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SCHOOL OF ENGINEERING AND APPLIED SCIENCE
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 2110: CIRCUIT THEORY LABORATORY
Experiment #2:
Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
EQUIPMENT
Lab Equipment
(1) DC Power Supply
(1) Function Generator
(1) Digital Multimeter (DMM)
(1) Digital Oscilloscope
(1) BNC T-Connector
(2) BNC Cables
Equipment Description
Agilent E3631A Triple Output DC Power Supply
Agilent 33522A Function/Arbitrary Waveform Generator
Agilent 34460A (DMM)
Agilent DSO1024A Digital Oscilloscope
One input to two output BNC connector
BNC to BNC Cable
Table 1 – Equipment List
COMPONENTS
Type
Resistor
Resistor
Resistor
Capacitor
LED
Value
2kΩ
3kΩ
— Ω
0.1µF
Red
Symbol Name
R1
R2
RLIMIT
C1
LED1
Multisim Part
Basic/Resistor
Basic/Resistor
Basic/Resistor
Basic/Capacitor
Diodes/LED/LED_red
Description
——Polyester Film, 104K
Red LED
Table 2 – Component List
OBJECTIVES

Review fundamental theory behind AC signals
Use the Agilent function generator to generate AC voltage waveforms
Use the Agilent digital oscilloscope to measure AC voltage waveforms
Compare and explain the results obtained from the DMM and the digital oscilloscope for
measurements of different periodic waveforms
Use the Agilent digital oscilloscope to measure the voltage drop across components in an AC
circuit
Use the Agilent digital oscilloscope to measure the phase shift between the AC voltage
waveforms
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
INTRODUCTION
In addition to Direct Current (DC) signals, Alternating Current (AC) signals are an important part of circuit
theory and design. The circuits encountered in the first lab dealt with DC signals only. The DC power
supply is used to produce the DC signals, and the DMM is used to measure the signals. DC voltages are
constant over time.
In this lab, circuits will have AC signals. AC voltages vary with time and are generally periodic, meaning
they repeat at a specific time interval. Figure 1 shows four common AC signals: the sine, square, and
triangle waveforms. We will use two new pieces of equipment to produce and measure these signals in
our circuits. The first piece of equipment, the function generator, will be used to produce AC signals.
The second piece of equipment, the oscilloscope, will be used to measure and visualize the AC signals
in the circuit.
Figure 1 – Common AC Waveforms
Figure 2 – Sine Wave Showing Vpp, Vpk, Vrms
AC Signal Characteristics

The voltage of an AC, time-varying signal can be described in various ways:
o
o
o
Peak-to-Peak Voltage: = −
Peak Voltage (Amplitude): = 2
Root-Mean-Squared Voltage:
=

Sine Wave:

Square Wave: =

Triangle Wave: =

√2

√3

The frequency (f) of a waveform is equal to the number of repetitions per unit time (unit is Hz).

The period (T) of a signal is the duration of one cycle of a repeating event (unit is seconds).
1
1
=

=

o

NOTE: When frequency is given in radians/second, ω is used ( = 2 ).
The phase shift (ᶲ) of one signal with respect to another is the ratio of the offset between them to
their period (assuming both signals have the same period) (unit is degrees or radians).

ℎ ℎ (ϕ) =
360° =
2 [ ]

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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Introduction to the Function Generator
A function generator is an electronic instrument that produces a voltage that varies with time. This
function or waveform that is output from the function generator can be used as the input signal to different
circuits in a variety of applications.
Figure 3 – Agilent 33522A Function Generator
The Basics:

A function generator produces time-varying voltage signals that can be used in AC circuits.
The function generators used in this lab have two independent output channels.
The time-varying signal can be configured using the following parameters:
o Waveform: basic types of waveforms are sine, square, and triangle
o Frequency: number of repetitions per unit time (Hz)
o Amplitude: voltage magnitude of the signal (may be defined by Vpk or Vpp)
o Offset: DC offset of the signal (in voltage) with respect to ground
o Phase Shift: offset of the signal (in time) with respect to an unshifted signal
Introduction to the Oscilloscope
An oscilloscope is an electronic measurement instrument that unintrusively monitors input signals and
then graphically displays these signals in a simple voltage versus time format .
Figure 4 – Agilent DSO1024A Digital Oscilloscope
The Basics:

