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Page
1

of
10

ECE 11

Exper
iment #2

The George Washington University

School of Engineering and Applied Science

Department of Electrical
and Computer Engineering

ECE 11

-

LAB

Experiment #
2

Ohm's Law,
DC Series

Circuits and DC

Parallel

Circuits

Equipment:

Lab Equipment

Equipment Descri
ption

(1

Set
) Digital Multimeter (DMM)

Keithley Model 175
Digital Multimeter

(DMM)

(2

Pairs

Banana to mini
-

(1 Set) DC Power Supply

Agilent E3631A

Triple Output DC Power Supply

Table
A

Equipment List

Components
:

Kit Part #

Spice Part
Name

Part Description

Symbol Name

(used in schematics
throughout this lab manual)

Resistor
R1

R

750
Ω Resistor

o
1

o

ㄮ1

h
Ω Resistor

o
2

o

P

h
Ω Resistor

o
P

Table
B

Components List

Objectives
:

To understand
DC series, parallel
,

and series
-
parallel combination circuit.

To c
onnect electronic
devices
on
a
board.

To
calculate
DC

voltage
across resistors in a
DC series circuit
.

To measure DC voltage across resist
ors 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 comb
ination circuit.

To measure DC current through resistors in a DC series
-
parallel combination circuit using
a DMM.

To c
alculate the total power dissipated by each resistor in a DC series
,
parallel
, and
series
-
parallel
combination

circuit
.

Page
2

of
10

ECE 11

Exper
iment #2

Prelab

Part

1:

Figure 1

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Figure 2

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Problem #1

DC
Series Circuit

Figure #1
shows a
DC circuit that has two resistors R1 and R2 connected in series with a
DC
Voltage Source (The
label

for the voltage source is VS1)
.

Circuit Analysis using Ohm's Law

Analyze the circuit in Figure #1.

Use VS1=9Vdc.

Find the nominal (expected) values for
the DC voltage, DC current and Power Consumption of R1 and R2. Show your steps of
calculations clearly and write down your calcu
lated results in Table 1

(see the lab section
below for table 1)
.

Problem #2

-

DC
Parallel Circuit

Figure 2 shows a
DC circuit that has tw
o resistors R2 and R3

connected in
parallel

with a
DC
Voltage Source (The
label

for the voltage source is VS2).

Cir
cuit Analysis using Ohm's Law

Analyze the circuit in Figure #2.

Use VS2=9Vdc.

Find the nominal (expected) values for
the DC Voltage, DC Current and Power Consumption of R2 and R3. Show your steps of
calculations clearly and write down your calculated
results in Table 2

(see the lab section
below for table 2).

A

B

C

Page
3

of
10

ECE 11

Exper
iment #2

Problem

#3

DC Series
-

Parallel Combination Circuit

Figure 3

DC Series

Parallel Combination Circuit

Many circuits have a combination of series and parallel resistors.
Figure #3

sho
ws a DC circuit
that has tw
o resistors R2 and R3

connected in
parallel
with one another. R2 and R3 together are
connected in series with
resistor R1
and
with
the

DC Voltage Source (The
label

for the voltage
source is VS3).

Circuit Analysis using Ohm's Law

Analyze the circuit in Figure #3.

Use VS3=9Vdc.

Find the nominal (expected) values for
the DC Voltage, DC Current and Power Consumption of R1, R2 and R3. Show your
steps of calculations clearly and write down your calculated results in Table 3

(see t
he lab
section below for table 3).

Page
4

of
10

ECE 11

Exper
iment #2

Prelab

Part
2
:

During the

lab, you will build the three circuits you have analyzed
in part 1 of the prelab
. You will
then measure the voltage
across
and
the
current

through each resistor

to

see if lines up with your

calculated values.
In order to make the measurements it is essential that you know how to hook
up the measurement equipment to the circuits you will build.

In this part of the prelab, instructions on how to measure voltage and current are discussed at

a
high level. You will be expected to know this and will potentially be quizzed on this knowledge at
the beginning of lab.

A.

HOW TO MEAURE VOLTAGE ACROSS A RESISTOR:

A Digital Multimeter (DMM) is a
multi
-
use
measurement device we use in the lab to measur
e
resistance, voltage, and current. You used a DMM in lab 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. In prelab part 1, figure #1 shows two resisto
rs.
After building the circuit on a breadboard, if we wish to measure the voltage across resistor R1,
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 meter to the
range

we expect the
voltage

to be: (
u
V, mV
, etc.)

