Description
write a lab report following the lab report template. I attached the lab manual and the excel sheet made during the lab.
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Lab 9
Capacitive and Inductive Reactances
Objective
In this lab students will measure capacitive and inductive reactance, verify them theoretically, and
will determine the effect of frequency on capacitive and inductive reactance.
Equipment
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•
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Digital multimeter (DMM)
Oscilloscope
Function Generator
Materials
•
•
•
Resistors (RS): 1 kΩ (to use with the capacitor), 10 kΩ (to use with the inductor)
Capacitor: value can range between 10 – 50 nF (non-electrolytic)
Inductors: 100 mH (or available value)
Instructions
Measure the value of your components: resistances RS, capacitance C, inductance L, inductor
resistance RL.
Note: The excel examples in this handout refer to cells and component values that can be
adjusted according to your own experiment.
a. Capacitive Reactance
1. To record measured data and to perform calculations, prepare an excel table with
columns corresponding to frequency , sensing resistor voltage , current magnitude
, capacitor voltage magnitude , time shift Δ (s), and phase shift (°), found
capacitive reactance ( ) , and computed capacitive reactance ( ) .
Example:
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2. Use frequency values from 100 Hz to 1000 Hz in increments of 100 Hz, as shown in the
example.
3. Build a series circuit with an AC voltage source (Vmax = 6 V, f = 100 Hz), the capacitor,
and the corresponding sensing resistor. The capacitor should be located between the
source and the sensing resistor.
4. Use the sensing resistor to calculate the magnitude of the current in the circuit , and its
phase shift with respect to the voltage drop across the capacitor. This information will
serve you to determine the current phasor = ∠ .
a. Start by recording the voltage drop across the sensing resistor in the
corresponding column in your table.
b. The current magnitude can be calculated by dividing the voltage across the
sensing resistor over the value of the sensing resistance.
Example: If the measured sensing resistor is exactly 1 kΩ, the formula to enter in
cell C2 in excel is: This can be done in excel by entering the following formula:
=B2/1
Important notes:
i. Replace B2 by the corresponding cell where the first sensing resistor
voltage is listed if it is different than above.
ii. This example assumes a 1 kΩ sensing resistor. Use the actual value of the
sensor resistor used with the capacitor. Resistance in kilohms will
result in a current magnitude in milliamperes.
c. To compute the phase shift based on the measured time shift, enter the measured
time shift in seconds in the corresponding column, then utilize the formula =
Δ ∙ ∙ 360° to convert to degrees in the next column.
Example: To calculate the phase shift for the first frequency, the formula entered
in cell F2 in the example is
=E2*A2*360
Where E2 corresponds to the time shift value in seconds, and A2 corresponds to
the initial frequency. Use cell notation corresponding to your own table.
5. Use differential measurement (Ch1-Ch2) to measure the magnitude of the voltage drop
across the capacitor, . Consider the voltage drop across the capacitor as your reference
( = 0°), therefore VC = ∠0.
a. Record the magnitude of the capacitor voltage in the corresponding column in
the table.
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6. Determine the capacitive reactance by using the magnitude of capacitor current and
voltage, and , as determined by steps 4 and 5 respectively. Reactance can be
calculated by finding the magnitude of the impedance | | = as shown below:
∠ =
=
=
∠0°
= ∠ −
∠
Example: To compute the reactance out of measured voltage and current values,
the formula entered in cell G2 in the example is
= D2/C2/1000
Where D2 corresponds to the magnitude of the voltage drop across the capacitor
and, and C2 corresponds to the magnitude of the current through the capacitor.
Use cell notation corresponding to your own table. If the current is expressed in
milliamperes, the denominator should include a factor of 1000 for correct
dimensional analysis, as shown above.
7. Calculate capacitive reactance , and compare it to the measured value ,
as determined in step 6. Capacitive reactance is defined as the reciprocal of the product of
the angular frequency and the capacitance value . Since the angular frequency =
2 , then
1
1
=
=
2
Use this formula to compute the calculated capacitive reactance, , .