An oscilloscope measures and displays voltage as it changes with time.
It consists of a display screen with an X & Y-axis and control panel as shown in Figure 1.
The X-axis of the display represents time.
The Y-axis represents voltage.
The control panel has individual controls for four separate input channels.
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Setting the Scales for the Oscilloscope’s X & Y-Axes
Let us begin by first getting acquainted with the most important controls/knobs on the oscilloscope. Near
the top of the oscilloscope are the “Horizontal” controls shown in Figure 5. The larger knob sets the
horizontal scaling in seconds/division. This control sets the X-axis scaling of the displayed waveform.
One horizontal “division” is the Δ-time between each vertical grid line. If you want to view faster
waveforms (higher frequency signals), then you will set the horizontal scaling to a smaller sec/div value.
If you want to view slower waveforms (slower frequency signals), then you typically set the horizontal
scaling to a higher sec/div setting. The smaller knob in the Horizontal section sets the horizontal position
of the waveform. In other words, this control moves the horizontal placement of the waveform left and
right.
Figure 5 – Oscilloscope Horizontal (X-axis) Controls
The controls/knobs closer the bottom of the oscilloscope (refer to Figure 6) in the Vertical section (just
above the input BNCs) set the vertical scaling of the oscilloscope. There are four pairs of vertical scaling
controls, one for each input channel. The larger knob for each input channel in the Vertical section sets
the vertical scaling factor in Volts/division. This is the Y-axis graphical scaling of your waveforms. One
vertical “division” is the ΔV between each horizontal grid line. If you want to view relatively large signals
(high peak-to-peak voltages), then you would typically set the Volts/div setting to a relatively high value. If
viewing small input signal levels, then you would set the Volts/div setting to a relatively low value. The
larger knob can be pressed in for finer tuning of the Volts/div scale, allowing for more precise
measurement. The smaller controls/knobs for each channel in the Vertical section are the position/offset
controls. You use this knob to move the waveform up and down on the screen.
Figure 6 – Oscilloscope Vertical (Y-axis) Controls
Key Points:

The value of the X-axis scale is set using the sec/div knob under the Horizontal section.
The value of the Y-axis scale is set using the Volts/div knob under the Vertical section.
The smaller knobs in each section can be used to move the signal around the display.
Pressing the 1, 2, 3, or 4 button will turn on/off the display of individual channels.
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Triggering
Another very important oscilloscope setup variable is the trigger level control/knob shown in Figure 7.
This control knob is located near the right-hand side of your scope’s front panel, just below the section
labeled Trigger. Triggering is probably the least understood aspect of an oscilloscope, but it is one the
most important capabilities of a scope that you should understand. Think of oscilloscope “triggering” as
“synchronized picture taking.” When an oscilloscope is capturing and displaying a repetitive input signal,
it may be taking thousands of pictures per second of the input signal. In order to view these waveforms
(or pictures), the picture taking must be synchronized to “something.” That “something” is a unique point
in time on the input signal.
Figure 7 – Oscilloscope Trigger Level Control
Key Points:

The oscilloscope’s trigger function synchronizes the horizontal sweep to produce a stable
waveform on the display.
Oscilloscopes display a moving wave. When the wave runs out of space on the display screen, it
continues, starting at the far left. When that section of the wave is not aligned with the section of
the wave already on the display screen, it is untriggered, and either appears to be moving as
shown in Figure 8.
Adjusting the trigger knob defines where on the wave to trigger (on the way up or the way down),
as illustrated below, until the wave becomes stable (see Figure 9).
It is common to simply push the Trigger knob on the oscilloscope to trigger at 50% of the signal,
but understanding how to manually trigger is an important skill to learn.
Trigger level set above waveform
Figure 8 – Untriggered Signal
Figure 9 – Properly Triggered Signal
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Multiple Channels
Figure 10 – Display Showing Two Channels

The oscilloscope in Figure 4 has four separate input channels, allowing four different signals to
be displayed on the screen simultaneously (Figure 10 shows an example with two signals).
The vertical position dials allow each signal to be shifted up and down independently of one
another. This can be done to separate overlapping signals and to position the signals to make it
easier to estimate their amplitudes. In Figure 10, the green signal (channel-2) has been shifted
slightly lower than channel-1.
Waveform Math

