=for timestamp
Mi Feb 15 16:48:42 CET 2006

=head2 60. Hausaufgabe

=head3 Wechselstromkreisanalyse

=for comment
Beispiel-Stromkreis im 10.tk-Format:
         Ig
     +---Ø---+
     |       |
     +     +-+-+
   Ug      |   |
     +   IcØ   ØIl
     |     |   |
     |    -+- +-+
     |     C  | |L
     |    -+- +-+
     |     |   |
     |     +-+-+
     |       |
     +-------+
Kompilation mit: recode utf-8..iso-8859-15 < /tmp/ZZ |
~/programmieren/genuineng/genuineword-0.96/ascii2fig 250 .3666 1 > /tmp/Z.fig

=helper MyBook::Helper::XFig

#FIG 3.2
Landscape
Center
Metric
A4      
100.00
Single
-2
1200 2
4 0 0 50 0 4 14 0.0000 0 0 250 50 200 
\001
4 0 0 50 0 4 14 0.0000 0 0 250 300 200 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1300 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1550 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 450 I\001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 450 g\001
4 0 0 50 0 4 14 0.0000 0 0 250 2800 450 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 700  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 750 1375 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 625 1375 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1500 625 1375 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1500 625 1750 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1750 625 2000 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2000 625 2250 625
4 0 0 50 0 4 14 0.0000 0 0 250 2300 700 O\001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2250 500 2500 750
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2500 500 2250 750
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2500 625 2750 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2750 625 3000 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 625 3250 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 750 3375 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3250 625 3375 625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 625 3375 625
4 0 0 50 0 4 14 0.0000 0 0 250 3550 700 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 750 1375 1000
4 0 0 50 0 4 14 0.0000 0 0 250 1550 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2800 950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3050 950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 750 3375 1000
4 0 0 50 0 4 14 0.0000 0 0 250 3550 950 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 1200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 1125 1375 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 1000 1375 1125
4 0 0 50 0 4 14 0.0000 0 0 250 1550 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 1200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 1200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 1250 2875 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 1125 2875 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 1125 2875 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 1125 3250 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3250 1125 3375 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 1125 3375 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3500 1125 3375 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 1000 3375 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3500 1125 3750 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 1250 3875 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 1125 3875 1125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 1125 3875 1125
4 0 0 50 0 4 14 0.0000 0 0 250 4050 1200 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 1450 U\001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 1450 g\001
4 0 0 50 0 4 14 0.0000 0 0 250 1300 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1550 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 1450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 1250 2875 1500
4 0 0 50 0 4 14 0.0000 0 0 250 3050 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3300 1450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3550 1450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 1250 3875 1500
4 0 0 50 0 4 14 0.0000 0 0 250 4050 1450 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 1700  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 1750 1375 1625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 1625 1375 1625
4 0 0 50 0 4 14 0.0000 0 0 250 1550 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 1700 I\001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 1700 c\001
4 0 0 50 0 4 14 0.0000 0 0 250 2800 1700 O\001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2750 1500 3000 1750
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 1500 2750 1750
4 0 0 50 0 4 14 0.0000 0 0 250 3050 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3300 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3550 1700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3800 1700 O\001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 1500 4000 1750
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4000 1500 3750 1750
4 0 0 50 0 4 14 0.0000 0 0 250 4050 1700 I\001
4 0 0 50 0 4 14 0.0000 0 0 250 4300 1700 l\001
4 0 0 50 0 4 14 0.0000 0 0 250 4550 1700 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 1950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 1750 1375 2000
4 0 0 50 0 4 14 0.0000 0 0 250 1550 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 1950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 1750 2875 2000
4 0 0 50 0 4 14 0.0000 0 0 250 3050 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3300 1950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3550 1950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 1750 3875 2000
4 0 0 50 0 4 14 0.0000 0 0 250 4050 1950 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 2200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 2000 1375 2250
4 0 0 50 0 4 14 0.0000 0 0 250 1550 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 2200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 2200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2500 2125 2750 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2750 2125 2875 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 2125 2875 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 2125 2875 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 2000 2875 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 2125 3250 2125
