document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261326>Question 261326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the voltage VL across an inductor L in an electrical circuit falls exponentially over time t. The relationship is VL = Vmax e^-t/T, Where T= L/R.<BR>\n" );
document.write( "If L= 4.5H and R = 270 calculate T?<BR>\n" );
document.write( "Vmax=10.4 volts<BR>\n" );
document.write( "Calculate V for values of t from o to 0.5 seconds at intervals of 0.01? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192532 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=192532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29 ALIGN=MIDDLE  ALT=\"VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "T = L/R<BR>\n" );
document.write( "L = inductance = 4.5<BR>\n" );
document.write( "R = resistance 270<BR>\n" );
document.write( "T = L/R = (4.5/270) = .016666666...<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "V[max] = 10.4 volts.\r<BR>\n" );
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document.write( "Calculate VL for values of t from 0 to .5 seconds at intervals of 0.01\r<BR>\n" );
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document.write( "When t = 0, the formula of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29 ALIGN=MIDDLE  ALT=\"VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+10.4+%2A+e%5E%28-0%2F.0166666666%29 ALIGN=MIDDLE  ALT=\"VL+=+10.4+%2A+e%5E%28-0%2F.0166666666%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.4+%2A+e%5E%280%29 ALIGN=MIDDLE  ALT=\"10.4+%2A+e%5E%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.4 ALIGN=MIDDLE  ALT=\"10.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When t = .1, the formula of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29 ALIGN=MIDDLE  ALT=\"VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+10.4+%2A+e%5E%28-.1%2F.0166666666%29 ALIGN=MIDDLE  ALT=\"VL+=+10.4+%2A+e%5E%28-.1%2F.0166666666%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.4+%2A+e%5E%28-6%29 ALIGN=MIDDLE  ALT=\"10.4+%2A+e%5E%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.025779023 ALIGN=MIDDLE  ALT=\".025779023\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When t = .4, the formula of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29 ALIGN=MIDDLE  ALT=\"VL+=+V%5Bmax%5D+%2A+e%5E%28-t%2FT%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VL+=+10.4+%2A+e%5E%28-.4%2F.0166666666%29 ALIGN=MIDDLE  ALT=\"VL+=+10.4+%2A+e%5E%28-.4%2F.0166666666%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.4+%2A+e%5E%28-24%29 ALIGN=MIDDLE  ALT=\"10.4+%2A+e%5E%28-24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.926139926%5E-10 ALIGN=MIDDLE  ALT=\"3.926139926%5E-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "t	v[max]	T	        VL = V[max] * e^(-(t/T))\r\n" );
document.write( "0	10.4	0.016666667	10.4\r\n" );
document.write( "0.01	10.4	0.016666667	5.707641015\r\n" );
document.write( "0.02	10.4	0.016666667	3.132419804\r\n" );
document.write( "0.03	10.4	0.016666667	1.719108438\r\n" );
document.write( "0.04	10.4	0.016666667	0.943466714\r\n" );
document.write( "0.05	10.4	0.016666667	0.517785511\r\n" );
document.write( "0.06	10.4	0.016666667	0.284166713\r\n" );
document.write( "0.07	10.4	0.016666667	0.155953999\r\n" );
document.write( "0.08	10.4	0.016666667	0.085589369\r\n" );
document.write( "0.09	10.4	0.016666667	0.046972442\r\n" );
document.write( "0.1	10.4	0.016666667	0.025779023\r\n" );
document.write( "0.11	10.4	0.016666667	0.014147828\r\n" );
document.write( "0.12	10.4	0.016666667	0.007764492\r\n" );
document.write( "0.13	10.4	0.016666667	0.004261244\r\n" );
document.write( "0.14	10.4	0.016666667	0.00233862\r\n" );
document.write( "0.15	10.4	0.016666667	0.001283462\r\n" );
document.write( "0.16	10.4	0.016666667	0.000704379\r\n" );
document.write( "0.17	10.4	0.016666667	0.000386571\r\n" );
document.write( "0.18	10.4	0.016666667	0.000212155\r\n" );
document.write( "0.19	10.4	0.016666667	0.000116433\r\n" );
document.write( "0.2	10.4	0.016666667	6.38998E-05\r\n" );
document.write( "0.21	10.4	0.016666667	3.5069E-05\r\n" );
document.write( "0.22	10.4	0.016666667	1.92463E-05\r\n" );
document.write( "0.23	10.4	0.016666667	1.05626E-05\r\n" );
document.write( "0.24	10.4	0.016666667	5.79686E-06\r\n" );
document.write( "0.25	10.4	0.016666667	3.18138E-06\r\n" );
document.write( "0.26	10.4	0.016666667	1.74598E-06\r\n" );
document.write( "0.27	10.4	0.016666667	9.58214E-07\r\n" );
document.write( "0.28	10.4	0.016666667	5.25879E-07\r\n" );
document.write( "0.29	10.4	0.016666667	2.88609E-07\r\n" );
document.write( "0.3	10.4	0.016666667	1.58392E-07\r\n" );
document.write( "0.31	10.4	0.016666667	8.69273E-08\r\n" );
document.write( "0.32	10.4	0.016666667	4.77067E-08\r\n" );
document.write( "0.33	10.4	0.016666667	2.6182E-08\r\n" );
document.write( "0.34	10.4	0.016666667	1.4369E-08\r\n" );
document.write( "0.35	10.4	0.016666667	7.88586E-09\r\n" );
document.write( "0.36	10.4	0.016666667	4.32785E-09\r\n" );
document.write( "0.37	10.4	0.016666667	2.37518E-09\r\n" );
document.write( "0.38	10.4	0.016666667	1.30352E-09\r\n" );
document.write( "0.39	10.4	0.016666667	7.15389E-10\r\n" );
document.write( "0.4	10.4	0.016666667	3.92614E-10\r\n" );
document.write( "0.41	10.4	0.016666667	2.15471E-10\r\n" );
document.write( "0.42	10.4	0.016666667	1.18253E-10\r\n" );
document.write( "0.43	10.4	0.016666667	6.48987E-11\r\n" );
document.write( "0.44	10.4	0.016666667	3.56171E-11\r\n" );
document.write( "0.45	10.4	0.016666667	1.95471E-11\r\n" );
document.write( "0.46	10.4	0.016666667	1.07277E-11\r\n" );
document.write( "0.47	10.4	0.016666667	5.88747E-12\r\n" );
document.write( "0.48	10.4	0.016666667	3.23111E-12\r\n" );
document.write( "0.49	10.4	0.016666667	1.77327E-12\r\n" );
document.write( "0.5	10.4	0.016666667	9.73193E-13\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "the graph of your equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C1%2C-1%2C12%2C10.4%2Ae%5E%28-%28x%2F%284.5%2F270%29%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1%2C1%2C-1%2C12%2C10.4%2Ae%5E%28-%28x%2F%284.5%2F270%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the following graph shows the smaller values a little better since the y values are taken up to 1 max only.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C1%2C-1%2C1%2C10.4%2Ae%5E%28-%28x%2F%284.5%2F270%29%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1%2C1%2C-1%2C1%2C10.4%2Ae%5E%28-%28x%2F%284.5%2F270%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "didn't matter too much as the drop off is very steep and the numbers after t = .2 are extremely small.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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