The outer conductor of the coaxial BNC cables used by oscilloscopes is always grounded.
Therefore, oscilloscopes cannot directly measure the voltage across a component unless one
end of the component is grounded. Instead, oscilloscope measurements are limited to nodevoltage measurements (node voltages are measured with respect to ground by definition).
For an oscilloscope to measure the voltage across a component, the node voltage waveforms on
each side of the component must be acquired and then subtracted.
The oscilloscopes in lab can perform the following math functions:
o Add, Subtract, Multiply, and FFT (Fast Fourier Transform)
Waveform Math is turned on and the Math menu is accessed by pressing the Math button located
between the buttons for channel-1 and channel-2.
Figure 11 shows the subtraction of two signals. The resulting signal is in the middle.
Figure 11 – Subtraction of Two Signals
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
PRELAB
Part I – Using an Oscilloscope
1. Review the preceding Introduction material on AC signals, the function generator, and the
oscilloscope prior to lab.
2. Review the specifications for the Agilent DSO1024A digital oscilloscope available in the data
sheet section of the ECE 2110 website.
3. Answer the following questions about the Agilent DSO1024A from the data sheet:
• What is the maximum peak input voltage?
• What is the input impedance?
• What is the maximum frequency for the oscilloscope?
• What is the sample rate?
4. Download and Review the “Using an Oscilloscope”  PowerPoint presentation from the
tutorials section of the ECE 2110 website. This will briefly explain how to use the oscilloscope.
Part II – Reading the Oscilloscope
Figure P.1 – Overlapping Sine Waves (Channel-1 – Blue, Channel-2 – Red)
The above graph shows two overlapping sine waves. The oscilloscope is set as follows:
• sec/div knob is set to 150µs
• Volts/div knob on channel-1 is set to 50V
• Volts/div knob on channel-2 is set to 20mV
1. Complete the following table based on Figure P.1:
Value
Vpp
Vpk
Vrms
Period (s)
Frequency (Hz)
Phase Difference (º)
Blue Waveform (CH1)
Red Waveform (CH2)
Table P.1 – Prelab Data
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Part III – General Oscilloscope Questions
Answer the following questions given the display in Figure 10 (12 divisions on the x-axis and 8 divisions
on the y-axis) and the sec/div and Volts/div knobs in Figure 5 and Figure 6.
1. What does the x-axis of the oscilloscope display represent? What does the y-axis represent?
2. What Math functions can the digital oscilloscope perform?
3. If the frequency of an AC signal were too high to be seen on the oscilloscope, would you increase
or decrease the sec/div?
4. If the frequency were too low, would you increase or decrease the sec/div?
5. If the largest sec/div you can set is 10s, what is the lowest frequency AC signal you can measure
with the digital oscilloscope (to see at least one full period)?
6. If the smallest sec/div you can set is 10µs, what is the highest frequency AC signal you can
measure with the digital oscilloscope (to see at least one full period)?
7. If the largest Volts/div you can set is 50V, what is the highest voltage you can measure in terms
of Vpp, Vpk, and Vrms with the oscilloscope?
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
LAB
Part I – Basic Oscilloscope Measurements
1. Configure the Agilent DSO1024A digital oscilloscope.
***The following steps should be done prior to each use of the oscilloscope.***
a. Turn on the oscilloscope.
b. Press the Default Setup button on the front panel.
Note: Default Setup will put the oscilloscope into a factory-preset configuration. Not only will
this set the scope’s X and Y scaling factors to preset values, but it will also turn off any
special modes of operation that one of your fellow students may have used. When beginning
new measurements with the scope, it is always good practice to begin with a default setup.
c. Press the channel-1 button to bring up its menu and change Probe from 10X to 1X.
d. Select Display and change Intensity to 100% by turning the selection knob.
e. Push Down in the menu twice to view the grid brightness setting. Set this to 100%.
f. On the same menu, change Screen from Normal to Inverted. This will invert the colors on
the display, providing a white background that is better for printing after images are saved.
2. Connect the BNC end of the BNC to mini-grabber test leads to channel-1.
3. Connect the mini-grabber ends of the test leads to the Probe Comp terminals of the oscilloscope
shown below in Figure 1.1. Attach the red lead to the left terminal (test signal output) and the
black lead to the right terminal (ground).
Figure 1.1 – Oscilloscope Probe Comp Terminal
4.
5.
6.
7.
Push the Trigger knob to set the triggering to 50%.
Adjust the vertical Volts/div knob until the entire signal is visible.
Adjust the horizontal sec/div knob until a square wave is seen on the display (see Figure 1).
Set up the desired measurements to be displayed.
a. Press the Measure button to bring up the measurement menu.
b. Ensure that CH1 is selected as the input channel to measure.
c. Select Voltage, scroll to Vmax, and push the select knob to add that measurement.
d. Select Voltage, scroll to Vmin, and push the select knob to add that measurement.
e. Select Time, scroll to freq, and select it to display the frequency of the signal.
8. Save a screenshot of the signal and measurements on the oscilloscope display.
***This is how you must capture images of the display to include in lab reports.***
b. Press the Save/Recall button to show the menu for saving a screenshot of the display.
c. Select Waveform and scroll down to select PNG to save as an image file
d. Select External to save to the USB drive.
e. Select New File and type a name or use the default name, and Save the file to your USB.
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Part II – Generating Sine, Square, and Triangle Waveforms
1. Configure the Agilent 33522A function generator for use with the oscilloscope.
***The following steps should be done prior to each use of the function generator.***
a. Turn on the function generator.
b. Select channel-1 by pressing the “1” above Channel Setup on the right-hand side.
c. Select Output Load and change it from 50Ω to High-Z.
i. Press the “Set To High Z” key below the display.
Note: The oscilloscope that we use has a high internal impedance/resistance (1MΩ), and it is
seen as a load to the function generator. Therefore, we must “tell” the function generator its load
impedance/resistance correctly in order to get the correct output signal from the function
generator. Keep in mind that this step is always necessary when connecting between the
function generator and the digital oscilloscope.
2. Select the desired Waveform.
a. Press the Waveform key.
b. Ensure that the Sine waveform is selected.
3. Configure the necessary Parameters:
a. Press the Parameters key.
b. Frequency: 4kHz
i. Select Frequency using the buttons below the display.
ii. Type in a “4” using the keypad on the right side.
iii. Select kHz from the unit options on the display.
c. Amplitude: 5.0Vpp
i. Select Amplitude using the buttons below the display.
ii. Type in a “5” using the keypad on the right side.
iii. Select Vpp from the unit options on the display.
d. Ensure the DC Offset is 0V.
e. Ensure the Phase is 0º.
4. Connect the BNC T-connector to the channel-1 output of the function generator.
5. Connect a BNC cable from the T-connector to the CH1 input of the digital oscilloscope.
6. Set up the DMM.
a. Configure the DMM to measure RMS AC Voltage.
b. Set the DMM for Auto Scale.
c. Connect a BNC to mini-grabber test lead to the open end of the BNC T-connector.
d. Connect a banana to alligator test lead to the DMM.
e. Connect the mini-grabber and alligator leads together so that the DMM will measure the AC
Voltage of the function generator once you turn it on.
7. Turn on channel-1 on the function generator.
a. Select channel-1 using the Channel Setup button on the right-hand side.
b. Press Output On in the lower left to enable the signal.
8. Configure the digital oscilloscope.
a. Select CH1 by pressing the “1” button on the oscilloscope. It will light up when pressed.
b. Adjust the vertical Volts/div knob until the entire signal is visible.
c. Adjust the horizontal sec/div knob until the desired waveform is seen on the display.
d. Add Measurements to the display as you did in Part I for Vpp, Vrms, and frequency.
9. Save a screenshot of the signal and measurements on the oscilloscope display.
10. Record the AC Voltage value from the DMM. Remember this is Vrms not Vpk or Vpp.
11. Change the signal to a Square waveform and repeat steps 8-10.
12. Change the signal to a Triangle waveform and repeat steps 8-10.
Note: The Triangle waveform is under the More section of the function generator’s Waveform
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Part III – Waveform Math
R1
A
B
V1
2.5 Vpk
4kHz

