document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88283>Question 88283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi there, posted the problem below before but forgot a part of it, \r<BR>\n" );
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document.write( "by equating real and imaginary parts find expressions for R6 and L in terms of R1, R2, R3, R4, R5 AND C given that the freq is one rad per second. w=freq <BR>\n" );
document.write( "(R1-j/wC)/(R4+R5) = (R2+R3)/(R6+jwL)\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64116 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=64116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Haven't had my caffeine fix for the day, so make sure you check my work step by step to<BR>\n" );
document.write( "catch any mistakes that I might make.<BR>\n" );
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document.write( "Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R1+-+j%281%2F%28wC%29%29%29%2F%28R4+%2B+R5%29+=+%28R2+%2B+R3%29%2F%28R6+%2B+j%28wL%29%29 ALIGN=MIDDLE  ALT=\"%28R1+-+j%281%2F%28wC%29%29%29%2F%28R4+%2B+R5%29+=+%28R2+%2B+R3%29%2F%28R6+%2B+j%28wL%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since you are told that w = 1 radian per second, let's simplify the problem a little by<BR>\n" );
document.write( "substituting 1 for w to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R1+-+j%281%2FC%29%29%2F%28R4+%2B+R5%29+=+%28R2+%2B+R3%29%2F%28R6+%2B+j%28L%29%29 ALIGN=MIDDLE  ALT=\"%28R1+-+j%281%2FC%29%29%2F%28R4+%2B+R5%29+=+%28R2+%2B+R3%29%2F%28R6+%2B+j%28L%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, since you are interested in solving for R6 + jL, let's get that term into the numerator<BR>\n" );
document.write( "by inverting both sides of the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R4+%2B+R5%29%2F%28R1+-+j%281%2FC%29%29+=+%28R6+%2B+j%28L%29%29%2F%28R2+%2B+R3%29 ALIGN=MIDDLE  ALT=\"%28R4+%2B+R5%29%2F%28R1+-+j%281%2FC%29%29+=+%28R6+%2B+j%28L%29%29%2F%28R2+%2B+R3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then multiply both sides by (R2 + R3) to eliminate the denominator on the right side and<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%29%2F%28R1-j%281%2FC%29%29+=+%28R6+%2B+j%28L%29%29 ALIGN=MIDDLE  ALT=\"%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%29%2F%28R1-j%281%2FC%29%29+=+%28R6+%2B+j%28L%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then multiply the left side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R1+%2B+j%281%2FC%29%29%2F%28R1+%2B+j%281%2FC%29%29 ALIGN=MIDDLE  ALT=\"%28R1+%2B+j%281%2FC%29%29%2F%28R1+%2B+j%281%2FC%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The numerator and the<BR>\n" );
document.write( "denominator of this multiplier are the complex conjugate of the denominator of the left<BR>\n" );
document.write( "side of the equation.  This multiplication will change the denominator of the left side<BR>\n" );
document.write( "of our equation from complex to real ... and note that the multiplier is a fraction<BR>\n" );
document.write( "that is equal to 1 so it doesn't affect the equation we have.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%2A%28R1%2Bj%281%2FC%29%29%29%2F%28%28R1-j%281%2FC%29%29%2A%28R1%2Bj%281%2FC%29%29%29+=+%28R6+%2B+j%28L%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying out the denominator on the left side results in it becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R1%5E2+-+j%5E2%281%2FC%29%5E2 ALIGN=MIDDLE  ALT=\"R1%5E2+-+j%5E2%281%2FC%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=j%5E2+=+-1 ALIGN=MIDDLE  ALT=\"j%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R1%5E2+%2B%281%2FC%29%5E2 ALIGN=MIDDLE  ALT=\"R1%5E2+%2B%281%2FC%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This<BR>\n" );
document.write( "makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%2A%28R1%2Bj%281%2FC%29%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29+=+%28R6+%2B+j%28L%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the denominator is no longer a complex number. Next you can multiply out the <BR>\n" );
document.write( "numerator by multiplying [(R1 + R5)*(R2 + R3)] times the two terms that make up the complex <BR>\n" );
document.write( "number in the numerator. This multiplication changes the left side numerator and the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%2A%28R1%29+%2Bj%28%28R4%2BR5%29%2A%28R2%2BR3%29%2A%281%2FC%29%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29+=+R6+%2B+j%28L%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now divide the denominator (which is real) into the real and the reactive components of<BR>\n" );
document.write( "the numerator to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%2A%28R1%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29%2Bj%28%28R4%2BR5%29%2A%28R2%2BR3%29%2A%281%2FC%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29=+R6+%2B+jL ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can set real and reactive components equal to find that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R6+=+%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%2A%28R1%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29 ALIGN=MIDDLE  ALT=\"R6+=+%28%28R4+%2B+R5%29%2A%28R2%2BR3%29%2A%28R1%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+%28%28R4%2BR5%29%2A%28R2%2BR3%29%2A%281%2FC%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29 ALIGN=MIDDLE  ALT=\"L+=+%28%28R4%2BR5%29%2A%28R2%2BR3%29%2A%281%2FC%29%29%2F%28R1%5E2%2B%281%2FC%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As I said at the \"git-go\", I suggest you track this step by step to catch any math errors.<BR>\n" );
document.write( "The general approach is correct, but this is sort of complex to type out and I may have<BR>\n" );
document.write( "introduced some glitches.  <BR>\n" );
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document.write( "Hope this helps ... </SPAN>\n" );
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