Example: The notation to enter this formula in cell H2 would be
=1/(2*pi()*A2*50E-9)
Important notes:
iii. Replace A2 by the corresponding cell where the first frequency value is
listed if it is different than this cell.
iv. This example assumes that a 50 nF capacitor value is used. Use the actual
value of your capacitor.
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8. To use the formula in the cells below using the corresponding frequency values, hover
the mouse over the lower right corner of the cell that contains the formula until the cursor
takes the form of a plus sign (+). Double click on + and the column will populate with the
reactance values corresponding to the rest of the frequencies.
9. Prepare a plot of found and computed capacitive reactances versus frequency. Include
axis labels and a legend to identify each data set.
b. Inductive Reactance
10. Repeat steps 1-6 and used to determine capacitive reactance, but implement the following
changes for inductive reactance:
a. Instead of current through the capacitor , use the current through the inductor .
b. Instead of capacitor voltage magnitude , use the inductor voltage magnitude .
c. Use frequency values from 1 kHz to 10 kHz in increments of 1kHz.
i. Enter frequency values in Hertz in the table. If using kiloHertz,
incorporate corresponding factors for proper dimensional analysis in
formulas.
d. Use the corresponding value for the sensing resistor, which is about 10 times
larger in magnitude than the sensing resistor used with the capacitor.
11. Calculate inductive reactance and compare to the measured value found. Inductive
reactance is defined as the product of the angular frequency and the inductance value
. Since the angular frequency = 2 , then
= = 2
Use this formula to compute the calculated inductive reactance.
Example: The notation to enter this formula would be
=2*pi()*A2*100E-3
Important notes:
i. Replace A2 by the corresponding cell where the first frequency value is
listed if it is different than this cell.
ii. This example assumes that a 100 mH inductor value is used. Use the
actual value of your inductor.
12. Repeat steps 8 and 9.
Simulation
1. Simulate the series circuit with the capacitor and the sensing resistor. Select one
frequency value within the range tested. Run the circuit for one period. Compare the
measured and simulated voltage and current.
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Voltage differential measurement in LTspice: Use differential measurement in
LTspice to measure the voltage across an element that is not adjacent to ground:
Position the cursor to measure voltage before the element of interest. Hold and drag
across the circuit element. This action would allow you to see a red voltage probe
before the element and a black probe after the element. A voltage trace appears in the
waveform window once the mouse is released.
To measure current in LTspice: Hover the mouse over the circuit element of interest
until it transforms into an arrow. Click and observe a current trace in the waveform
window. If needed, the circuit element can be rotated 180° to flip the direction of the
current.
Cursors in LTspice: To activate cursors, right click on the trace name. In the
expression editor window select Attached Cursor:1st. Observe the crosshair cursor in
the middle of the screen. To select it, hover over the crosshair lines until you see a
number 1. Click, hold the mouse, and move from side to side to observe how this
cursor follows the trace. (Eliminate gridlines if they obstruct the view of the cursor).
A secondary cursor can be attached to another trace. The positions and differential
positions of the cursors appear in a small window in the lower right of the screen.
2. Repeat simulation steps 1 and 2 using inductors.
Analysis
How does frequency affect impedance in a capacitive and inductive load? Explain in terms of
reactance and phase shift.
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1
Laboratory Exercise ##
Laboratory Title
MM/DD/YYYY
Name M. Lastname
Abstract—Summarize in a couple of sentences the purpose of this lab based on the objectives listed on the
handout, the procedure done and anticipated results. Define all symbols used in the abstract. Do not cite
references in the abstract. This document will also summarize IEEE recommendations for technical papers.
INTRODUCTION
Introduction is the section of the paper where all new and relevant concepts are to be defined, so the reader can
understand the rest of the report. This document in particular is a simplified template based on the IEEE format found
online.