R2
C
Figure 3.1 – AC Circuit #1
1. Assemble the circuit illustrated in Figure 3.1. R1 = 2kΩ, R2 = 3kΩ
2. Complete the digital oscilloscope setup as described above for CH2.
3. Connect one set of the BNC to mini-grabber test leads to measure the voltage of Node A with
respect to Node C (GND) on CH1 of the oscilloscope.
4. Connect another BNC to mini-grabber test lead to measure the voltage of Node B with respect to
Node C (GND) on CH2 of the oscilloscope.
1. Note: The voltage across R1 cannot be measured directly because the outer conductor of the
oscilloscope input channel is always shorted to ground. Therefore, we must use node voltages to
determine the voltage across R1.
5. Use the Volts/div knobs and the vertical position knobs to position CH1 above CH2, so that the
channels do not overlap.
6. Save a screenshot showing CH1 above CH2. Label CH1, V1 and CH2, VR2 in your lab report.
7. Press the Math button and subtract CH2 from CH1 (A – B).
8. Press the buttons for CH1 and CH2 twice to turn them off, leaving only the Math waveform
visible on the oscilloscope display.
9. Save a screenshot of just the Math waveform, A – B. Label this signal as VR1 in your lab report.
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Part IV – Phase Shift
R1
A
B
V1
2.5 Vpk
4kHz

C1
C
Figure 4.1 – AC Circuit #2
1. Assemble the circuit illustrated in Figure 4.1. R1 = 2kΩ, C1 = 0.1µF
2. Connect one set of the BNC to mini-grabber test leads to measure the voltage of Node A with
respect to Node C (GND) on CH1 of the oscilloscope.
3. Connect another BNC to mini-grabber test lead to measure the voltage of Node B with respect to
Node C (GND) on CH2 of the oscilloscope.
4. Use the Volts/div knobs and the vertical position knobs to position CH1 above CH2, so that the
channels do not overlap.
5. Save a screenshot showing CH1 above CH2. Label CH1, VR1 and CH2, VC1 in your lab report.
6. Press the vertical position knobs for CH1 and CH2 to center both signals on the y-axis. This
should position them so that they do overlap.
7. Save a screenshot showing CH1 and CH2 overlapping. Label this figure appropriately in your
lab report.
8. Measure the phase shift between VC1 and VR1.
a. Press the Measure button, then Time.
b. Scroll down the list and select Phas A→B.
c. Save a screenshot showing the phase shift.
9. Use the Cursors feature to more accurately measure the phase shift between VC1 and VR1.
a. Press the Cursors button twice to turn on cursors.
b. Use the selection knob to move the first cursor to the peak of your first signal.
c. Press CurA once to deselect Cursor A, and press CurB once to select it.
d. Move Cursor B to the peak of the second signal.
e. Save a screenshot showing the two signals, cursors, and time shift ∆X.
Note: At this point, the display will show ∆X, which is the time difference between the peaks.
We can use this information together with the frequency of the signal to calculate the phase
shift. The frequency tells us the period of the signal, and ∆X is the percentage of the period
that the two signals differ. The same percentage of 360° is the phase shift we are looking for.
Part V – AC Circuit Analysis Using Multisim
1. The GTA will describe how to simulate an AC circuit in Multisim and obtain time-varying voltage
differences across circuit elements.
2. There is also a Tutorial on the ECE 2110 website that explains how to perform an AC simulation
in Multisim. In particular, look at pages: 20-23.
3. Perform simulations for the AC Circuits #1 and #2 from Figure 3.1 and Figure 4.1 in the lab, and
include your results in the lab report.
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
Part VI – Blinking LED Circuit
RLIMIT
LED1
Red
Vs
5V
Figure 6.1 – LED DC Circuit
1. Design a circuit based on Figure 6.1 to illuminate the LED.
a. Use the DC power supply set to 5V as Vs.
b. Refer to the data sheet for the AND130CR Red LED to determine its typical forward
voltage. This will be equal to the voltage drop across the LED.
c. Calculate the necessary value for RLIMIT to ensure that the current through the circuit is
no more than 30mA.
Note: RLIMIT is being used to limit the current allowed to flow through the LED. Limiting
resistors are always necessary when working with LEDs to ensure that we do not burn
them out. Too much voltage or current can easily ruin an LED.
d. Round up to the closest available resistor for RLIMIT. Using a resistance higher than the
calculated RLIMIT ensures that the current is less than or equal to 30mA.
2. Build the circuit from Figure 6.1 on the breadboard using your calculated RLIMIT and observe the
behavior of the LED.
3. Replace Vs with a square wave produced by the function generator as shown in Figure 6.2.
a. Waveform: Square
b. Frequency: 1Hz
c. Amplitude: 5.0VPP
d. Offset: 2.5V
RLIMIT
Vs
2.5 Vpk
1 Hz

