%% bare_jrnl_compsoc.tex
%% V1.3
%% 2007/01/11
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.7 or later) with an IEEE Computer
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%%
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%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
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%% http://www.ieee.org/
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%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
%%*************************************************************************
% *** Authors should verify (and, if needed, correct) their LaTeX system ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices can trigger bugs that do ***
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% Use the testflow package mentioned above to verify correct handling of
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% should be used if it is desired that the figures are to be displayed in
% draft mode.
%
% The Computer Society usually requires 12pt for submissions.
%
\documentclass[12pt,journal,compsoc]{IEEEtran}
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
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% \documentclass[12pt,journal,compsoc]{../sty/IEEEtran}
% Some very useful LaTeX packages include:
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% *** MISC UTILITY PACKAGES ***
%
\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
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% usage:
% \ifpdf
% % pdf code
% \else
% % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
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% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.
\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
\usepackage{url}
\usepackage{hyperref}
\hypersetup{colorlinks=false,pdfborder={0 0 0}}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
\errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}
\usepackage[utf8]{inputenc}
\usepackage[ngerman,greek,english]{babel}
% *** CITATION PACKAGES ***
%
\ifCLASSOPTIONcompsoc
% IEEE Computer Society needs nocompress option
% requires cite.sty v4.0 or later (November 2003)
\usepackage[nocompress]{cite}
\else
% normal IEEE
\usepackage{cite}
\fi
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 4.0 (2003-05-27) and later if using hyperref.sty. cite.sty does
% not currently provide for hyperlinked citations.
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% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.
%
% Note that some packages require special options to format as the Computer
% Society requires. In particular, Computer Society papers do not use
% compressed citation ranges as is done in typical IEEE papers
% (e.g., [1]-[4]). Instead, they list every citation separately in order
% (e.g., [1], [2], [3], [4]). To get the latter we need to load the cite
% package with the nocompress option which is supported by cite.sty v4.0
% and later. Note also the use of a CLASSOPTION conditional provided by
% IEEEtran.cls V1.7 and later.
% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/
% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
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% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/
% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/
%\usepackage{mdwmath}
%\usepackage{mdwtab}
% Also highly recommended is Mark Wooding's extremely powerful MDW tools,
% especially mdwmath.sty and mdwtab.sty which are used to format equations
% and tables, respectively. The MDWtools set is already installed on most
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% http://www.ctan.org/tex-archive/macros/latex/contrib/mdwtools/
% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.
%\usepackage{eqparbox}
% Also of notable interest is Scott Pakin's eqparbox package for creating
% (automatically sized) equal width boxes - aka "natural width parboxes".
% Available at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/
% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%\usepackage[tight,normalsize,sf,SF]{subfigure}
%\else
%\usepackage[tight,footnotesize]{subfigure}
%\fi
% subfigure.sty was written by Steven Douglas Cochran. This package makes it
% easy to put subfigures in your figures. e.g., "Figure 1a and 1b". For IEEE
% work, it is a good idea to load it with the tight package option to reduce
% the amount of white space around the subfigures. Computer Society papers
% use a larger font and \sffamily font for their captions, hence the
% additional options needed under compsoc mode. subfigure.sty is already
% installed on most LaTeX systems. The latest version and documentation can
% be obtained at:
% http://www.ctan.org/tex-archive/obsolete/macros/latex/contrib/subfigure/
% subfigure.sty has been superceeded by subfig.sty.
%\ifCLASSOPTIONcompsoc
% \usepackage[caption=false]{caption}
% \usepackage[font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
% \usepackage[caption=false]{caption}
% \usepackage[font=footnotesize]{subfig}
%\fi
% subfig.sty, also written by Steven Douglas Cochran, is the modern
% replacement for subfigure.sty. However, subfig.sty requires and
% automatically loads Axel Sommerfeldt's caption.sty which will override
% IEEEtran.cls handling of captions and this will result in nonIEEE style
% figure/table captions. To prevent this problem, be sure and preload
% caption.sty with its "caption=false" package option. This is will preserve
% IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
% (recommended due to many improvements over 1.2) of subfig.sty supports
% the caption=false option directly:
%\ifCLASSOPTIONcompsoc
% \usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
% \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
%
% The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/
% The latest version and documentation of caption.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/caption/
% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/
%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
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% Documentation is contained in the stfloats.sty comments as well as in the
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% does not allow \baselineskip to stretch. Authors submitting work to the
% IEEE should note that IEEE rarely uses double column equations and
% that authors should try to avoid such use. Do not be tempted to use the
% cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does
% not format its papers in such ways.
