
two resistors. What is the total power dissipated
in the circuit? Compute the power generated by
the voltage source. Are your results consistent
with Kirchhoffs voltage law (KVL)? Choose
resistor and voltage source values similar but
NOT equal to what used in the template shown in
the next page.
Disconnect the source and measure the equivalent
resistance of the series connection. Are your
results consistent with Ohms law?
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Example of an actual measurement (use as
template)
In an experiment, we had VS 5 V, R1 4.7 kW,
R2 10 kW
With this circuit it was measured VR1 1.6 V,
VR2 3.4 V and I 0.35 mA.
By using KVL in the circuit drawn in the previous
slide, we have
I VS / (R1 R2) 5 V / 14.7 kW 0.34 mA
By using Omhs law, it is then found
VR1 VS R1 / (R1 R2) 5 V 4.7 kW / 14.7
kW 1.599 V
VR2 VS R2 / (R1 R2) 5 V 10 kW / 14.7 kW
3.401 V
The theoretical results obtained by using KVL
agree with the measured data.
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The power delivered by the voltage source is IVS
1.7mW.
The power dissipated in the resistor R1 is IVR1
0.544mW.
The power dissipated in the resistor R2 is IVR2
1.156mW.
The total power dissipated in the circuit is
Pdissipated (0.544 1.156)mW and this equals
the power supplied to the circuit Psupplied
1.7mW by the voltage source.
The voltage source sees an equivalent resistance
of Req VS / I 14.7 kW which is equal to the
total series resistance of R1 and R2.
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Circuit 2 Current Divider and KCL
Connect two resistors and a current supply in
parallel in a circuit.
Use the multimeter to measure the voltage V and
the currents I, I1 and I2 flowing in your
circuit. Compute the power dropped across the
two resistors and the power generated by the
current source. Are your results consistent with
Kirchhoffs current law (KCL)?
Choose resistor and current source values
similar but NOT equal to what used in the
template shown in the next page.
Disconnect the source and measure the equivalent
resistance of the parallel connection. Are your
results consistent with Ohms law?
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Example of an actual measurement (use as
template)
In an experiment, we had IS 2 mA, R1 4.7 kW,
R2 10 kW
With this circuit it was measured I1 1.36 mA,
I2 0.64 mA and V 6.37 V.
By using KCL in the circuit drawn in the previous
slide, we have
V IS R1 R2 / (R1 R2) 2 mA 3.2 kW 6.4 V
By using Omhs law, it is then found
I1 V / R1 6.4 V / 4.7 kW 1.36 mA
I2 V / R2 6.4 V / 10 kW 0.64 mA
The theoretical results obtained by using KCL
agree with the measured data.
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The power delivered by the current source is VIS
12.8mW.
The power dissipated in the resistor R1 is VI1
8.7mW.
The power dissipated in the resistor R2 is VI2
4.1mW.
The total power dissipated in the circuit is
Pdissipated (8.7 4.1)mW and this equals the
power supplied to the circuit Psupplied 12.8mW
by the voltage source.
The current source sees an equivalent resistance
of Req V / IS 3.2 kW which is equal to the
total parallel resistance of R1 and R2.
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Circuit 3 Series-Parallel Combination with
Voltage Source
Connect three resistors and the power supply to
form the circuit below.
Use the multimeter to measure the voltages VR1,
VR2 and VR3, and the currents I, I1 and I2
flowing in your circuit. Compute the power
dropped across the resistors and the power
generated by the power supply. Are your results
consistent with Kirchhoffs current and voltage
laws (KCL and KVL)?
Choose resistor and voltage source values similar
but NOT equal to what used in the template shown
in the next page.
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Example of an actual measurement (use as
template)
In an experiment, we had VS 6.32 V, R1 4.7
kW, R2 10 kW and R3 1 kW.
With this circuit it was measured VR1 VR2
4.81 V, VR3 1.51 V, I3 1.53mA, I2 0.49mA
and I1 1.04mA.
The equivalent resistance seen by the voltage
source is
Req R3 R1 R2 / (R1 R2) 1 kW 3.2 kW
4.2 kW
By using Omhs law, the current I from VS is
found as
I VS / Req 6.32 V / 4.2 kW 1.505 mA
Therefore, the voltage drop across R3 is VR3
R3 I 1.505 V.
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The voltage across the pair of resistors R1 and
R2 is found as
VR1 VR2 VS - VR3 (6.32 - 1.505) V 4.815 V
Using Ohms law, the currents through R1 and R2
are found
I1 VR1 / R1 4.815 V / 4.7 kW 1.024 mA
I2 VR2 / R2 4.815 V / 10 kW 0.481 mA
Within experimental error of less than 5, the
theoretical results obtained by using KCL and KVL
to solve the circuit agree with the measured data.
Also, notice that VS VR3 VR1 and I I1
I2, proving that both KVL and KCL are satisfied.
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The power delivered by the voltage source is IVS
9.67mW.
The power dissipated in the resistor R3 is IVR3
2.34mW.
The power dissipated in the resistor R2 is I2VR2
2.32mW.
The power dissipated in the resistor R1 is I1VR1
4.93mW.
The total power dissipated in the circuit is
Pdissipated (2.34 2.32 4.93)mW and this
equals the power supplied to the circuit
Psupplied 9.67mW by the voltage source.
The voltage source sees an equivalent resistance
of Req VS / I 4.2 kW which is equal to the
total resistance of R3 in series with the
parallel of R1 and R2.
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Circuit 4 Series-Parallel Combination with
Current Source
Connect three resistors and the power supply to
form the circuit below.
Use the multimeter to measure the voltages VR1,
VR2, VR3, and Vp, and the currents I, I1 and I2
flowing in your circuit. Compute the power
dropped across the resistors and the power
generated by the power supply. Are your results
consistent with Kirchhoffs current and voltage
laws (KCL and KVL)?
Choose resistor and current source values similar
but NOT equal to what used in the template shown
in the next page.
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Example of an actual measurement (use as
template)
In an experiment, we had IS 2 mA, R1 4.7 kW,
R2 10 kW and R3 1 kW.
With this circuit it was measured VR1 VR2
6.30 V, VR3 1.98 V, I IS 2mA, I2 0.64mA
and I1 1.36mA.
The equivalent resistance seen by the current
source is
Req R3 R1 R2 / (R1 R2) 1 kW 3.2 kW
4.2 kW
By using Omhs law, the voltage Vp from IS is
found as
Vp IS Req 2 mA 4.2 kW 8.4 V
Therefore, the voltage drop across R3 is VR3
R3 I R3 IS 2.0 V.
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The voltage across the pair of resistors R1 and
R2 is found as
VR1 VR2 Vp - VR3 (8.4 - 2) V 6.4 V
Using Ohms law, the currents through R1 and R2
are
I1 VR1 / R1 6.4 V / 4.7 kW 1.362 mA
I2 VR2 / R2 6.4 V / 10 kW 0.64 mA
Within experimental error of less than 4, the
theoretical results obtained by using KCL and KVL
to solve the circuit agree with the measured data.
Also, notice that Vp VR3 VR1 and I I1
I2, proving that both KVL and KCL are satisfied.
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The power delivered by the current source is IVp
16.8mW.
The power dissipated in the resistor R3 is IVR3
4.0mW.
The power dissipated in the resistor R2 is I2VR2
4.1mW.
The power dissipated in the resistor R1 is I1VR1
8.7mW.
The total power dissipated in the circuit is
Pdissipated (4.0 4.1 8.7)mW and this
equals the power supplied to the circuit
Psupplied 16.8mW by the voltage source.
The current source sees an equivalent resistance
of Req Vp / IS 4.2 kW which is equal to the
total resistance of R3 in series with the
parallel of R1 and R2.
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LAB REPORT