4 0 0 50 0 4 14 0.0000 0 0 250 3300 2200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3625 2250 3625 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3625 2125 3625 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 2125 3625 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 2125 4000 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4125 2250 4125 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4000 2125 4125 2125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4125 2125 4125 2125
4 0 0 50 0 4 14 0.0000 0 0 250 4300 2200 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 2450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 2250 1375 2500
4 0 0 50 0 4 14 0.0000 0 0 250 1550 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2800 2450 C\001
4 0 0 50 0 4 14 0.0000 0 0 250 3050 2450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3300 2450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3625 2250 3625 2500
4 0 0 50 0 4 14 0.0000 0 0 250 3800 2450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4125 2250 4125 2500
4 0 0 50 0 4 14 0.0000 0 0 250 4300 2450 L\001
4 0 0 50 0 4 14 0.0000 0 0 250 4550 2450 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 2700  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 2500 1375 2750
4 0 0 50 0 4 14 0.0000 0 0 250 1550 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 2700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 2700  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2500 2625 2750 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 2750 2875 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2750 2625 2875 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 2625 2875 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 2625 2875 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 2625 3250 2625
4 0 0 50 0 4 14 0.0000 0 0 250 3300 2700  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3625 2625 3625 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 2625 3625 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3625 2500 3625 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 2625 4000 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4000 2625 4125 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4125 2625 4125 2625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   4125 2500 4125 2625
4 0 0 50 0 4 14 0.0000 0 0 250 4300 2700 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 2950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 2750 1375 3000
4 0 0 50 0 4 14 0.0000 0 0 250 1550 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 2950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 2750 2875 3000
4 0 0 50 0 4 14 0.0000 0 0 250 3050 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3300 2950  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3550 2950  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 2750 3875 3000
4 0 0 50 0 4 14 0.0000 0 0 250 4050 2950 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 3200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 3000 1375 3250
4 0 0 50 0 4 14 0.0000 0 0 250 1550 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 3200  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 3200  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 3125 2875 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 3125 2875 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2875 3000 2875 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 3125 3250 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 3250 3375 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3250 3125 3375 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 3125 3375 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3500 3125 3375 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3500 3125 3750 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3750 3125 3875 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 3125 3875 3125
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3875 3000 3875 3125
4 0 0 50 0 4 14 0.0000 0 0 250 4050 3200 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 3450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 3250 1375 3500
4 0 0 50 0 4 14 0.0000 0 0 250 1550 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1800 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2050 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2300 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2550 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 2800 3450  \001
4 0 0 50 0 4 14 0.0000 0 0 250 3050 3450  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 3250 3375 3500
4 0 0 50 0 4 14 0.0000 0 0 250 3550 3450 \001
4 0 0 50 0 4 14 0.0000 0 0 250 50 3700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 300 3700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 550 3700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 800 3700  \001
4 0 0 50 0 4 14 0.0000 0 0 250 1050 3700  \001
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 3625 1375 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1500 3625 1375 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1375 3500 1375 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1500 3625 1750 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   1750 3625 2000 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2000 3625 2250 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2250 3625 2500 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2500 3625 2750 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   2750 3625 3000 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3000 3625 3250 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3250 3625 3375 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 3625 3375 3625
2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2
   3375 3500 3375 3625
4 0 0 50 0 4 14 0.0000 0 0 250 3550 3700 \001