Keep this document as reference. Each section will describe its function, followed by useful advice and instructions
from IEEE regarding the preparation of technical manuscripts. When preparing your lab report, make sure all the
current text is deleted.
Do not change the font sizes or line spacing to squeeze more text into a limited number of pages. Use italics for
emphasis; do not underline.
PROCEDURE
Describe on your own words the procedure followed in lab. If required, make reference to diagrams and schematics.
Use a paragraph format. Use narrative form, not imperative statements. Do not repeat what is written in the lab handout.
This section is relatively short.
RESULTS AND ANALYSIS
Present and describe the calculated, measured, and simulated values using tables or graphs. Provide an example of
your calculations.
This is the most important section of the lab report, because it demonstrates the level of understanding of the concepts
studied through experimentation. Discuss the meaning of the obtained results and other general observations. Although
the main objective of this section is not to calculate the percentage of error, it is correct to explain discrepancies if
obtained results follow expected trends. The most important question to answer in this section is: Why did the circuit
behave in a given way? Elaborate on the thought process that you follow to achieve a conclusion.
Some Common Mistakes
The word “data” is plural, not singular. A graph within a graph is an “inset,” not an “insert.” The word “alternatively”
is preferred to the word “alternately” (unless you really mean something that alternates). Use the word “whereas”
instead of “while” (unless you are referring to simultaneous events). Do not use the word “essentially” to mean
“approximately” or “effectively.” Do not use the word “issue” as a euphemism for “problem.”
Be aware of the different meanings of the homophones “affect” (usually a verb) and “effect” (usually a noun),
“complement” and “compliment,” “discreet” and “discrete,” “principal” (e.g., “principal investigator”) and “principle”
(e.g., “principle of measurement”). Do not confuse “imply” and “infer.”
Prefixes such as “non,” “sub,” “micro,” “multi,” and “ultra” are not independent words; they should be joined to the
words they modify, usually without a hyphen. There is no period after the “et” in the Latin abbreviation “et al.” (it is
also italicized). The abbreviation “i.e.,” means “that is,” and the abbreviation “e.g.,” means “for example” (these
abbreviations are not italicized).
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An excellent style manual and source of information for science writers is [5]. A general IEEE style guide and an
Information for Authors are both available at http://www.ieee.org/web/publications/authors/transjnl/index.html
Schematics and Diagrams
Diagrams and schematics, if required, should be included within the text as needed. Draw the circuit analyzed with
the real value of the components. Include any other relevant schematics. Give a number and caption to each diagram.
(E.g., Figure 1. RCL circuit.). Caption of figures goes under the figure. Caption of tables goes above the table. Diagrams
should be clear and readable when printed in black and white.
To insert images in Word, position the cursor at the insertion point and either use Insert | Picture | From File or copy
the image to the Windows clipboard and then Edit | Paste Special | Picture (with “float over text” unchecked)
If you are importing your graphics into this Word template, please use the following steps: Under HOME, drop down
the options under the icon PASTE, and select PASTE SPECIAL. A dialog box will open, select Picture, then click OK.
Always describe a picture, figure, or table in the paragraph(s) before it. For example, “Fig. 1 shows an increment in
magnetization as the applied field increases.”
Fig. 1. Magnetization as a function of applied field. Note that “Fig.” is abbreviated. There is a period after the
figure number, followed by two spaces. It is good practice to explain the significance of the figure in the caption.
Math
If you are using Word, use either the Microsoft Equation Editor or the MathType add-on (http://www.mathtype.com)
for equations in your paper (Insert | Object | Create New | Microsoft Equation or MathType Equation). “Float over
text” should not be selected.
Units
Use either SI (MKS) or CGS as primary units. (SI units are strongly encouraged.) English units may be used as
secondary units (in parentheses). For example, write “15 Gb/cm 2 (100 Gb/in2).” An exception is when English units
are used as identifiers in trade, such as “3½-in disk drive.” Avoid combining SI and CGS units, such as current in
amperes and magnetic field in oersteds. This often leads to confusion because equations do not balance dimensionally.