• Write a clearly legible Technical Report
• using the guidelines suggested in the next slide.
  
• Describe the measurements your team made
• on the four circuits used as templates.
• On another sheet of paper, attached to the
  report,
• Answer and explain the following 2 questions
• How do you connect a multimeter when measuring
• the voltage across a resistor?
• How do you connect a multimeter when measuring
• the current flowing through a resistor?

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Guidelines for writing a Technical Report

• Title Should be descriptive of the experiment
  undertaken. Also, list the names of the people
  participating (i.e. attending class on the day of
  the lab session) in the experiment. Absentees do
  not earn credit!
• Objective In one or two sentences, describe the
  reason or objective for planning and performing
  the experiment.
• Circuit Drawing/Schematic A schematic diagram
  of the circuit(s) used in the experiment must be
  included, with the appropriate labels and
  component values. You can use PSPICE or copy from
  the templates in these notes.
• Equipment It may be appropriate to record the
  serial number and model of the equipment used
  during the lab session. Very often, faulty
  results may be obtained because of a faulty meter
  or other equipment. Only the serial number can
  prove that that was the case.
• Procedure Briefly describe in chronological
  order what was measured and the instrument or
  other equipment used. Avoid long explanations,
  but make sure to be complete enough to allow
  another person to repeat the experiment for
  verification.
• Data Tables Measured and calculated/theoretical
  values should be reported or summarized in data
  tables, with their respective units.

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• 7) Calculations Usually, all experiments
  require a certain number of calculations before
  final results are obtained. Sample calculations
  that are completely identified should be
  included. It is not necessary to repeat the same
  equations many times in different sections of the
  report and show all the algebraic manipulations
  to get to the final answer. Just include the most
  important ones.
• Graphs Often, measured and calculated data are
  too long to be reported in a data table. In such
  cases, a graph plotting one quantity versus
  another, or measured versus theoretical values
  can be very desirable, especially in determining
  trends between data. Graphs require guidelines of
  their own, but all must include a title, axes
  labels, legends for the markers, and use linear
  or log scales depending on the relationship
  between quantities. Use best-fit lines to
  extract parameters, such as slopes and
  intercepts, using theoretical known relationships
  ONLY. Do not use polynomial fits with fractional
  exponents if there are not theoretically derived
  equations suggesting such a polynomial behavior!
  The key point to remember is that a graph should
  be as clear as possible for the viewer to
  understand the trend or relationship between the
  quantities plotted against each other.
• Results and Conclusions This is the most
  important part of the experiment. The entire
  experiment is to be considered a failure if the
  student does not understand the results and
  decide how to express the conclusion. The
  conclusion should be as brief as possible, yet
  still summarize what the outcome of the project
  or experiment has been. Saying that all
  measurements were good and everything agrees with
  KCL and KVL is NOT a kind of a good conclusion!