Lab 1: Basic Circuitry - CS Course Webpages - Texas A&M University

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TEXAS A&M UNIVERSITY


ENGR 111B:

Foundations of Electrical &
C
omputer Engineering




Lab
2
:
KVL / KCL and DC Motor Modeling




Team
Members
: _________________________






_________________________



Section

Number: _____
_____

Team Number: _____
_____




This Lab is
due

in two weeks
.





Written By:

Lorne Liechty



Alex Johnson


Guided By:

Dr. Jeff McDougall



Dr. Narasimha Reddy



Dr. Hank Walker


Concepts built upon the original Tekbot labs designed by Oregon State University



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ritten by Texas A&M University



1

Lab
2
:
KVL / KCL
and DC Motor Modeling

Time Limit:
2

week
s


OVERVIEW


Congratulations on beginning your fun and exciting career as a student of
Electrical
or

Computer Engineering. In order to begin even the most basic laboratory
exercise it is necessary to review a few fu
ndamental principles. This lab will cover the
following material.

-

Schematics

-

Resistor Combinations: Series and Parallel

-

Protoboards

-

KVL, KCL, and Ohm’s Law

-

Measuring Voltage, Current, and Resistance


BACKROUND



To assist students in completing the exerci
ses required by this lab, the following
background information has been provided. It is recommended that
each student read all
of the following information as a beneficial review of the topics required.


SCHEMATICS, PARALLEL and SERIES CONNECTIONS


Schema
tics are a fundamental tool utilized in most electronic projects.
Schematics describe the components used in a circuit and their relative electronic
orientation. Schematics can be highly complex and show every connection all the way
down to individual tr
ansistors

on a microprocessor
, or they can be general and show
simply
the
basic connections of circuit elements. Below is a schematic that, by the end of
this lab, you will be expected to analyze:



Figure B1:

A simple circuit schematic






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2

Again, here

is the same schematic with labels on each element for your reference:



Figure B2:

Labeling of simple circuit


In this schematic each voltage source and resistor represents an individual circuit
element. Other circuit elements that will be introduced th
roughout the course of this
semester
include

capacitors, inductors, and transistors
. These circuit elements

are
connected in four different
ways
:

series, parallel, Y, and delta
.
In this
lab,

we will only
deal with series and parallel element combinations
.
To avoid confusion it may be
important to mention that the ground symbol attached to the bottom of the circuit is not
an actual circuit element, but is rather a reference.
The placement of the ground
identifies the node designated to have zero volts and o
ther voltages in the circuit are
stated relative to the ‘ground’ node.


One method to identify whether or not circuit elements are connected in series or
parallel is to first identify the nodes of the circuit. In the circuit we have been
viewing,

there ar
e
three

nodes
.
Two of the nodes in this circuit are labeled in the schematic above.
The third node has been identified as the ground node, which runs along as the bottom
connection line on the schematic.
A node is the interconnection of two or more circu
it
elements.



A parallel connection is made when two, or more, two
-
terminal circuit
elements are connected between two nodes.



A series connection is made when two circuit elements are connected by only
one node AND no other elements are connected at the

joining node.




Figure B3:

Connections and Nodes

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3

Here you can see that this circuit contains one set of resistors in parallel (R2 and R3), and
that the voltage source (V1) is in series with the resistor (R1).


Often, the theoretical representation of a

circuit can be reduced through resistor
combinations. This is particularly useful for reducing a network to a voltage source and a
single resistor.


Reducing the parallel resistors of Figure B3 results in Figure B4
:


Figure B4:

First circuit simplifi
cation


Equivalent Resistance for

Parallel Resistors:



When drawn this way, it can easily be seen that the parallel set of resistors was also in
series with the other resistor (R1).


Reducing the series combination of R1 and Req
1 of figure B4 results in Figure B5:

Figure B5:

Second circuit simplification



Equivalent Resistance for

Series Resistors:




Figure B5

shows a completely reduced schematic equivalent of the circuit we began with
in Figure B1
.