Square Wave
Offset = 2.5V
LED1
Red
Figure 6.2 – Blinking LED Circuit
4. Turn on the function generator after the circuit is assembled. The LED should blink on and off
once per second (1Hz).
5. Increase the frequency to find the frequency at which the LED appears to stop blinking. The
human eye will eventually be unable to perceive the flickering.
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Experiment #2: Introduction to Lab Equipment: Function Generator, Oscilloscope, and Multisim
POST-LAB ANALYSIS
1. Is it possible to directly measure the AC voltage across a resistor using the digital oscilloscope?
Explain why or why not.
2. What steps are necessary to determine the AC voltage across a resistor using an oscilloscope?
3. What is the standard AC voltage (Vrms) and frequency (Hz) used in most wall outlets in the USA?
Why is the frequency important for regular incandescent light bulbs?
REFERENCES

Agilent Technologies. “DSO1000 Educator’s Training Resources: Lab Guide and Tutorial for
Undergraduate Electrical Engineering and Physics Students.”
http://cp.literature.agilent.com/litweb/pdf/54136-97000.pdf.
ECE 2110: Circuit Theory
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SCHOOL OF ENGINEERING AND APPLIED SCIENCE
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 2110: CIRCUIT THEORY LABORATORY
Experiment #3:
Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
EQUIPMENT
Lab Equipment
(1) DC Power Supply
(1) Digital Multimeter (DMM)
Equipment Description
Agilent E3631A Triple Output DC Power Supply
Agilent 34460A (DMM)
Table 1 – Equipment List
COMPONENTS
Type
Resistor
Resistor
Resistor
Value
750Ω
1.5kΩ
3kΩ
Symbol Name
R1
R2
R3
Multisim Part
Basic/Resistor
Basic/Resistor
Basic/Resistor
Description
——-
Table 2 – Component List
OBJECTIVES

