=for timestamp Mi Sep 21 18:03:46 CEST 2005 =head2 5. Hausaufgabe =head3 Analyse eines verzweigten Stromkreises =for comment Beispiel-Stromkreis im 10.tk-Format: +-+ +-+1+--+-------+-------+ | +-+ | | | | | | +--+--+ | +-+ Þ+ | | | | | | | | +++ | | | | |4| | | +++ +++ +++ +++ | |2| |3| | |6| | +++ +++ +++ +++ | | | |5| | | | | +++ | | | | | | | | +--+--+ | | | | | +-----------+-------+-------+ 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 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 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4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 3250 4125 3500 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 3500 4125 3750 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 3750 4125 4000 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 4000 4125 4250 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 4250 4125 4500 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 4500 4125 4750 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 4750 4125 5000 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5000 4125 5125 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5125 4125 5125 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5250 4125 5125 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5125 4000 5125 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5250 4125 5500 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5500 4125 5750 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5750 4125 6000 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 6000 4125 6250 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 6250 4125 6500 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 6500 4125 6750 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 6750 4125 7000 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 7000 4125 7125 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 7125 4125 7125 4125 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 7125 4000 7125 4125 4 0 0 50 0 4 14 0.0000 0 0 250 7300 4200 \001 =hend =over =item Gegeben M bis M betragen M<10{,}0 \,\Omega>, M sei variabel. M =item Gesucht M, M, M<\\> M, M =item Rechnung M M M M M M M<\renewcommand{\arraystretch}{2.5}\begin{array}{ll}I_6(R_6) = I_6 = \frac{U_6}{R_6} & = \dfrac{U}{\left(R_1 + \dfrac{1}{\frac{1}{R_6} + \frac{5}{2 R_1}}\right) \Biggl(\dfrac{1}{R_6} + \dfrac{5}{2 R_1}\Biggr) R_6} = \\ & = \dfrac{9{,}00 \,\mathrm{V}}{\left(10{,}0 \,\Omega + \dfrac{1}{\frac{1}{R_6} + 0{,}250 \frac{1}{\,\Omega}}\right) \Biggl(\dfrac{1}{R_6} + 0{,}250 \frac{1}{\,\Omega}\Biggr) R_6};\end{array}> M<\renewcommand{\arraystretch}{2.5}\begin{array}{ll}P_6(R_6) = P_6 = U_6 I_6 & = \dfrac{U^2}{\left(R_1 + \dfrac{1}{\frac{1}{R_6} + \frac{5}{2 R_1}}\right)^2 \Biggl(\frac{1}{R_6} + \frac{5}{2 R_1}\Biggr)^2 R_6} = \\ & = \dfrac{81{,}0 \,\mathrm{V}^2}{\left(10{,}0 \,\Omega + \dfrac{1}{\frac{1}{R_6} + 0{,}250 \frac{1}{\,\Omega}}\right)^2 \Biggl(\dfrac{1}{R_6} + 0{,}250 \frac{1}{\,\Omega}\Biggr)^2 R_6};\end{array}> =for comment_maxima R1:10.0*ohm; U:9.00*volt; R2:R1; R3:R1; R4:R1; R5:R1; R45:R4 + R5; R345:1/(1/R1 + 1/R45); R23456:1/(1/R2 + 1/R345 + 1/R6); R:R1 + R23456; I:U/R; U2:R23456*I; U6:U2; I6:U6/R6; P6:U6*I6; =item Grenzwertbetrachtungen M<< \renewcommand{\arraystretch}{1.5} \begin{array}{llcl} {} \lim\limits_{R_6 \to 0 \,\Omega} & R(R_6) & = & 10{,}0 \Omega; \\ {} \lim\limits_{R_6 \to \infty \,\Omega} & R(R_6) & = & 14{,}0 \Omega; \\ {} \lim\limits_{R_6 \to 0 \,\Omega} & I(R_6) & = & 0{,}900 \,\mathrm{A}; \\ {} \lim\limits_{R_6 \to \infty \,\Omega} & I(R_6) & = & 0{,}643 \,\mathrm{A}; \\ {} \lim\limits_{R_6 \to 0 \,\Omega} & I_6(R_6) & = & 0{,}900 \,\mathrm{A}; \\ {} \lim\limits_{R_6 \to \infty \,\Omega} & I_6(R_6) & = & 0 \,\mathrm{A}; \\ {} \lim\limits_{R_6 \to 0 \,\Omega} & P_6(R_6) & = & 0 \,\mathrm{W}; \\ {} \lim\limits_{R_6 \to \infty \,\Omega} & P_6(R_6) & = & 0 \,\mathrm{W}; \end{array} >> =back =helper MyBook::Helper::Gnuplot # File automatically generated by Plot.pm # 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 "\nR_6\n" set ylabel "" set xrange [ -0.010000 : 50.000000 ] set yrange [ -0.010000 : 14.000000 ] set grid set xtics 10.000000 set ytics 4.000000 # Function definitions func0(x) = 1./(1./x + 0.25) + 10. func1(x) = 9.00/(1./(1./x + 0.25) + 10.) func2(x) = 9.00/((1./(1./x + 0.25) + 10.)*(1./x+0.250)*x) func3(x) = 81./((1./(1./x + 0.25) + 10.)**2. * (1./x + 0.250)**2. * x) # Plotting plot func0(x) t "R(R_6)" w l lt 1, func1(x) t "I(R_6)" w l lt 2, func2(x) t "I_6(R_6)" w l lt 3, func3(x) t "P_6(R_6)" w l lt 4 =hend =for latex \vfill{} =helper MyBook::Helper::Gnuplot # File automatically generated by Plot.pm # 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 "\nR_6\n" set ylabel "" set xrange [ -0.010000 : 20.000000 ] set yrange [ -0.010000 : 1.000000 ] set grid set xtics 4.000000 set ytics 0.200000 # Function definitions func0(x) = 1./(1./x + 0.25) + 10. func1(x) = 9.00/(1./(1./x + 0.25) + 10.) func2(x) = 9.00/((1./(1./x + 0.25) + 10.)*(1./x+0.250)*x) func3(x) = 81./((1./(1./x + 0.25) + 10.)**2. * (1./x + 0.250)**2. * x) # Plotting plot func0(x) t "R(R_6)" w l lt 1, func1(x) t "I(R_6)" w l lt 2, func2(x) t "I_6(R_6)" w l lt 3, func3(x) t "P_6(R_6)" w l lt 4 =hend (Benötigte Zeit: 78 min (inkl. Eintippen, Grafik und Formatierung; reine Arbeitszeit 44 min))