If you must use mixed units, clearly state the units for each quantity in an equation.
The SI unit for magnetic field strength H is A/m. However, if you wish to use units of T, either refer to magnetic
flux density B or magnetic field strength symbolized as µ0H. Use the center dot to separate compound units, e.g.,
“A·m2.”
Figures and Tables
Place figure captions below the figures; place table titles above the tables. If your figure has two parts, include the
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labels “(a)” and “(b)” as part of the artwork. Please verify that the figures and tables you mention in the text actually
exist. Please do not include captions as part of the figures. Do not put captions in “text boxes” linked to the figures. Do
not put borders around the outside of your figures. Use the abbreviation “Fig.” even at the beginning of a sentence. Do
not abbreviate “Table.” Tables are numbered with Roman numerals. In this case, Table I is presented as example. Use
letters for table footnotes.
TABLE I
UNITS FOR MAGNETIC PROPERTIES
Symbol
B
Quantity
H
m
magnetic flux
magnetic flux density,
magnetic induction
magnetic field strength
magnetic moment
M
magnetization
4M
j
J
magnetization
specific magnetization
magnetic dipole
moment
magnetic polarization
,
susceptibility
mass susceptibility
permeability
r
w, W
N, D
relative permeability
energy density
demagnetizing factor
Conversion from Gaussian and
CGS EMU to SI a
1 Mx → 10−8 Wb = 10−8 V·s
1 G → 10−4 T = 10−4 Wb/m2
1 Oe → 103/(4) A/m
1 erg/G = 1 emu
→ 10−3 A·m2 = 10−3 J/T
1 erg/(G·cm3) = 1 emu/cm3
→ 103 A/m
1 G → 103/(4) A/m
1 erg/(G·g) = 1 emu/g → 1 A·m2/kg
1 erg/G = 1 emu
→ 4 10−10 Wb·m
1 erg/(G·cm3) = 1 emu/cm3
→ 4 10−4 T
1 → 4
1 cm3/g → 4 10−3 m3/kg
1 → 4 10−7 H/m
= 4 10−7 Wb/(A·m)
→ r
1 erg/cm3 → 10−1 J/m3
1 → 1/(4)
Vertical lines are optional in tables. Statements that serve as captions for the entire table do not need footnote letters.
a
Gaussian units are the same as cgs emu for magnetostatics; Mx = maxwell, G = gauss, Oe = oersted; Wb = weber, V = volt, s = second, T =
tesla, m = meter, A = ampere, J = joule, kg = kilogram, H = henry.
Figure axis labels are often a source of confusion. Use words rather than symbols. As an example, write the quantity
“Magnetization,” or “Magnetization M,” not just “M.” Put units in parentheses. Do not label axes only with units. As
in Fig. 1, for example, write “Magnetization (A/m)” or “Magnetization (A m−1),” not just “A/m.” Do not label axes
with a ratio of quantities and units. For example, write “Temperature (K),” not “Temperature/K.”
Multipliers can be especially confusing. Write “Magnetization (kA/m)” or “Magnetization (103 A/m).” Do not write
“Magnetization (A/m) 1000” because the reader would not know whether the top axis label in Fig. 1 meant 16000
A/m or 0.016 A/m. Figure labels should be legible, approximately 8 to 12 point type.
References
Number citations consecutively in square brackets [1]. The sentence punctuation follows the brackets [2]. Multiple
references [2], [3] are each numbered with separate brackets [1]–[3]. When citing a section in a book, please give the
relevant page numbers [2]. In sentences, refer simply to the reference number, as in [3]. Do not use “Ref. [3]” or
“reference [3]” except at the beginning of a sentence: “Reference [3] shows … .” Please do not use automatic endnotes
in Word, rather, type the reference list at the end of the paper using the “References” style.