3)

Attach
the two leads/wires coming from the DMM to points A and B in figure #1

a.

In this way, the DMM is “
ACROSS
” R1

4)

Read the value of the voltage measured on the DMM

These are the four conceptual steps to measuring voltage. Du
ring lab, the exact procedure will
be demonstrated and explained. But it is expected that be familiar with these conceptual steps
prior to the lab. Questions like, “how does one measure the voltage across R2” may appear on a
prelab quiz. If you do not u
nderstand these steps, be certain to discuss this with your GTA prior
to lab.

Page
5

of
10

ECE 11

Exper
iment #2

B.

HOW TO MEAURE CURRENT THROUGH A RESISTOR:

Current is measured “through” an electrical device

and is done very different compared to
measuring voltage
. In prelab part 1, figu
re #1 shows 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 meas
ure
Current

by pressing “A” on the DMM front panel

(A is for AMPS)

2)

Set the meter to the
range

we expect the current to be: (uA, mA, etc.)

3)

Break the circuit where we wish to measure the current

a.

In figure #1, we would disconnect
/break

the circuit at point B

b.

Then we can place the two leads/wires of the DMM at the breakpoint as shown in
figure #3

i.

The DMM is now in series with the circuit. Because it is series, we know
the current will be the same as it will be through R1 and R2.

c.

Now the current will travel f
rom the circuit, THROUGH the DMM, and back to the
circuit

4)

Read the value of the current traveling through the DMM

a.

This is the value of the current in the series circuit

Figure 4

DC Series Circuit

w/DMM inserted

Prelab
Problem #4
: Dr
aw the circuit in figure #3. Show how you would attach the DMM to
measure the voltage across R3.

Current

A

B

C

B

䑍a

(“A”

䵯摥)

Page
6

of
10

ECE 11

Exper
iment #2

L
ab
:

Part
1

DC
Series Circuit

Measurements

1)

Construct the circuit of
Fi
gure #1

DC
S
eries Circuit

using your

2)

Use the
Agilent E3631A Triple
Output DC Power Supply

as VS
1 and set the voltage to
9
Vdc

using the following procedure:

a.

Do not yet connect the
Agilent

b.

P
ress the
Power Button

to turn it on.

c.

Press
Output On/Off

once to turn on the output.

d.

Press the
+25V

butt
on to tell the power supply that we want to alter the output
from the
25
V terminals.

e.

Use the
dial

to
change

the display value to
9 volts
.

Note: You can safely ignore
the value of the right most digit for this experiment.

f.

Once you have reached 9
V, Press
Out
put On/Off

once to turn the output OFF
while you hook up the circuit.

g.

Plug the ‘banana’ end of your cables into the
25
V terminals of your power supply
.

h.

Attaching the mini
-

i.

C
heck whether your circuit configuration is correct or
not!

j.

If your circuit configuration is correct, p
ress the
Output On/Off

to apply
9 Volts to

3)

Use the DMM (Keithley Model175) to measure the

DC voltage

across

R1 and R2

and
record it in table 1 using the following procedure:

a.

Switch on the Kei
thley 175 DMM.

b.

Be sure the AC
-
DC button is unselected (DC is implied by absence of AC label).

c.

Measure DC voltage by pressing the V button.

d.

Select the appropriate voltage range by pressing one of the range buttons or
enable “Auto Range” in order to get the
maximum number of significant digits
during

measurement

e.

Connect the DMM into your circuit.
Make sure the DMM is connected

in
parallel with the resistor across which you are going to measure the
voltage!

f.

Record the voltage (value and corresponding units) fr
om the LCD screen

4)

Use the DMM (Keithley Model175) to measure the DC current through R1 and R2 and
record it in table 1.

a.

Measure DC current by pressing the A button.

b.

Select the appropriate current range by pressing one of the range buttons

c.

There is no auto
-
range for current, you must set it to the range from your
calculations

d.

Break your circuit at the point you wish to measure current.
Connect the DMM
in series with your circuit as discussed in the prelab.

e.

Record the current (value and corresponding units
) from the LCD screen

5)

Calculate
the
p
ower c
onsumption of R
1

and R
2

from the measure
d DC
v
oltage and DC
c
urrent of R
1

and R
2

and record it in table 1.

Page
7

of
10

ECE 11

Exper
iment #2

Circuit
Simulations in PSPICE

Simulate the circuit in Figure 1 using PSPICE (GTA will show you how to

configure it in
PSPICE step by step). Find the simulated voltage, current and power consumption of
each resistor using the voltage, current and power probes respectively in PSPICE.