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4

PROTOBOARDS, KVL / KCL, and OHM’S LAWS


Protoboards


A protoboard is a device that provides an electrical connection between
components via compression fittings. A protoboard’s physical layout is very similar to
that of a spreadsheet, only in a
protoboard each hole is connected to at least one other
hole. The interconnections of these holes are what make a protoboard useful. The lab
protoboards have holes grouped into
four

sets of columns
.
Each of the columns are
labeled either red or blue for
the outermost columns or a, b, c, d, or e for the left inner
most column and f, g, h, i, or j for the right inner most column. Likewise, each row is
labeled 1 through 63.


The following explanation of the electrical connections of the holes is
extremely

important!
The outermost columns are electrically connected in a north
-
south configuration forming two long nodes in each column. These long nodes, called
bussing strips, are ideal for providing power and ground. The red column of holes is
electrically

connected and similarly the holes in the blue column are electrically
connected;
however,

the outer columns are electrically isolated from each other
.
The
center groupings of columns are connected differently;

the inner most columns are
organized into set
s of 5
-
hole nodes in an East
-
West configuration, where the holes in
each row are electrically connected. Therefore, the hole at location 1a is connected to the
hole at location 1b, 1c, 1d, and 1e forming an electrical node with five connecting points.
Ho
wever, hole 1a is not connected to hole 2a, or hole 3a, or hole 2b, or hole 1f
.
Hole 1a
is only connected to the other holes on its row in its set of columns
.
Likewise, the same
system of connections is repeated for columns f, g, h, i, and j.

You will have

two such
protoboards side
-
by
-
side on your robot.




Figure B6:

Protoboard connections


Using our knowledge of the interconnections of the holes,
we can consider each
grouping of connected holes to be a node
. As we know that each node is separated by a
c
ircuit element, we can assemble circuits by placing resistors, capacitors, or other
elements on the protoboard between the nodes.
Note
:
Placing a short circuit between
nodes produces a larger node.

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5

To assist in understanding this concept, examine the fami
liar circuit below:



Figure B7:

A simple circuit revisited


This circuit can be assembled on a protoboard as shown here:




Figure B8:

Protoboard arrangement for simple circuit


Mastery of the protoboard is essential for successful laboratory experiment
s.


KVL / KCL


Next,

we will discuss Kirchoff’s Voltage Law (KVL) and Kirchoff’s Current Law
(KCL)
.
These two laws are fundamental to circuit analysis. It can be noted that KVL and
KCL are nothing more than conservation equations.




Kirchoff’s Voltage La
w:
The sum of the voltage drops around any closed
loop equate to zero.





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6



Kirchoff’s Current Law:
The sum of the currents entering any node minus
the sum of the currents leaving that same node is equal to zero.




The analysis of the circuit begins by identifying the loops of the circuit and then
analyzing the voltage drops and rises within the loop. Loops have been identified in
Figure B9.




Figure B9:

Loops of simple circuit



The positive and negative s
igns next to each circuit element identify the positive
and negative terminals of that element in regards to the elec
tric field. More simply stated

the positive terminal is assumed to have a higher potential (voltage) than the negative
terminal. In the c
ase of an inappropriate assumption, the value of the voltage drop across
an element will be negative. A helpful point in labeling the terminals is that,
you will
always know that the end of the power supply with the longer bar will be the positive
termina
l.

Further, resistors will develop a voltage in opposition to current flow, so the
positive sign should be placed on the resistor’s terminal where current is entering.



The signs attached to the terminals and the directions of the loops are important in
that they allow for a set convention in how to sum the voltages around the loops. Simply,
start at any point on a loop and moving in the direction of the loop, add the voltage if you
are entering the positive terminal and subtract the voltage if you are e
ntering the negative
terminal.
Therefore,

if we follow this convention, our KVL equation starting from the
ground point on loop 1 will look like:




In using KCL, we need to choose a node of the circuit and look at the currents
ente
ring and leaving it. We can choose any node regardless of how many circuit
elements are attached to it, but for this
explanation,

we will examine the node at the top
of resistors R2 and R3
.
First, start by labeling arbitrary directions for the currents en
tering
and leaving the node. Current will always travel from a higher to a lower voltage so you
can approximate the directions according to the estimated voltage drops across circuit
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7

elements.
Next,

simply add the currents entering and equate them to the

currents leaving
.
The equation for that node should look like this:



Ohm’s Laws



Ohm’s laws are another set of
equations that

are invaluable in electrical
engineering
.
A simple
step
-
by
-
step

process in solving for voltages, current
s and power
consumption in the circuit from Figure B1 should give you a sufficient explanation as to
how to use them
.
The in the process below each resistor is valued at 1 kOhm and the
power supply V1 is equal to 7.2 volts.


