ET2_Uebung_BEI/ET2_L_Ergebnisse.tex

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\section{Ergebnisse}
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\textbf{\arabic{acounter} {Blitzableiter}} %\textbf{\arabic{acounter} Blitzableiter} \textbf{\arabic{acounter} {Blitzableiter}}
\stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\ 
$u=-133{,}7\,\volt$\\
\textbf{\arabic{acounter} Drahtschleife} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\ 
$u=-36{,}39\,\milli\volt$\\
\textbf{\arabic{acounter} Metallstab} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\ 
$|B_z|=0{,}398\,\frac{\volt\second}{\square\metre}$\\
\textbf{\arabic{acounter} Spannungsverlauf} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$f=40\,\hertz$\\
$\overline{|u|}=6\,\volt$\\
$U=7{,}30\,\volt$\\
$F=1{,}22$\\
$P=0{,}533\,\watt$\\
\textbf{\arabic{acounter} Phasenanschnitt} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$U=261\,\volt$\\
\textbf{\arabic{acounter} Rechteckspannung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$u_1=1{,}5\,\volt \qquad u_2=-3{,}5\,\volt\\
U=2{,}29\,\volt$\\
%% Blatt 13
\textbf{\arabic{acounter} Scheinersatzwiderstände} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter} \setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }\\
$R_r=520\,\ohm\\
L_r=60\,\milli\henry
G_p=693\,\ohm\\
L_p=239\,\milli\henry\\
\varphi'_r=23{,}5\,\degree\\
\varphi'_p=-37{,}6\,\degree$\\
\textbf{\arabic{acounter} Verbraucherleistung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$p(t)=1079\,\watt+1318\,\volt\ampere\cdot \sin(2\omega t+0{,}96)\\
S=1318\,\volt\ampere\\
P=1079\,\watt\\
Q=-756\,\mathrm{var}$\\
\textbf{\arabic{acounter} Blindleistungskompensation} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$I_N=20{,}63\,\ampere\\
\varphi_N=32,52\degree\\
C=153{,}6\,\micro\farad$\\
\textbf{\arabic{acounter} Energieübertragung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$X_C=-25\,\ohm\\
P_{VR_L}=46{,}7\,\watt\\
P_W=583\,\watt $\\
\textbf{\arabic{acounter} Wechselstrommotor} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$I=15{,}5\,\ampere\\
C=80{,}6\,\micro\farad\\
I'=12{,}1\,\ampere $\\
\clearpage
\textbf{\arabic{acounter} Parallelschaltung von L und C} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$i_L(t_2)=2{,}92\,\ampere $\\
\textbf{\arabic{acounter} Werte $R_L$ und $L$ einer Spule} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$I=1\,\ampere\\
R_L=12{,}5\,\ohm\\
L=0{,}219\,\henry $\\
%% Blatt 14
\textbf{\arabic{acounter} Zeigerdiagramm} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }\\
$\underline{U}_e=15\,\volt\cdot e^{+j90\degree}$\\
\textbf{\arabic{acounter} Gesamtwiderstand} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
Induktiv\\
\textbf{\arabic{acounter} Brückenschaltung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{U}_a=130\,\volt\cdot e^{j83\,\degree}$\\
\textbf{\arabic{acounter} Zeigerdiagramm Netzwerk} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$R_1=13{,}89\,\kilo\ohm$\\
\textbf{\arabic{acounter} Blind- Wirk- und Scheinleistung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{Z}=84{,}85\,\ohm\cdot e^{-j45\,\degree}=(60-j60)\,\ohm\\
\uline{I}=2{,}71\,\ampere\cdot e^{j45\,\degree}=(1{,}916+j1{,}916)\,\ampere\\
\uline{I}_{R_C}=1{,}21\,\ampere\cdot e^{-j18{,}4\,\degree}=(1{,}150-j0{,}383)\,\ampere\\
\uline{I}_{C}=2{,}42\,\ampere\cdot e^{+j71{,}6\,\degree}=(0{,}766+j2{,}30)\,\ampere\\
\uline{U}_{R_C}=242\,\volt\cdot e^{-j18{,}4\,\degree}\\
\uline{U}_{R_L}=54{,}2\,\volt\cdot e^{j45\,\degree}\\
\uline{U}_L=54.2\,\volt\cdot e^{j135\,\degree}\\
S=623\,\volt\ampere\\
P=447\,\watt\\
Q=-447\,\volt\ampere r $\\
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\textbf{\arabic{acounter} Komplexe Wechselstromrechnung Netzwerk Strom} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }\\
$\uline{I_2}=53{,}92\,\milli\ampere\cdot e^{j176{,}32\,\degree}$\\
\textbf{\arabic{acounter} Übergang Zeitabhängige zu Komplexen Größen} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{I}_L=34{,}45\,\milli\ampere\cdot e^{j50{,}83\,\degree}\\
i_L(T)=-25{,}79\,\milli\ampere$\\
\textbf{\arabic{acounter} Leitwert} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$R=500\,\ohm\\
B_C=2{,}175\,\milli\siemens$\\
\textbf{\arabic{acounter} Strom L-R-C} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{I}=0{,}4058\,\ampere\cdot e^{j67{,}4\,\degree}=(0{,}156+j0{,}375)\,\ampere $\\
\textbf{\arabic{acounter} Überlagerungsmethode} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{I}_C=(578{,}41+j279{,}99)\,\milli\ampere=642{,}6\,\milli\ampere\cdot  e^{+j25{,}38\,\degree}$\\
