document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72401>Question 72401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The electrical resistance R of a wire varies as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter from the same material?\r<BR>\n" );
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document.write( "Please show me how you came across the solution.Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51757 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=51757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation for computing the resistance of a wire is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%28K%2AL%29%2Fd%5E2 ALIGN=MIDDLE  ALT=\"R+=+%28K%2AL%29%2Fd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where R is resistance in ohms, L is length in meters, and d is the diameter of the wire in <BR>\n" );
document.write( "centimeters. Notice that R varies directly as L and inversely as the square of the diameter.<BR>\n" );
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document.write( "The problem is that we don't know K which is just a constant of proportionality. But with<BR>\n" );
document.write( "the information given in the problem we can find K. We know for a wire that is 20 meters<BR>\n" );
document.write( "long and has a diameter of 0.6 cm, the resistance is 36 ohms.  Plug those values into the<BR>\n" );
document.write( "equation above and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+%28K%2A20%29%2F0.6%5E2 ALIGN=MIDDLE  ALT=\"36+=+%28K%2A20%29%2F0.6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the squaring and division on the right side and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+K%2A55.5556 ALIGN=MIDDLE  ALT=\"36+=+K%2A55.5556\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then divide both sides by 55.5556 to solve for K.  When you do, you find that K = 0.6480.<BR>\n" );
document.write( "This value of K takes into account the material used for the wire as well as the fact that <BR>\n" );
document.write( "we will express the length of the wire in meters and the diameter of the wire in centimeters,<BR>\n" );
document.write( "not meters.<BR>\n" );
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document.write( "Now return to the original equation and substitute 0.6480 for K to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%28%280.6480%29%2AL%29%2Fd%5E2 ALIGN=MIDDLE  ALT=\"R+=+%28%280.6480%29%2AL%29%2Fd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you have an equation you can do something with.  You know the new piece of wire has a<BR>\n" );
document.write( "length of 60 meters and a diameter of 1.2 centimeters.  Substitute those into the equation<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%28%280.6480%29%2A60%29%2F%281.2%29%5E2 ALIGN=MIDDLE  ALT=\"R+=+%28%280.6480%29%2A60%29%2F%281.2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time ... If you work this out you should get 27 ohms for the value of R (the resistance).<BR>\n" );
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document.write( "Hope this helps you with this problem.  <BR>\n" );
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