1.

Reduce the circuit into the sim
plest equivalent circuit possible. This was done
earlier in the lab, so that process can be revisited for assistance with this step.
Hint: The end equivalent resistor should be 1500 Ohms.


2.

Solve for the current flowing out of the power supply. This is of
ten referred to as
the total current in a DC circuit, since there will never be more current in any
point of this circuit than what is coming out of the power supply. The current can
be solved for using Ohm’s law:


Therefore,

the v
oltage at the power supply divided by the resistance should be
equal to the total current through the circuit
.
Measure the voltage output of your
battery

with your Digital Multi
-
Meter, and use that value for the value of your
power supply.
Hint: The total

current should be approximately 4.8 mA or 0.0048
A.


3.

Solve for the individual voltage drops across each element or equivalent element
in series with the power supply, which will therefore have the same current
flowing through it. These will also be solve
d for using the same law as the
previous step.
Therefore,

the voltage drop across the resistor R1 will be the total
current multiplied by the resistance
. T
he voltage drop across the equivalent
resistance of the parallel resistors R2 and R3 will be solved
for in the same way
.
An important thing to note in this is that the voltage drops across parallel
branches are equal.


4.

The only things left to solve for are the currents through R2 and R3. These can
easily be found using the same law as the previous two s
teps.
Hint: The current
through each resistor should be approximately equal to 2.4 mA or 0.0024 A.


5.

Now that we know all the currents in the circuit we can easily calculate the power
in the entire circuit and in each element using the other of Ohm’s laws:


Hint: The total power dissipated in the circuit is equal to the total current
multiplied by the total voltage. It should be equal to approximately 17.28 mW.

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8


Other forms of Ohm’s Laws exist as combinations of the two laws. You sh
ould learn
to be familiar with them so that you can recognize the different forms and use them
where applicable. Also, please remember that this process is not the only way to solve
for these values, which are called the DC biasing values.


DIGITAL MULTI
-
METER



Measuring tools are necessary in all disciplines of engineering. In electrical
engineering,

the Digital Multi
-
Meter (DMM) has become a nearly indispensable tool due
to its unification of multiple measuring devices
including

a volt
-
meter, an ohm
-
me
ter, an
amp
-
meter, and others
.
As useful as a DMM is, it can be easily broken or return false
results if used incorrectly.
Be sure to obey the following rules exactly when using your
DMM to measure voltage and current
.




When you connect a measurement de
vice to a circuit, you want to affect the
function of the circuit as little as possible. As such, it is important to consider the internal
resistance of your measurement tool. A good volt
-
meter has relatively infinite resistance;
therefore,

according to
the rule of parallel resistances
you should always measure
voltage in parallel with the element you are measuring
, which is illustrated bellow

in
Figure B10 and its associated equations
:




Figure B10:
Diagram of proper

Volt
-
Meter connection










If you were to connect them in
series,

you would change the current through the circuit
and return an incorrect value.




A good amp
-
meter has nearly zero resistance, therefore according to the rule of
series resistors
you should always place the amp
-
meter in series with the device you
are measuring.

If you connected the amp
-
meter in parallel, then you would effectively
short out the element you were trying to measure and change the current
flow
through the
circuit
.
These points have been illustrated below

in Figure B11 and its associated
equations
:



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9


Figure B11:
Diagram of proper

Amp
-
Meter Connection





If you connect your
am
meter
incorrectly,

you will very likely damage the DMM or at the
least return an incorrect value from that which you are trying to measure
.
If you connect
your multi
-
meter leads

backwards do not worry, your answer will simply return negative
and you can correct when entering the data.