Please note that the references at the end of this document are in the preferred referencing style. Give all authors’
names; do not use “et al.” unless there are six authors or more. Use a space after authors’ initials. Papers that have not
been published should be cited as “unpublished” [4]. Papers that have been accepted for publication, but not yet
specified for an issue should be cited as “to be published” [5]. Papers that have been submitted for publication should
be cited as “submitted for publication” [6]. Please give affiliations and addresses for private communications [7].
Capitalize only the first word in a paper title, except for proper nouns and element symbols. For papers published in
translation journals, please give the English citation first, followed by the original foreign-language citation [8].
Abbreviations and Acronyms
Define abbreviations and acronyms the first time they are used in the text, even after they have already been defined
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in the abstract. Abbreviations such as IEEE, SI, ac, and dc do not have to be defined. Abbreviations that incorporate
periods should not have spaces: write “C.N.R.S.,” not “C. N. R. S.” Do not use abbreviations in the title unless they
are unavoidable (for example, “IEEE” in the title of this article).
Equations
Number equations consecutively with equation numbers in parentheses flush with the right margin, as in (1). First
use the equation editor to create the equation. Then select the “Equation” markup style. Press the tab key and write the
equation number in parentheses. To make your equations more compact, you may use the solidus ( / ), the exp function,
or appropriate exponents. Use parentheses to avoid ambiguities in denominators. Punctuate equations when they are
part of a sentence, as in
∞
∫ ( , ) = [ 2 /2( 0 )] ∙ ∫0 exp(− | − |) −1 1 ( 2 ) 0 ( 1 )
(1)
Be sure that the symbols in your equation have been defined before the equation appears or immediately following.
Italicize symbols (T might refer to temperature, but T is the unit tesla). Refer to “(1),” not “Eq. (1)” or “equation (1),”
except at the beginning of a sentence: “Equation (1) is … .”
Other Recommendations
Use one space after periods and colons. Hyphenate complex modifiers: “zero-field-cooled magnetization.” Avoid
dangling participles, such as, “Using (1), the potential was calculated.” [It is not clear who or what used (1).] Write
instead, “The potential was calculated by using (1),” or “Using (1), we calculated the potential.”
Use a zero before decimal points: “0.25,” not “.25.” Use “cm3,” not “cc.” Indicate sample dimensions as “0.1 cm
0.2 cm,” not “0.1 0.2 cm2.” The abbreviation for “seconds” is “s,” not “sec.” Do not mix complete spellings and
abbreviations of units: use “Wb/m2” or “webers per square meter,” not “webers/m2.” When expressing a range of
values, write “7 to 9” or “7-9,” not “7~9.”
A parenthetical statement at the end of a sentence is punctuated outside of the closing parenthesis (like this). (A
parenthetical sentence is punctuated within the parentheses.) In American English, periods and commas are within
quotation marks, like “this period.” Other punctuation is “outside”! Avoid contractions; for example, write “do not”
instead of “don’t.” The serial comma is preferred: “A, B, and C” instead of “A, B and C.”
CONCLUSION
Summarize the technical findings in a couple of sentences. Everything mentioned in this section has already been
presented in the report. A reader should be able to get a very good idea of the lab content by reading only the abstract
and the conclusion sections. A conclusion that reads: “Overall, this lab was a success” is not acceptable because does
not have technical relevance.
REFERENCES
[1] G. O. Young, “Synthetic structure of industrial plastics (Book style with paper title and editor),” in Plastics, 2nd ed. vol. 3, J. Peters, Ed.
New York: McGraw-Hill, 1964, pp. 15–64.
[2] W.-K. Chen, Linear Networks and Systems (Book style). Belmont, CA: Wadsworth, 1993, pp. 123–135.
[3] H. Poor, An Introduction to Signal Detection and Estimation. New York: Springer-Verlag, 1985, ch. 4.
[4] B. Smith, “An approach to graphs of linear forms (Unpublished work style),” unpublished.
[5] M. Young, The Techincal Writers Handbook. Mill Valley, CA: University Science, 1989.
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