To understand DC series, parallel, and series-parallel combination circuit
To connect electronic devices on a breadboard
To calculate DC voltage across resistors in a DC series circuit
To measure DC voltage across resistors in a DC series circuit using a DMM
To calculate DC current through resistors in a DC parallel circuit
To measure DC current through resistors in a DC parallel circuit using a DMM
To calculate DC current through resistors in a DC series-parallel combination circuit
To measure DC current through resistors in a DC series-parallel combination circuit using a DMM
To calculate the total power dissipated by each resistor in a DC series, parallel, and seriesparallel combination circuit
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Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
INTRODUCTION
Ohm’s Law
This lab will focus on Ohm’s Law, one of the most fundamental laws governing electrical circuits. It
states that voltage is equal to current multiplied by resistance. For a given current, an increase in
resistance will result in a greater voltage. Alternately, for a given voltage, an increase in resistance will
produce a decrease in current. As this is a first order linear equation, plotting current versus voltage for a
fixed resistance will yield a straight line. The slope of this line is the conductance, and conductance is the
reciprocal of resistance.
=
Equation 1 – Ohm’s Law
Resistors in Series
An important concept to understand in any electrical circuit is the difference between series and parallel.
A series path is defined by a single loop in which all components are arranged one after the other. The
current is the same at all points in the loop and may be found by dividing the total voltage by the total
resistance. The voltage drops across any resistor may then be found by multiplying that current by the
individual resistor value. The equivalent resistance of resistors in series is simply the sum of the
resistances (see Equation 2).
= 1 + 2 + ⋯ +
Equation 2 – Series Equivalent Resistance
R1
R2
R3
Vs
=
Vs
Req
R1 + R2 + R3
Figure 1 – Example Series Equivalent Resistance
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Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
Resistors in Parallel
Resistors in parallel share two common nodes. The voltage is the same across all resistors and will
be equal to the applied source voltage. The total supplied current may be found by dividing the voltage
source by the equivalent parallel resistance. It may also be found by summing the currents in all of the
branches. The current through any resistor branch may be found by dividing the source voltage by the
resistor value. The current is the same at all points in the loop and may be found by dividing the total
voltage by the total resistance. The voltage drops across any resistor may then be found by multiplying
that current by the individual resistor value. The equivalent resistance of resistors in parallel can be found
by summing the reciprocal of all parallel resistors, then finding the reciprocal of that (see Equation 3).
=
1
1
1
+ + ⋯ +
1
1
2 Equivalent Resistance
Equation 3 – Example Parallel
Vs
R2
R1
=
Vs
R eq
R1 || R2
Figure 2 – Parallel Equivalent Resistance
Resistors in Series-Parallel Combination
Most circuits will use some combination of components connected in series and in parallel. Simple
series-parallel circuits may be viewed as interconnected series and parallel branches. Each of these
branches may be analyzed through basic series and parallel techniques such as the application of
voltage divider and current divider rules. It is important to identify the most simple series and parallel
ECE 2110: Circuit Theory
3
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
Measuring Voltage Across a Resistor
A Digital Multimeter (DMM) is a multi-use measurement device that we use in the lab to measure
resistance, voltage, and current. The DMM was used in Experiment #1 to measure the resistance of a
resistor. In this lab, you will use the DMM to measure voltage.
Voltage is measured across an electrical device. Figure 3 shows a series circuit with two resistors.
After building the circuit on a breadboard, if we wish to measure the voltage across resistor R2, we would
do the following using the DMM:
1. Set the DMM to measure Voltage by pressing “V” on the DMM front panel.
2. Set the DMM to the range we expect the voltage to be (uV, mV, V, etc.).
Note: In general, the Auto-Range setting can be used for voltage and resistance. This setting will
automatically adjust the DMM to the proper range. However, there is no auto-range functionality
available for measuring current.
3. Attach the positive lead coming from the DMM to the positive side of R2 and the negative lead to
the negative side of R2.
a. In this way, the DMM is measuring ACROSS R2.
4. Record the value of the voltage measured on the DMM.
These are the four conceptual steps to measuring voltage. During lab, the exact procedure will be
demonstrated and explained. It is expected that you be familiar with these conceptual steps prior to the
lab. If you do not understand these steps, be certain to discuss this with the GTA prior to lab.
XMM1
R1
V
R2
Vs
Figure 3 – DMM Measuring Voltage Across R2
ECE 2110: Circuit Theory
4
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
Measuring Current Through a Resistor
Current is measured through an electrical device. It must be measured in an entirely different way than
voltage is measured. Figure 4 shows a circuit with two resistors. After building the circuit on a
breadboard, if we wish to measure the current through resistor R1, we need to BREAK the circuit where
we wish to measure the current. We would do the following using the DMM:
1. Set the DMM to measure Current by pressing “A” (Amperes) on the DMM front panel.
2. Set the meter to the range we expect the current to be: (uA, mA, etc.).
Note: We cannot use the auto-range setting on the DMM to measure current. The range must
be set manually. Pressing the auto-range button will set the DMM to measure current through
the 10A (white) input.
3. Break the circuit where we wish to measure the current.
a. In Figure 4, we would disconnect/break the circuit between resistors R1 and R2.
b. The DMM is then inserted in series between R1 and R2, allowing the current in the circuit
to actually flow through the DMM, enabling it to measure the current.
Note: Because the DMM is in series, we know the current will be the same as it will be
through R1 and R2.
4. Record the value of the current measured on the DMM.
a. This is the value of the current at all points through the entire series circuit.
XMM1
R1
A
R2
Vs
Figure 4 – DMM in Series Measuring Current Through Circuit
ECE 2110: Circuit Theory
5
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
PRELAB
Part I – DC Series Circuit
R1
750Ω
Vs
9V
R2
1.5kΩ
Figure P.1 – DC Series Circuit
Figure P.1 shows a DC circuit that has two resistors R1 and R2 connected in series with a DC Voltage
Source.
1. Analyze the circuit in Figure P.1.
2. Calculate the nominal (expected) values for the DC voltage, DC current, and DC power
consumption of R1 and R2 (be sure to clearly show all calculations).
3. Record your results in Table 1.1 below.
Part II – DC Parallel Circuit
Vs
9V
R2
1.5kΩ
R3
3kΩ
Figure P.2 – DC Parallel Circuit
Figure P.2 shows a DC circuit that has two resistors R2 and R3 connected in parallel with a DC Voltage
Source.
1. Analyze the circuit in Figure P.2.
2. Calculate the nominal (expected) values for the DC voltage, DC current, and power
consumption of R2 and R3 (be sure to clearly show all calculations).
3. Record your results in Table 2.1 below.
ECE 2110: Circuit Theory
6
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
Part III – DC Series-Parallel Combination Circuit
R1
750Ω
Vs
9V
R2
1.5kΩ
R3
3kΩ
Figure P.3 – DC Series-Parallel Combination Circuit
Many circuits have a combination of series and parallel resistors. Figure P.3 shows a DC circuit that has
two resistors R2 and R3 connected in parallel with one another. R2 and R3 together are connected in
series with resistor R1 and the DC Voltage Source.
1. Analyze the circuit in Figure P.3.
2. Calculate the nominal (expected) values for the DC voltage, DC current, and power
consumption of R1, R2, and R3 (be sure to clearly show all calculations).
3. Record your results in Table 3.1 below.
Part IV – How to Measure Voltage and Current
During the lab, you will build the three circuits you have analyzed in the prelab. You will then measure
the voltage across and the current through each resistor to compare these experimental results to your