%\ifCLASSOPTIONcaptionsoff
% \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley and Jeff Goldberg.
% This package may be useful when used in conjunction with IEEEtran.cls'
% captionsoff option. Some IEEE journals/societies require that submissions
% have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.3.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% For subfigure.sty:
% \let\MYorigsubfigure\subfigure
% \renewcommand{\subfigure}[2][\relax]{\MYorigsubfigure[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat/subfig command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a
% page by themselves.
% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/misc/
% Read the url.sty source comments for usage information. Basically,
% \url{my\_url\_here}.
% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex). ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )
% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}
\begin{document}
%
% paper title
% can use linebreaks \\ within to get better formatting as desired
\title{Excersise solution theme 6.}
%
%
% author names and IEEE memberships
% note positions of commas and nonbreaking spaces ( ~ ) LaTeX will not break
% a structure at a ~ so this keeps an author's name from being broken across
% two lines.
% use \thanks{} to gain access to the first footnote area
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%
%
%\IEEEcompsocitemizethanks is a special \thanks that produces the bulleted
% lists the Computer Society journals use for "first footnote" author
% affiliations. Use \IEEEcompsocthanksitem which works much like \item
% for each affiliation group. When not in compsoc mode,
% \IEEEcompsocitemizethanks becomes like \thanks and
% \IEEEcompsocthanksitem becomes a line break with idention. This
% facilitates dual compilation, although admittedly the differences in the
% desired content of \author between the different types of papers makes a
% one-size-fits-all approach a daunting prospect. For instance, compsoc
% journal papers have the author affiliations above the "Manuscript
% received ..." text while in non-compsoc journals this is reversed. Sigh.
\author{Joset Geovanni Pacheco Castillo% <-this % stops a space
\IEEEcompsocitemizethanks{\IEEEcompsocthanksitem Joset Geovanni Pacheco Castillo is with Instituto Tecnológico Superior Zacatecas Occidente\protect\\
% note need leading \protect in front of \\ to get a newline within \thanks as
% \\ is fragile and will error, could use \hfil\break instead.
\IEEEcompsocthanksitem }}% <-this % stops a space
%\thanks{Manuscript received \today;}
% note the % following the last \IEEEmembership and also \thanks -
% these prevent an unwanted space from occurring between the last author name
% and the end of the author line. i.e., if you had this:
%
% \author{....lastname \thanks{...} \thanks{...} }
% ^------------^------------^----Do not want these spaces!
%
% a space would be appended to the last name and could cause every name on that
% line to be shifted left slightly. This is one of those "LaTeX things". For
% instance, "\textbf{A} \textbf{B}" will typeset as "A B" not "AB". To get
% "AB" then you have to do: "\textbf{A}\textbf{B}"
% \thanks is no different in this regard, so shield the last } of each \thanks
% that ends a line with a % and do not let a space in before the next \thanks.
% Spaces after \IEEEmembership other than the last one are OK (and needed) as
% you are supposed to have spaces between the names. For what it is worth,
% this is a minor point as most people would not even notice if the said evil
% space somehow managed to creep in.
% The paper headers
\markboth{Computer Science Journal of IEEE,~Vol.~1, No.~1, 2013}%
{Joset Geovanni Pacheco Castillo : Excersise solution theme 6.}
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
%
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers. ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.
% The publisher's ID mark at the bottom of the page is less important with
% Computer Society journal papers as those publications place the marks
% outside of the main text columns and, therefore, unlike regular IEEE
% journals, the available text space is not reduced by their presence.
% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2007 IEEE}
% or like this to get the Computer Society new two part style.
%\IEEEpubid{\makebox[\columnwidth]{\hfill 0000--0000/00/\$00.00~\copyright~2007 IEEE}%
%\hspace{\columnsep}\makebox[\columnwidth]{Published by the IEEE Computer Society\hfill}}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark (Computer Society jorunal
% papers don't need this extra clearance.)
% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}
% for Computer Society papers, we must declare the abstract and index terms
% PRIOR to the title within the \IEEEcompsoctitleabstractindextext IEEEtran
% command as these need to go into the title area created by \maketitle.
\IEEEcompsoctitleabstractindextext{%
% IEEEtran.cls defaults to using nonbold math in the Abstract.