Also important is the manner in which you connect the leads in the multi
-
meter
itself. When measuring voltage your multi
-
meter leads should be c
onnected in the
following way:



Figure B12:
Volt
-
Meter DMM connections


When measuring current your multi
-
meter leads should be connected in this manner:



Figure B13:
Amp
-
Meter DMM Connections



Another way in which your DMM may be useful is to measure

resistance. To
measure the resistance of an element,
use the following
rules:

(1)
Disconnect the element
or combination of elements from the circuit
. (2)
Measure the element or combination of
elements
.
An ohm
-
meter uses an internal power source to suppl
y a test voltage to the
eleme
nt for resistance calculations. It forces in a current, measures the voltage change,
and uses Ohm’s Law to calculate the resistance. Therefore,

it is important that no other
power supplies are connected to the element when meas
uring resistance.

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10

LAB EXERCISES


The following exercises will reinforce the concepts of circuit building, voltage
measurements and current measurements. You will need a Protoboard, a Digital Multi
-
Meter (DMM), a power supply, and three resistors. A digi
tal multi
-
meter and resistors
are provided in your lab kits, and
as

a power supply, we will use the output of the
battery
.
For all results to be submitted, a copy of the results form should be downloaded
from
Blackboard Vista.
The completed results can th
en be submitted as a file
attachment.


PART

1:
RELATING CALCULATIONS TO MEASUREMENTS




The first exercise will require you to physically prove KVL and KCL
.
This will
be done through constructing the simple circuit
shown in
F
igure
L
1, measuring its DC
bia
s values, and substituting them into both KVL and KCL.



Figure L1:

A Simple Circuit

using 1kOhm resistors



Use figure B8 from the protoboard section of the background
section

to assist you if
necessary. A tool which may assist you in determining whi
ch resistor color bands are
associated with what value can be fou
nd at
www.dannyg.com/examples/res2/resistor.htm
.
You can also double check your resistor values with your DMM before you pla
ce them
into your circuit. For our power supply
, we will use the
center output

of the Lego
“brick
.


in Figure L2.


Since your front robot wheel cannot take much force, remove your protoboard tray from
the robot before assembling the circuit. Alternatively

remove the protoboards from the
tray.

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11


Figure L2:
“Brick” Outputs


You plug one of the RJ12
-
like cables into this output. Use a cable that has exposed white
and black wires on one end. You plug the RJ12
-
like plug into the center output. (RJ12 is
a type o
f telecommunications wiring, consisting of six wires. The standard plug has the
locking tab in the center. Lego has unique plugs with the locking tab on the right side of
the plug). The white wire will have positive output, and
should be connected to the r
ed
bussing strip of the protoboard. The black wire is ground and
should be connected to the
blue bussing strip
, as shown in Figure B6
.

A

general rule in circuit prototyping is to use
red wires for connections to the positive output of a source, and black o
r green wires for
connect
ions to ground; this creates a circuit which is easier to work with when
troubleshooting.

However our RJ12 cable uses white for positive. Your tool kit includes a
spool of red wire, but
it

is highly recommended that multiple wire c
olors be used when
working on the labs.


Your
Lego
brick must be programmed with the
NI
P
ower

program to
supply power to the
outputs. Bring your brick to your TA to have them download the program. You turn on
the outputs by turning on your brick and selecti
ng and running the program. Similarly,
you stop the program and turn off your brick at the end of lab. It is a little tricky to reach
under the protoboard tray to hit the button sequences at first, and you may have to
remove your protoboard tray. After a w
hile, you will be able to push the button sequence
by feel.



Once your circuit has been assembled, proceed with the following steps to prove
KVL and KCL:


1.

Measure the voltage across the
RJ12 wires

and record its value in Table R1

under
both

the Measured a
nd the Calculated headings. Using the your knowledge of
Ohm’s Laws, KVL, and KCL, calculate the remaining values for the voltages and
currents across R1, R2, and R3, and enter them into Table R1. The general
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12

procedure is performed in a step
-
by
-
step metho
d in the background section as an
example if necessary; it is found under the Ohm’s laws heading.


2.

Measure the
voltage across each element in F
igure L1 and record the values in
Table R1. Remember to follow the proper method for measuring voltage,

by
placi
ng the probes of the DMM in parallel with the element being measured

and
by making sure that the function dial of the DMM is set to the proper DC voltage
range
. The picture provided in Figure
L3

shows a practical method for doing this
by placing the probe

leads onto the exposed leads of the resistor.




