document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697149>Question 697149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The potential difference across a circuit is given by the complex number\r<BR>\n" );
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document.write( "V = 40 + j35 volts\r<BR>\n" );
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document.write( "and the current is given by the complex number\r<BR>\n" );
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document.write( "I = 6 + j3 amps\r<BR>\n" );
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document.write( "a) sketch the appropriate phasors on an Argand diagram.\r<BR>\n" );
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document.write( "b) find the phase difference (i.e. the angle &#934; )between the phasors for voltage \r<BR>\n" );
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document.write( "   V and the current I.\r<BR>\n" );
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document.write( "c) Find the power (watts) given that P = V x I x cos &#934; </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430081 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=430081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> V = 40 + j35 volts and I = 6 + j3 amps <BR>\n" );
document.write( "a) sketch the appropriate phasors on an Argand diagram. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C45%2C-5%2C45%2C%0D%0Agrid%280%29%2Cgreen%28line%280%2C0%2C32%2C28%29%29%2C%0D%0Agreen%28arrow%2832%2C28%2C40%2C35%29%29%2Cblue%28arrow%280%2C0%2C6%2C3%29%29%2C%0D%0Alocate%286.5%2C3%2CI+=+6+%2B+j3%29%2Clocate%2833%2C38%2CV+=+40+%2B+j35%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "b) find the phase difference<BR>\n" );
document.write( "The angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > between the voltage V and the real, x-axis can be found from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28alpha%29=35%2F40=0.875 ALIGN=MIDDLE  ALT=\"tan%28alpha%29=35%2F40=0.875\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+0.71883 ALIGN=MIDDLE  ALT=\"alpha+=+0.71883\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians (rounded)<BR>\n" );
document.write( "The angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta ALIGN=MIDDLE  ALT=\"beta\"   DISABLED_style= \"max-width:90%; height:auto;\" > between the current I and the real, x-axis can be found from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28beta%29=3%2F6=0.5 ALIGN=MIDDLE  ALT=\"tan%28beta%29=3%2F6=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta+=+0.46365 ALIGN=MIDDLE  ALT=\"beta+=+0.46365\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians (rounded)<BR>\n" );
document.write( "We can calculate very close approximations of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=phi ALIGN=MIDDLE  ALT=\"phi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28phi%29 ALIGN=MIDDLE  ALT=\"cos%28phi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=phi=alpha-beta=0.71883-0.46365=0.25518 ALIGN=MIDDLE  ALT=\"phi=alpha-beta=0.71883-0.46365=0.25518\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians (approx <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.6%5Eo ALIGN=MIDDLE  ALT=\"14.6%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > in degrees)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28phi%29=cos%280.25518%29=0.9676 ALIGN=MIDDLE  ALT=\"cos%28phi%29=cos%280.25518%29=0.9676\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( " <BR>\n" );
document.write( "c) Find the power (watts) given that P = V x I x cos &#934;<BR>\n" );
document.write( "The magnitudes of V and I are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=sqrt%2840%5E2%2B35%5E2%29=53.151 ALIGN=MIDDLE  ALT=\"V=sqrt%2840%5E2%2B35%5E2%29=53.151\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=sqrt%286%5E2%2B3%5E2%29=6.7082 ALIGN=MIDDLE  ALT=\"I=sqrt%286%5E2%2B3%5E2%29=6.7082\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=V%2AI%2Acos%28phi%29=53.151%2A6.7082%2A0.9676=highlight%28345%29 ALIGN=MIDDLE  ALT=\"P=V%2AI%2Acos%28phi%29=53.151%2A6.7082%2A0.9676=highlight%28345%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >watt </SPAN>\n" );
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