% This preserves the distinction between vectors and scalars. However,
% if the journal you are submitting to favors bold math in the abstract,
% then you can use LaTeX's standard command \boldmath at the very start
% of the abstract to achieve this. Many IEEE journals frown on math
% in the abstract anyway. In particular, the Computer Society does
% not want either math or citations to appear in the abstract.
% Note that keywords are not normally used for peerreview papers.
%\begin{IEEEkeywords}
%Computer Society, IEEEtran, journal, \LaTeX, paper, template.
%\end{IEEEkeywords}
}
% make the title area
\maketitle
% To allow for easy dual compilation without having to reenter the
% abstract/keywords data, the \IEEEcompsoctitleabstractindextext text will
% not be used in maketitle, but will appear (i.e., to be "transported")
% here as \IEEEdisplaynotcompsoctitleabstractindextext when compsoc mode
% is not selected if conference mode is selected - because compsoc
% conference papers position the abstract like regular (non-compsoc)
% papers do!
\IEEEdisplaynotcompsoctitleabstractindextext
% \IEEEdisplaynotcompsoctitleabstractindextext has no effect when using
% compsoc under a non-conference mode.
% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle
1. -What is the potential difference needed to stop an electron that has
an initial velocity of 5.0x10\textsuperscript{5}m / s?
The first thing we must do is identify the data that the problem gives
us and the data we can obtain from what was learned in the unit:
\par\null
\begin{equation}
\(V=5.0x10^5m/s\ \ \ \ \ \ \ m=9.11x10^{-31}kg\)
\end{equation}
\begin{equation}
\(q=-1.6x10^{-19}C\)
\end{equation}
\par\null
Now that we have the data, it is necessary to identify the necessary
formulas to solve the problem:
\par\null
\begin{equation}
\(\Delta u=q\Delta v=-\Delta K\)
\end{equation}
\begin{equation}
\(-\Delta K=Kin-Kfn\)
\end{equation}
\begin{equation}
\(K=\frac{1}{2}mv^2\)
\end{equation}
Having these formulas, we can clear the formula we need:
\par\null
\begin{equation}
\(\Delta v=\frac{Kin}{q}=\frac{mV^2}{2q}\)
\end{equation}
It only remains to replace the values in the formula:
\par\null
\begin{equation}
\(\left[\frac{\left(9.11x10^{-31}kg\right)\left(5.0x10^5ms\right)}{2\left(-1.6x10^{-19}C\right)}\right]\)
\end{equation}
Giving us as a result:
\par\null
\begin{equation}
\(\Delta v=-0.71v\)
\end{equation}
\par\null\par\null
2. - A current of 1.30 A flows in a wire. How many electrons pass
through any point in 1 second?
As with any problem, the first thing is to identify the data that you
have:
\par\null
\begin{equation}
\(I=1.30A\ \ \ \ \ 1e=1.6x10^{-19}C\)
\end{equation}
Now that we have the data, we proceed to identify the formula that will
help us solve the problem:
\par\null
\begin{equation}
\(I=\frac{\Delta Q}{\Delta t}\)
\end{equation}
Taking into account this formula, we know that:
\par\null
\begin{equation}
\(1A=\frac{1C}{s}\)
\end{equation}
So, taking into account the formula and the equivalence of amperes and
coloumbs, we can proceed to solve the problem:
\par\null
\begin{equation}
\(I=\frac{\Delta Q}{\Delta t}=\frac{1.30C}{1s}\left(\frac{1e}{1.6x10^{-19}C}\right)\)
\end{equation}
Giving us as a result:
\par\null
\begin{equation}
\(8.125x10^{18}C\)
\end{equation}
\par\null\par\null
3. - An electrical device drives a current of 6.50 A to 240V.
A)~If the voltage drops 15\% what will the current be ?. Assuming
nothing else changes.
B)~ If the resistance of the device is reduced 15\%. What will be the
current at a voltage of 240V ?.