Figure L3:

Picture example of measuring voltage in parallel


An

alternate

method which can be used involves placing a dummy wire into a
hole on the same node as the element being measured. Remember the
red probe
is for the positive terminal and the black probe is for the negative terminal. If
your answer is negative it is only because you connected the probes backwards.


3.

Measure the current through each element in figure L1 and record the values in
Tabl
e R1.
Remember to follow the prope
r method for measuring current.
Select the proper DC amperage range on the function dial of the DMM, and place
the probes of the multi
-
meter in series with the element to be measured. To place
the probes in series the c
ircuit will have to be broken (i.e. a wire removed) and the
DMM must then be placed into the circuit so that the current to be measured will
flow through the DMM.
If this process is not followed exactly, there is a very
good chance that the DMM will be da
mage
d, if you are unsure of your
measurement technique ask your
TA

or Peer Teacher to assist you.

Remember, using the DMM in ammeter mode

(dial on DCA range)

is
essentially a short circuit:
dangerous and you must be very cautious!

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13


4.

Calculate the percent er
ror between the values you have just measured and the
ones that
were

calculated using theoretical values
at the beginning of the lab
.
Percent error can be calculated according to the following formula:



and record the error in Tabl
e R1.


Dealing with Inaccuracies


5.

To verify KVL and KCL at this point, you need only sum the values you have
measured. However, these values may not exactly equal the ones which you
theoretically calculated, and therefore the values would not sum to exact
ly zero as
they should.
This can be explained by considering

the tolerances of each element.
Since all devices are built within a certain tolerance range, a
ssum
e

that each
resistor

has a tolerance of +/
-

10%
.

W
hat are the maximum and minimum
theoretical

values for each voltage and current? Record these values in Table R2.

Do this analysis by varying only one element in the circuit at a time.

Hint: To
find one set of values, draw the same circuit, with the same voltage source value,
but add +10% to each

resistor value. The min and max voltage across V1 will be
equal to its measured value.


6.

Now perform the KVL and KCL equations
as
shown
under number

3
of the
results section
with the empirical values from Table R1. Your final answers
should all be nearly

zero
.

If not, you may need to go back through the previous
steps to check that you have measured and / or connected everything correctly.


7.

Using the values in Table R1, calculate and record the power dissipated by each
resistor and the total power delive
red by the batteries and record the results in
Table R3. Note the relationship between power delivered and
power
dissipated.



PART

2: MODEL
ING

THE MOTOR
S



The DC motors contained within the robot’s chas
sis

are

represented in
our
schematics by a circle c
ontained within a square. While the
complete
analytical analysis
of DC motors is beyond the scope of these labs, we can often model a motor’s operation
as a simple resistive element for basic operations.



To begin your analysis of the DC motors, construc
t the following circuit

shown in
Figure
L4
:

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14


Figure
L4
:

DC Motor Connections

for Testing


The capacitor is included in parallel with the motor to suppress voltage spikes cause
d

by
the motor

as it turns
. This will make the voltages at other points in the
circuit easier to
measure. Capacitors will be explained in detail in Lab
4
.
Capacitor codes are explained
at the following website:
http://wiki.xtronics.com/index.php/Capacitor_Codes
.

If

you are
having trouble constructing this circuit, you may use the protoboard diagram given below

in Figure
L5
:


Figure
L5
:
Protoboard Guide to DC

Motor Connections for Testing


To connect to the motors, take
two

RJ12 cable with white/black wiring end an
d plug into
each

of the Lego motors. It is a little trick to get past the chassis structure to insert the
plug. Run the wire so that it can easily go up to your protoboard tray (even though you
may have the tray off for this lab). The
white connection is m
otor positive, and the black
connection is motor negative. The motor will turn in different directions depending on the
voltage across these two connections.


Once the circuit has been successfully constructed, continue with the following steps.


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15

1.

Each moto
r has an internal resistance associated with it. However, this internal
resistance can change based upon the state of the motor. Disconnect the left
motor from the circuit and measure its internal resistance. Record this value in
the Table R4. Repeat f
or the right motor.


2.