Record

your
simulated
results in Table 1
.

Data Analysis

Analyze and interp
ret Table 1. Include the answers to the following questions when you
are analyzing data:

What is the total voltage across R1 and R2? Is it equal to the DC source
voltage VS1? If it is (not), why?

What are the currents flowing through R1 and R2? Are they e
qual? If they
are (not), why?

Resistors

Electrical Quantities
(units)

R1

R2

Calculated Nominal
Results

Voltage

(V)

Current

(mA)

Power

(mW)

Measured

Results

Voltage

(V)

Current

(mA)

Power

(mW)

Simulated

Results

in PSPICE

Voltage

(V)

Current

(mA)

Power

(mW)

Table
1

DC
Series C
ircuit Data Table

Page
8

of
10

ECE 11

Exper
iment #2

Part
2

-

DC
Parallel Circui
t Measurements

Construct the circuit of Figure #
2

Use the
Agilent E3631A Triple Output
DC Power Supply

as VS
2

and set the voltage
to
9
Vdc.

Use the procedure you followed in part 1 to set VS2.

Use the DMM (Keithley Model175) to measure the DC Voltage and DC Current of R
2

and R
3
.

Find the measured Power Consumption of R
2

and R
3

from the me
asured DC
Voltage and DC Current of R
2

and R
3
.

Record
your measured results in Table 2
.

Circuit
Simulations in PSPICE

Simulate the circuit in Figure 2

using PSPICE
.
Find the simulated voltage, current and
power consumption of each resistor using the v
oltage, current and power probes
respectively in PSPICE. Record your simulated
results in Table 2
.

D
ata Analysis

Analyze and interpret Table 2. Include the answers to the following questions when you
are analyzing data:

What is the total current through t
he 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?

What are voltages across R2 and R3? Are they equal? If they are (not), why?

Resistors

Electrical Quantities(units)

R2

R3

Calculated Nominal
Results

Voltage

(V)

Current (mA)

Power (mW)

Measured Results

Voltage

(V)

Current (mA)

Power (mW)

Simulated Results
in PSPICE

Voltage

(V)

Current (mA)

Power (mW)

Table
2

DC
Parallel
Circuit Data Table

Page
9

of
10

ECE 11

Exper
iment #2

Part
3

DC Series

-

Parallel
Combin
ation

Circuit

Circuit Measurements

Construct the circuit of Figure #
3

Use the
Agilent E3631A Triple Output DC Power Supply

as VS
3

and
set the voltage
to
9
Vdc.

Use the DMM (Keithley Model175) to measure the DC Voltage and DC Current of
R1,
R2 and R3.

Find the measured Power Consumption of
R1,
R2 and R3 from the measured DC
Voltage and DC Current of
R1,
R2 and R3.

results in Table
3
.

Circuit
Simulations in PSPICE

Simulate the circuit in Figure
3

using PSPICE. Find the simulated voltage, current and
power consumption of each resistor using the voltage, current and power probes
respectively in PSPICE. Record your
simulated results in Table
3
.

Data Analysis

Analyze and interpret Table 3. Include the answers to the following questions when you
are analyzing data:

What is the current through
R1
? What are the currents through R2 and R3?
What is the
mathematic
relation
ship
among the currents through R1, R2 and
R3?

What are voltages across
R1,
R2 and R3?
What is the mathematic
relationship among the
across

R1, R2 and R3?

Resistors

Electrical Quantities(units)

R
1

R
2

R3

Calculated
No
minal Results

Voltage

(V)

Current (mA)

Power (mW)

Measured
Results

Voltage

(V)

Current (mA)

Power (mW)

Simulated
Results in
PSPICE

Voltage

(V)

Current (mA)

Power (mW)

Table
3

DC
Series

Parallel

Combination

C
irc
uit Data
Table

Page
10

of
10

ECE 11

Exper
iment #2

Further Analysis:

Describe

the relationship between the total currents flowing through the whole circuit and

the currents through each resistor in Figure 1, 2 and 3
,
respectively
.

Describe

the

relationship between the
source

(power supply)

voltage

and the
v
oltage
drop
across
each resistor in Figure 1, 2 and 3, respectively.

Compare the nominal results with the measured results
and the simulated results
of
Table
1,

Table

2

and Table 3
.

Explain any differences between the nominal and
measured
/simulated

results of
those Data Tables.