We will start this problem as always, identifying the data:
\par\null
\begin{equation}
\(I=6.50A\ \ \ \ V=240v\)
\end{equation}
First we will solve point A. For this we must identify the formula that
helps us solve it:
A)
\par\null
\begin{equation}
\(I=\frac{V}{R}\)
\end{equation}
This would be the main formula, based on it we cleared the formula that
calculates the voltage:
\par\null
\begin{equation}
\(V=I\cdot R\)
\end{equation}
Now we have to perform some V clearances to know how it will affect the
current:
\par\null
\begin{equation}
\(Vf=0.85\ \ \ \ \ Vi=0.85\left(6.50A\right)R\)
\end{equation}
Taking into account this information, we can calculate the current:
\par\null
\begin{equation}
\(If=\left(0.85\right)\left(6.50A\right)\left(1\right)=5.525A\)
\end{equation}
Giving us the final result:
\par\null
\begin{equation}
\(5.525A\)
\end{equation}
\par\null
B)~The next thing is to calculate subsection B. And given that in this
subsection the data are the same, we will concentrate on the formulas.
Bearing in mind that the variation will be the resitencia, the necessary
formulas will be the following:
\par\null
\begin{equation}
\(R=\frac{V}{I}\ \ \ Ri=\frac{V}{Ii}\ \ \ Rf=\frac{V}{If}\)
\end{equation}
Taking these formulas as a reference, we will perform a clearance to
know how to calculate the current in this subsection:
\par\null
\begin{equation}
\(\frac{Rf}{Ri}=0.85\ \ \ \ \frac{\frac{V}{If}}{\frac{V}{Ii}}=0.85=\frac{IiV}{IfV}\)
\end{equation}
Because both currents share the data V, it is eliminated from both
leaving as follows:
\par\null
\begin{equation}
\(\frac{Ii}{If}\)
\end{equation}
Knowing this formula, it only remains to clear the formula If:
\par\null
\begin{equation}
\(If=\frac{Ii}{0.85}=\frac{6.50A}{0.85}=7.64A\)
\end{equation}
Giving us the final result:
\par\null
\begin{equation}
\(7.64A\)
\end{equation}
\par\null\par\null
4. -What is the diameter of a 1 meter tungsten wire that has a
resistance of 0.32 \(\Omega\)?
The first thing will be to identify the data:
\par\null
\begin{equation}
\(p=5.6x10^{-8}\selectlanguage{greek}Ω.\selectlanguage{english}m\ \ \ \ i=1m\ \ \ \ \)
\end{equation}
Taking into account these data, the necessary formula for this problem
would be:
\par\null
\begin{equation}
\(R=p\frac{i}{A}\)
\end{equation}
Because we do not have all the data required by the formula, we need to
know how to calculate the missing data:
\par\null
\begin{equation}
\(A=\pi r^2\ \ \ A=\frac{pi}{R}\)\(A=\pi\left(\frac{d^2}{4}\right)\)
\end{equation}
Taking into account these formulas, it is possible to arrive at the
correct formula by means of clearings:
\par\null
\begin{equation}
\(r=\frac{d}{2}\ \ \ \ d=2r\)
\end{equation}
Having all the above data as a reference, it is possible to do the
following:
\par\null
\begin{equation}
\(\pi\frac{d^2}{4}=\frac{pi}{R}\)
\end{equation}
With this we can now clear the diameter formula:
\par\null
\begin{equation}
\(d^2=\frac{4pi}{\pi R}\ \ \ \ d=\sqrt{\frac{4pi}{\pi R}}\)
\end{equation}
It only remains to substitute values in the formula to arrive at the
solution:
\par\null
\begin{equation}
\(d=\sqrt{\frac{\left(4\right)\left(5.6x10^{-8}\Omega.m\right)\left(1m\right)}{\left(\pi\right)\left(0.32\Omega\right)}}=4.7x10^{-4}m\)
\end{equation}
Obtaining as final result:
\par\null
\begin{equation}
\(d=4.7x10^{-4}m\)
\end{equation}
\par\null\par\null
5. -What is the resistance of a 4.5m copper wire that has a diameter of
1.5mm?
When we read the problem carefully, we realize that it is very similar
to the previous one, with the difference of requesting another data as a
result. With this in mind, the main formula will be the same:
\par\null
\begin{equation}
\(R=p\frac{i}{A}\)
\end{equation}
Having this formula we must review the data we have:
\par\null
\begin{equation}
\(i=4.5m\ \ \ \ d=1.5mm=0.015m\ \ \ \ p=1.68x10x^{-8}\Omega.m\)
\end{equation}
Given that; As it was said before, the problem is very similar to the
previous one, it is possible to calculate R in the following way:
\par\null
\begin{equation}
\(R=p\frac{i4}{\pi\left(d^2\right)}\)
\end{equation}
\begin{equation}
\(R=\frac{4pi}{\pi d^2}\)
\end{equation}
Having this formula, it only remains to replace values:
\par\null
\begin{equation}
\(R=\frac{\left(4\right)\left(1.68x10^{-8}\right)\left(4.5\right)}{\left(\pi\right)\left(0.015\right)^2}=4.2x10^{-2}\Omega\)
\end{equation}
Giving us as a result:
\par\null
\begin{equation}
\(R=4.2x10^{-2}\Omega\)
\end{equation}
\par\null\par\null
6. -What is the maximum power consumption of a 3V discman that drives a
maximum current of 270mA?