=hend

=over

=item Wechselstromwiderstände von Kondensator und Spule

M<R_{C_\omega} = \frac{1}{\omega C};>

M<R_{L_\omega} = \omega L;>

M<\omega_0 = \frac{1}{\sqrt{L C}};>

M<\hat U_G = \sqrt{2} \, U_{G_{\text{eff}}};>

=item Terme für den Gesamtwiderstand und die Ströme M<I_{G_\omega}(t)>,
M<I_{C_\omega}(t)>, M<I_{L_\omega}(t)>

⇒ M<R_\omega = \dfrac{1}{\frac{1}{R_{C_\omega}} + \frac{1}{R_{L_\omega}}} =
\dfrac{\omega L}{\omega^2 L C + 1};>

⇒ M<I_{G_\omega}(t) = \frac{U_{G_\omega}(t)}{R_\omega} = \hat U_G \sin
\omega t \cdot \frac{\omega^2 L C + 1}{\omega L};>

⇒ M<I_{C_\omega}(t) = \frac{U_{G_\omega}(t)}{R_{C_\omega}} = \hat U_G \sin \omega
t \cdot \omega C = \underbrace{\hat U_G \cdot \omega C}_{\hat I_{C_\omega}} \cdot
\sin \omega t;>

⇒ M<I_{L_\omega}(t) = \frac{U_{G_\omega}(t)}{R_{L_\omega}} = \hat U_G \sin \omega
t \cdot \frac{1}{\omega L};>

=item Grenzwertbetrachtungen

=over

=item *

Betrachtung des Gesamtwiderstandes M<R_\omega>:

M<\lim\limits_{\omega \to 0 \frac{1}{\mathrm{s}}} R_\omega = 0 \,\Omega;>
(Einsetzen)

M<\lim\limits_{\omega \to \infty \frac{1}{\mathrm{s}}} R_\omega = 0 \,\Omega;>
(Grad des Polynoms des Zählers kleiner als der des Nenners)

M<R_{\omega_0} = \dfrac{L}{\sqrt{L C} \left(\frac{1}{LC} LC + 1\right)} =
\sqrt{\frac{L}{2 C}};>

Anschaulich: Bei M<\omega \to 0 \frac{1}{\mathrm{s}}> liegt Gleichstrom vor;
der Kondensator leitet also gar nicht und die Spule ideal. Bei M<\omega \to
\infty \frac{1}{\mathrm{s}}> leitet die Spule gar nicht und der Kondensator
ideal.

=item *

Betrachtung des Stroms durch den Kondensator M<C_{L_\omega}(t)>:

M<\lim\limits_{\omega \to 0 \frac{1}{\mathrm{s}}} I_{C_\omega}(t) = 0
\,\mathrm{A};> (Einsetzen)

Bei Gleichstrom ist der Kondensator ein Nichtleiter, M<I_{C_\omega}(t)> ist
Null.

M<\lim\limits_{\omega \to \infty \frac{1}{\mathrm{s}}} I_{C_\omega}(t)> ist
nicht definiert (Sinus konvergiert nicht). Stattdessen Betrachtung von M<\hat
I_{C_\omega}>:

M<\hat I_{C_\omega} = \hat U_G \cdot \omega C \to \infty \,\mathrm{A}> für
M<\omega \to \infty \frac{1}{\mathrm{s}};>

M<I_{C_{\omega_0}}(t) = \hat U_G \sin \sqrt{\frac{t^2}{LC}} \cdot
\sqrt{\frac{C}{L}};>

=item *

Betrachtung des Stroms durch die Spule M<I_{L_\omega}(t)>:

M<\lim\limits_{\omega \to 0 \frac{1}{\mathrm{s}}} I_{L_\omega}(t) =
\lim\limits_{\omega \to 0 \frac{1}{\mathrm{s}}} \frac{\hat U_G}{L} \frac{\sin
\omega t}{\omega} = \lim\limits_{\omega \to 0 \frac{1}{\mathrm{s}}} \frac{\hat
U_G}{L} \frac{\sin \omega t}{\omega t} \cdot t = \frac{\hat U_G}{L} \cdot t;>
(M<\lim\limits_{x \to 0} \frac{\sin x}{x} = 1>)

Damit nimmt der Strom proportional mit der Zeit zu. Dies entspricht unseren
Erwartungen: Da die Spule bei Gleichstrom (M<\omega \to 0
\frac{1}{\mathrm{s}}>) ein idealer Leiter ist, ist ihr Widerstand Null und
damit geht der Strom für M<t \to \infty \,\mathrm{s}> gegen Unendlich.

M<\lim\limits_{\omega \to \infty \frac{1}{\mathrm{s}}} I_{L_\omega}(t) = 0
\,\mathrm{A};> (Zähler "schwankt" zwischen M<-\hat U_G> und M<\hat U_G>, Nenner
geht gegen Unendlich)

Die Spule ist bei "unendlich frequenten" Wechselstrom ein Nichtleiter.

M<I_{L_{\omega_0}}(t) = \hat U_G \sin \sqrt{\frac{t^2}{LC}} \cdot
\sqrt{\frac{C}{L}};>

=back

=item Abschließende Bemerkungen

Im Resonanzfall ist M<I_{C_{\omega_0}}(t)> für alle Zeitpunkte M<t> gleich
M<I_{L_{\omega_0}}(t)>!