calculated values. In order to make the measurements, it is essential that you know how to connect the
measurement equipment to the circuits you will build.
1. Review the Introduction to today’s lab and ensure you are familiar with the proper way to
measure voltage across and current through resistors.
Note: It is imperative that you understand that you must change the way your DMM is connected
to the circuit before switching between measuring voltage and measuring current. If you attempt
to measure current across a resistor, you will pull a dangerous amount of current and likely blow
the fuse on the DMM. Setting a current limit on the power supply will at least help to prevent
blowing the fuse on the DMM.
2. Question: What is the overload protection (maximum current allowed) for the mA current input on
the Keithley 175 DMM? Use the specification sheet for the Keithley 175 to determine the answer.
3. Question: Can the auto-range feature of the DMM be used when measuring current? Explain.
4. Redraw the circuit in Figure P.3 showing how you would attach the DMM to measure the current
through R2.
ECE 2110: Circuit Theory
7
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
LAB
Part I – DC Series Circuit Measurements
R1
750Ω
Vs
9V
R2
1.5kΩ
Figure 1.1 – DC Series Circuit
1. Build the DC Series Circuit in Figure 1.1 on your breadboard.
2. Set the +25V Output on the Agilent DC power supply to 9V using the following procedure:
a. Do not connect the power supply to your circuit until it is properly configured.
b. Turn on the power supply.
c. Press Output On/Off once to turn on the output.
d. Press the +25V button to alter the output from the +25V terminals, and change the
display value to 9V.
e. Press Output On/Off again to turn the output OFF while you connect the circuit.
f. Connect the banana end of the banana to alligator test leads to the +25V terminals and
the alligator ends to the circuit.
g. If your circuit configuration is correct, press Output On/Off to apply 9V to your circuit.
3. Measure the voltage across R1 and R2 with the DMM and record it in Table 1.1 using the
following procedure:
a. Turn on the Keithley 175 DMM.
b. Ensure the DMM is set to measure DC values and not AC.
c. Enable auto-range on the DMM to get the maximum number of significant figures
available during measurements.
d. Connect the DMM to your circuit.
Note: Make sure the DMM is connected in parallel with the resistor across which you are
going to measure the voltage!
e. Record the voltage in Table 1.1.
4. Measure the current through R1 and R2 with the DMM and record it in Table 1.1.
b. Press the A button to switch to current mode.
c. Break the circuit at the point you wish to measure current.
d. Connect the DMM in series with your circuit as discussed in the Prelab.
e. Select the appropriate current range by pressing one of the range buttons.
Note: As explained in the prelab, there is no auto-range feature for current measurement.
You must set it to the correct range based on the expected value from your calculations.
f. Record the current in Table 1.1.
5. Calculate the power consumption of R1 and R2 from the measured DC voltage and DC current
of R1 and R2 and record it in Table 1.1.
ECE 2110: Circuit Theory
8
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
6. Multisim Simulation:
a. Simulate the circuit from Figure 1.1 in Multisim.
b. Find the simulated voltage, current, and power consumption for each resistor by
performing a DC Operating Point Analysis.
Note: The GTA will give a brief overview of how to setup the circuit in Multisim and
perform the necessary analysis. You should be familiar with Multisim from the
introductory labs, so this overview will be short and focused on the simulation itself. The
analysis can be found under Simulate → Analyses → DC Operating Point.
c. Record your simulated results in Table 1.1.
7. Calculate the percent error between your calculated and measured results and record it in
Table 1.1. Compare and discuss your results in the analysis section of the lab report.
Resistor
Electrical Quantity
R1
R2
Calculated
Voltage (V)
Measured
Simulated
Calculated
Current (mA)
Measured
Simulated
Calculated
Power (mW)
Measured
Simulated
Voltage
Percent Error (%)
Current
Power
Table 1.1 – DC Series Circuit Data
ECE 2110: Circuit Theory
9
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
Part II – DC Parallel Circuit Measurements
Vs
9V
R2
1.5kΩ
R3
3kΩ
Figure 2.1 – DC Parallel Circuit
1.
2.
3.
4.
5.
Ensure the +25V Output on the Agilent DC power supply is still set to 9V.
Measure the voltage across R2 and R3 with the DMM and record it in Table 2.1.
Measure the current through R2 and R3 with the DMM and record it in Table 2.1.
Calculate the power consumption of R2 and R3 from the measured DC voltage and DC current
of R2 and R3 and record it in Table 2.1.
6. Multisim Simulation:
a. Build the circuit from Figure 2.1 in Multisim.
b. Find the simulated voltage, current, and power consumption for each resistor by
performing a DC Operating Point Analysis.
c. Record your simulated results in Table 2.1.
7. Calculate the percent error between your calculated and measured results and record it in
Table 2.1. Compare and discuss your results in the analysis section of the lab report.
Resistor
Electrical Quantities
R2
R3
Calculated
Voltage (V)
Measured
Simulated
Calculated
Current (mA)
Measured
Simulated
Calculated
Power (mW)
Measured
Simulated
Voltage
Percent Error (%)
Current
Power
Table 2.1 – DC Parallel Circuit Data
ECE 2110: Circuit Theory
10
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
Part III – DC Series-Parallel Combination Circuit
R1
750Ω
Vs
9V
R2
1.5kΩ
R3
3kΩ
Figure 3.1 – DC Series-Parallel Combination Circuit
1.
2.
3.
4.
5.
Ensure the +25V Output on the Agilent DC power supply is still set to 9V.
Measure the voltage across R1, R2, and R3 with the DMM and record it in Table 3.1.
Measure the current through R1, R2, and R3 with the DMM and record it in Table 3.1.
Calculate the power consumption of R1, R2, and R3 from the measured DC voltage and DC
current and record it in Table 3.1.
6. Multisim Simulation:
a. Build the circuit from Figure 3.1 in Multisim.
b. Find the simulated voltage, current, and power consumption for each resistor by
performing a DC Operating Point Analysis.
c. Record your simulated results in Table 3.1.
7. Calculate the percent error between your calculated and measured results and record it in
Table 3.1. Compare and discuss your results in the analysis section of the lab report.
Electrical Quantities
Resistor
R1
R2
R3
Calculated
Voltage (V)
Measured
Simulated
Calculated
Current (mA)
Measured
Simulated
Calculated
Power (mW)
Measured
Simulated
Voltage
Percent Error (%)
Current
Power
Table 3.1 – DC Series-Parallel Combination Circuit Data
ECE 2110: Circuit Theory
11
SEAS
Experiment #3: Ohm’s Law, Series, Parallel, and Series-Parallel Circuits
POST-LAB ANALYSIS
1. Analyze and interpret the data collected in each of the Data Tables throughout the lab. Explain
any interesting pieces of data, outliers, or important considerations.
2. Describe the relationship between the total voltage and current in the whole circuit and the
voltage across and current through every resistor in each part of the lab.
a. Part I – DC Series Circuit
i. Is the total voltage across R1 and R2 equal to the 9V source? Why or why not?
ii. Are the currents flowing through R1 and R2 equal? Why or why not?
b. Part II – DC Parallel Circuit
i. What is the total current through the whole circuit? What are the currents
through R2 and R3? What is the relationship between the total current and the
currents flowing through each resistor?
ii. What are voltages across R2 and R3? Are they equal? Why or why not?
c. Part III – DC Series-Parallel Combination Circuit
i. What is the mathematical relationship of the currents through R1, R2, and R3?
ii. What is the mathematical relationship of the voltages across R1, R2, and R3?
3. Compare the calculated (nominal) results with the measured results in Table 1.1, Table 2.1,
and Table 3.1. Be sure to complete the percent error section for each table and analyze the
error. Explain any possible reasons for the error.
ECE 2110: Circuit Theory
12
Experiment #1:
Introduction to Lab Equipment: Power Supply, DMM, Breadboard, and Multisim
Student’s Name
ECE 2110-31: Circuit Theory
GTA: GTA’s Name
September 8, 2014 (Date you submit report)
1. Introduction
The purpose of this experiment was…
2. Background Information
PE =
NV − MV
NV
*100
Equation 2.1 – Percentage Error (PE) Equation, Nominal Value (NV), Measured Value (MV)
3. Methods and Materials
Equipment
Agilent E3631A Triple Output DC Power Supply
Keithley Multimeter – Model 175