Once the motor is running, you will be unable to measure its resistance directly.
Therefore, r
econnect only the left motor and turn on the circuit; making sure that
the wheel is unloaded (i.e. freely spinning, unobstructed, not on the

ground).
Measure the voltage

across the resistor combination

and
the
current

through the
battery
,

and record the values in Table R5. Repeat this process for the right
motor.


3.

Using your knowledge of KVL, KCL, and Ohm’s Laws calculate the internal
resist
ance of the unloaded motor
s
. Record the values in Table R4.


4.

Now measure the voltage across
the parallel combination of resistors R1 and R2,
when
the

motors

are

loaded.
To load the motor simply apply some form of
resistance to its turning, such as draggi
ng your finger
LIGHTLY

along the tire as
it is moving.
Be careful that you do NOT
slow

the motor
down too much
, as
this will damage it
.

After recording th
e
s
e

values
in Table R6

of the results
section, use KVL, KCL, and Ohm’s Laws to c
alculate the loaded
internal
resistance

of the motor

and record its value in Table R4.


As is now apparent, t
he resistance of the motor is dependent upon the motor’s load. This
will also have an effect on the power being dissipated by the motor:


5.

Using the values you have re
corded in the previous steps, calculate the power
dissipated by the motor
s

in each of the three states. Record the results in Table
R7.


A huge amount of data on Lego motors, including NXT, can be found at
http://w
ww.philohome.com
. This includes plots showing motor current vs. load and
speed.
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16

RESULTS
: to be uploaded onto
elearning.tamu.edu


1.

BASIC CIRCUIT VALUES



Measured

Calculated

% Error

Voltage

(V)

Current

(mA)

Voltage

(V)

Current

(mA)

Voltage

Current

V1













R1













R2













R3













Table R1


2.

VALUES INCLUDING 10% TOLERANCES



Voltage

(V)

Current

(m
A
)

Min



Max

Min



Max

V1



~





~



R1



~





~



R2



~





~



R3



~





~



Table R2


3.

KVL:

_____________________________

KCL:

_______________________________


4.

POWER IN CIRCUIT



V1

R1

R2

R3

Power
(mW)









Table R3


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17




5.

INTERNAL MOTOR RESISTANCES



Disconnected

Unloaded

Loaded

Left Motor

Resistance

(O
hms)




Right Motor

Resistance
(Ohms)







Table R4


6.

DC MOTOR CIRCUIT (UNLOADED)



Voltage across R1 || R2
(V)

Current through V1
(mA)

Left Motor





Right Motor





Table R5


7.



DC MOTOR CIRCUIT (LOADED)



Voltage Across

R1 and R2

(V)

Lef
t Motor





Right
Motor





Table R6


8.

POWER CONSUMED BY MOTOR



Disconnected

Unloaded

Loaded

Left Motor
Power (mW)







Right Motor
Power (mW)







Table R7



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18

REPORT
: to be uploaded onto
elearning.tamu.edu


Reports are a necessary part of
all t
hings

done in engineering. It does not matter
how wonderful a solution to a problem may be if no one can understand the
explanation

or worse yet, if it is not documented at all. As such
,

a report will be required with every
lab that
you complete for

this

class. These will allow you to review what you have
learned in the lab, and explore more possibilities beyond what was covered in the
exercises.


SPECIFICATIONS




The standard requirements of each lab report will be as follows:


-

Each lab MUST include a
cover page which states:

o

The names of all team members

o

Course number and section

o

Due date

o

The lab name and number

-

All reports are to be typed

-

Reports must be single spaced, with a single space between paragraphs

-

There is no page requirement, but all questi
ons must be sufficiently
answered


REPORT REQUIREMENTS FOR THIS LAB



Answer the following questions:


-

How do you measure voltage? (give
explanation and
diagram)

-

How do you measure current? (give
explanation and
diagram)

-

Why can measuring cu
rrent in parall
el damage an am
meter.

-

What is K
irchoff’s
V
oltage
L
aw
?

-

What is K
irchoff’s
C
urrent
L
aw
?

-

What are Ohm’s Laws?

-

Describe a simple model of a DC motor

as explored in the lab
.

-

What happens to the power
used in the circuit
?