The first thing is to identify our data:
\par\null
\begin{equation}
\(I=270mA=0.27A\ \ \ \ V=3v\)
\end{equation}
Knowing the data it is easy to know what formula will be used, which is:
\par\null
\begin{equation}
\(P=IV\)
\end{equation}
What remains to be done is very simple, only values in the formula are
substituted:
\par\null
\begin{equation}
\(P=\left(0.27A\right)\left(3v\right)=0.81w\)
\end{equation}
Arriving at the result, which is:
\par\null
\begin{equation}
\(P=0.81w\)
\end{equation}
\par\null
7. -A microwave oven is designed to produce 3.3kw of heat when connected
to a 240V source. What should your resistance be?~
As always, the first thing is to know what data you have:
\par\null
\begin{equation}
\(V=240v\ \ \ \ P=3.3kw=3.3x10^3w\)
\end{equation}
Knowing this, we look for the correct formula:
\par\null
\begin{equation}
\(P=\frac{V^2}{R}\ \ \ \ R=\frac{V^2}{P}\)
\end{equation}
It only remains to substitute values in the formula to obtain the
result:
\par\null
\begin{equation}
\(R=\frac{240^2v}{3.3x10^3w}=17.45\Omega\)
\end{equation}
Giving us the final result, which is:
\par\null
\begin{equation}
\(R=17.45\Omega\)
\end{equation}
\par\null\par\null
8. - You buy a 75w electric bulb in Europe, where electricity is 240v.
If you use that electric bulb in U.S.A. where the voltage is 120v. How
will the brightness of the bulb change with respect to Europe?
Because in this case, it is not necessary to perform an operation to
obtain a specific data. We will take the formual to compare the
brightness of the bulb in both places. For this we will follow the
following formula:
\par\null
\begin{equation}
\(P=\frac{V2}{R}\)
\end{equation}
From here we start with the comparison:
\par\null
\begin{equation}
\(\frac{Pusa}{Peur}=\frac{\frac{Vusa^2}{R}}{\frac{Veur^2}{R}}\)
\end{equation}
Since R is the same in both cases, they are eliminated among themselves,
being as follows:
\par\null
\begin{equation}
\(\frac{Vusa^2}{Veur^2}\)
\end{equation}
We know that the V value of U.S.A. It's half the size of Europe.
Therefore it is represented as follows:
\par\null
\begin{equation}
\(\left(\frac{1}{2}\right)^2=\frac{1}{4}\)
\end{equation}
So, thanks to this data we know that. The brightness of the bulb in
U.S.A. it is \(\frac{1}{4}\) with respect to Europe.
\par\null
9. -At a cost of \$ 0.095 kw / hr. How much does it cost you to leave
your backyard focus of 25w day and night for a year?
To solve this problem we must create our own formula, which we will call
cost. To do this we have to put our data in the same units of
measurement.
The first thing will be to convert the Kw to W:
\par\null
\begin{equation}
\(\left(\frac{0.095}{Kwh}\right)\left(\frac{1Kw}{1000W}\right)\)
\end{equation}
Now that we have the formula to convert the Kw to W, it is necessary to
convert the total time into hours:
\par\null
\begin{equation}
\(\left(365days\right)\left(\frac{24hrs}{1day}\right)\)
\end{equation}
Once we have all our data in the same units, we proceed to create our
formula:
\par\null
\begin{equation}
\(Cost=\left(25w\right)\left(\frac{0.095}{Kwh}\right)\left(\frac{1Kw}{1000W}\right)\left(365days\right)\left(\frac{24hrs}{1day}\right)\)
\end{equation}
Thanks to the fact that in this way we convert the units, the days are
eliminated, the hours, the Kw and the W. are eliminated, leaving as a
final result:
\par\null
\begin{equation}
\(Cost=20\ Dollars\)
\end{equation}
\selectlanguage{english}
\FloatBarrier
\end{document}