Components (Quantity and
Type)
(1) 9.1 Ω Resistor
(1) 200 Ω Resistor
(1) 3.9 kΩ Resistor

Table 3.1 – Equipment and Components List
OR
Equipment:
• (1) Agilent E3631A Triple Output DC Power Supply
• (1) Keithley Model 175 Digital Multimeter (DMM)
• (1) Pair of Banana to alligator test leads
Components:
• (1) 200Ω Resistor
• (1) 3.9KΩ Resistor
• (1) 4.7MΩ Resistor
Experiment #1
Student’s Name
Page 2 of 4
4. Experimental Procedures
4.1 Prelab
4.2 Resistance Measurement
4.4 Resistance Determination Using Voltage and Current

5. Measurements and Results
6. Analysis and Discussion
7. Conclusion
Experiment #1
Student’s Name
Page 3 of 4
8. References

GWU SEAS ECE Department. “Experiment #1: Introduction to Lab Equipment: Power Supply,
DMM, Breadboard, and Multisim.” The ECE 2110 Course Website, Fall 2014.
http://www.seas.gwu.edu/~ece11/fall14/labs/labs/ECE_2110_Experiment_1.pdf

Thomas, Roland E., Albert J. Rosa, and Gregory J. Toussaint. The Analysis and Design of Linear
Circuits. 7th ed. Hoboken, NJ: Wiley, 2012.
9. Appendices
Experiment #1
Student’s Name
Page 4 of 4

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