document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72966>Question 72966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the resistance of an electric wire is directly proportional to the length of the wire and inversely proportional to the square of the diameter. Write a formula expressing this property using R for resistance, L for length, and D for diameter. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52189 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's write the equation first and then we'll discuss it.<BR>\n" );
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document.write( "The equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+k%2A%28L%2FD%5E2%29 ALIGN=MIDDLE  ALT=\"R+=+k%2A%28L%2FD%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where R, L, and D are as defined in your problem and k is something we'll call a constant<BR>\n" );
document.write( "of proportionality.<BR>\n" );
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document.write( "The first thing to notice is that L is in the numerator of the fraction.  As a result, when<BR>\n" );
document.write( "L gets bigger then R will also get bigger. This is called \"directly proportional.\"<BR>\n" );
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document.write( "Then you need to notice that D is in the denominator. (As a matter-of-fact D squared is<BR>\n" );
document.write( "in the denominator.) As a result, when D gets bigger, R will get smaller. This is called<BR>\n" );
document.write( "inversely proportional.<BR>\n" );
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document.write( "You can sort of get the idea by saying that if the diameter were 1, then the resistance<BR>\n" );
document.write( "would be k*L.  But if the diameter were 100, then the resistance would be k*L divided by<BR>\n" );
document.write( "100.  So the resistance would be considerably smaller.<BR>\n" );
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document.write( "k is just something that is thrown in to make the equation balance.  It accommodates such<BR>\n" );
document.write( "things as the type of wire (for example, steel wire or copper wire). It also takes into account<BR>\n" );
document.write( "the units of measurement.  For example the length may be in meters, or yards, or feet,<BR>\n" );
document.write( "and the wire size may be millimeters, inches, mils, or specific wire gauges.  These could<BR>\n" );
document.write( "all change on you and the basic equation would stay the same, but the value of k would change.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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