=item Graph des Gesamtwiderstandes in Abhängigkeit von M<\omega>

=helper MyBook::Helper::Gnuplot

# File automatically generated by Webplot, a webfrontend for Gnuplot written by
# Ingo Blechschmidt <iblech@web.de>, on Wed, 15 Feb 2006 17:39:22 CET.

# Global settings
set samples 10000
unset border
set xtics axis
set ytics axis
set xzeroaxis lt -1
set yzeroaxis lt -1

# Coordinate system settings
set title ""
set xlabel "\nomega/(1/s)\n"
set ylabel "R/Omega\n"
set xrange [ -0.000001 : 10.000000 ]
set yrange [ -0.000001 : 0.600000 ]
set grid
set xtics 1000.000000
set ytics 1000.000000

set xtics ("0" 0, "sqrt(1/C)" 1)

# Function definitions
func0(x) = x/(x**2.+1.)

# Plotting
plot func0(x) t "R_omega" w l lt 1

=hend

Interessant ist, dass der Gesamtwiderstand bei M<\omega = \sqrt{\frac{1}{C}}>
ist (ermittelbar durch den Ansatz M<R_\omega' = 0
\frac{\mathrm{Vs}}{\mathrm{A}}>). Dieses M<\omega> ist nicht von M<L> abhängig!

=item Graph der maximalen Generatorstromstärke in Abhängigkeit von M<\omega>

=helper MyBook::Helper::Gnuplot

# File automatically generated by Webplot, a webfrontend for Gnuplot written by
# Ingo Blechschmidt <iblech@web.de>, on Wed, 15 Feb 2006 17:54:22 CET.

# Global settings
set samples 10000
unset border
set xtics axis
set ytics axis
set xzeroaxis lt -1
set yzeroaxis lt -1

# Coordinate system settings
set title ""
set xlabel "\nomega/(1/s)\n"
set ylabel "I/A\n"
set xrange [ -0.010000 : 5.000000 ]
set yrange [ -0.010000 : 5.000000 ]
set grid
set xtics 1000.000000
set ytics 1000.000000

set xtics ("0" 0, "1/sqrt(LC)" 1)

# Function definitions
func0(x) = (x**2.+1.)/x

# Plotting
plot func0(x) t "I_G_max_omega" w l lt 1

=hend

Interessant ist, dass die Scheitelstromstärke des Generators bei M<\omega_0>
minimal ist (ermittelbar durch den Ansatz M<\hat I_{G_\omega}' = 0
\,\mathrm{C}>).

=item Graph der maximalen Energie in Abhängigkeit von M<\omega>

M<E_{\text{max}_\omega} = E_{L_{\text{max}_\omega}} +
E_{C_{\text{max}_\omega}} = \frac{1}{2} L \omega^2 \cdot \hat Q^2 \cos^2 \omega
t + \frac{1}{2} \frac{1}{C} \cdot \hat Q^2 \sin^2 \omega t = \frac{1}{2} \hat
Q^2 \left(\cos^2 \omega t + \sin^2 \omega t\right) \left(L \omega^2 +
\frac{1}{C}\right) = \frac{1}{2} \hat Q^2 \left(L \omega^2 +
\frac{1}{C}\right);>

Also nimmt der maximale Energieinhalt mit größer werdendem M<\omega> zu; es
ergibt sich kein Umkehrpunkt.

=helper MyBook::Helper::Gnuplot

# File automatically generated by Webplot, a webfrontend for Gnuplot written by
# Ingo Blechschmidt <iblech@web.de>, on Wed, 15 Feb 2006 17:54:22 CET.

# Global settings
set samples 10000
unset border
set xtics axis
set ytics axis
set xzeroaxis lt -1
set yzeroaxis lt -1

# Coordinate system settings
set title ""
set xlabel "\nomega/(1/s)\n"
set ylabel "E/J\n"
set xrange [ -0.010000 : 5.000000 ]
set yrange [ -0.010000 : 5.000000 ]
set grid
set xtics 1000.000000
set ytics 1000.000000

# Function definitions
func0(x) = x**2

# Plotting
plot func0(x) t "E_max_omega" w l lt 1

=hend

=back

(Benötigte Zeit: 140 min)