\textbf{\arabic{acounter} Momentan Leistung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$u_R(T)=-114{,}1\,\milli\volt\\
u_L(T)=-50{,}5\,\milli\volt\\
u_C(T)=119{,}7\,\milli\volt\\
p(T)=0{,}427\,\milli\watt$\\
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\textbf{\arabic{acounter} CLR Netzwerk} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }\\
$S=243{,}32\,\milli\volt\ampere\\
P=141{,}50\,\milli\watt\\
Q=-197{,}93\,\milli\,\var$\\
\textbf{\arabic{acounter} Wirkleistung vs. Blindleistung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
--\\
\textbf{\arabic{acounter} Wirkleistung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$R_v=17{,}24\,\ohm\\
C=19{,}14\,\micro\farad\\
P_{v\text{,}max}=14{,}5\,\milli\watt$
\textbf{\arabic{acounter} Abgebbare Wirkleistung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$F_ \% =-78{,}8\, \%$\\
\textbf{\arabic{acounter} Wirkleistung Spannungsquelle} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$P=-16{,}31\,\milli\watt$\\
\textbf{\arabic{acounter} Dualitätskonstante} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$L_2=100\,\milli\henry\\
C_2=5\,\micro\farad$
\textbf{\arabic{acounter} Dualitätskonstante verlustbehaftete Bauelemente} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$R_G=1\,\milli\henry\\
G_R=2\,\milli\siemens\\
C_L=100\,\nano\farad$\\
\textbf{\arabic{acounter} Vierpol Y-Parameter} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{Y}_L=\frac{1}{j\omega\cdot L}=-j\frac{1}{\omega\cdot L}\\
\uline{Y}_{11}=\frac{1}{3}\cdot \uline{Y}_L\\
\uline{Y}_{12}=-\frac{1}{6}\cdot \uline{Y}_L\\
\uline{Y}_{22}=\uline{Y}_{11}=\frac{1}{3}\cdot \uline{Y}_L=\\
\uline{Z}_{11}=\uline{Z}_{24}= 4\cdot j\omega\cdot L\\
\uline{Z}_{12}=\uline{Z}_{21}= 2\cdot j\omega\cdot L$\\
\textbf{\arabic{acounter} Spannung Vierpol} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{U}_0=130{,}4\,\milli\volt$\\
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\textbf{\arabic{acounter} Stromortskurve} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }\\
$\uline{I}=236\,\milli\ampere\cdot e^{(j35{,}2\,\degree)}=(193+j136)\,\milli\ampere$\\
\textbf{\arabic{acounter} Leitwerts-, Widerstandsortskurve} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
--
\textbf{\arabic{acounter} Ortskurve} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$f_g=828{,}9\,\hertz\\
a=-4{,}9\,\deci\bel$\\
\textbf{\arabic{acounter} Stromortskurve} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$I_{max}=5{,}55\,\milli\ampere $\\
\textbf{\arabic{acounter} Widerstandstransformation} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$X_L{_p}=12{,}2\,\kilo\ohm\\
X_{C_s}=-5{,}6\,\kilo\ohm\\
{X_{L_s}}=+2{,}6\,\kilo\ohm\\
X_{C_p}=-4{,}2\,\kilo\ohm $\\
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\textbf{\arabic{acounter} Brückenschaltung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{U}_{ab}=+j100\,\volt=100\,\volt\cdot e^{+j90\degree} $
\textbf{\arabic{acounter} Wechselstrombrücke} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$ \uline{Z}_2=(1+j0{,}5)\,\kilo\ohm\\
R_2=1{,}25\,\kilo\ohm\\
L_2=2{,}5\,\milli\henry$\\
\textbf{\arabic{acounter} Wechselstrombrücke} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$X=+\frac{R^2}{X_L}$\\
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\textbf{\arabic{acounter} Übertrager im Leerlauf} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }\\
$Z_1=23\,\ohm\cdot e^{j77{,}44\,\degree}\\
P=500\,\watt\\
Q=2245\,var\\
\omega L_1=22{,}45\,\ohm\\
\omega M=10\,\ohm\\
\omega L_2=4{,}45\,\ohm$\\
\textbf{\arabic{acounter} Übertrager mit kapazitiver Last} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{U}_2=0{,}398\,\volt\cdot e^{-j174{,}3\,\degree}\\
\uline{U}_2=0{,}42\,\volt\cdot e^{+j18{,}4\,\degree}\\
P_2=178\,\micro\watt $\\
\textbf{\arabic{acounter} Übertrager mit Verbindung zum Eingang} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{U}_{ab}=200\,\volt\cdot e^{j73{,}74\,\degree}\\
\uline{U}_S=317\,\volt\cdot e^{j79{,}8\,\degree}\\
\uline{I}=0{,}689\,\ampere\cdot e^{-j8{,}43\,\degree}\\ 
\uline{U}_{ab}=159\,\volt\cdot e^{+j71{,}7\,\degree}\\
P=12{,}2\,\watt$\\
\textbf{\arabic{acounter} Impedanzmatrix} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{Z}_{11}=(730+j100)\,\ohm\\
\uline{Z}_{12}=\uline{Z}_{21}=1200\,\ohm\\
\uline{Z}_{22}=(2000-j200)\,\ohm $\\
\textbf{\arabic{acounter} Netztransformator} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$U_2=105{,}1\,\volt\\
I_1=118\,\milli\ampere\\
\widehat{B}=1{,}095\,\tesla$\\
\textbf{\arabic{acounter} 3-Phasen Spannungssystem} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{I}_N=10{,}6\,\ampere\cdot e^{j14{,}7\,\degree} $\\
\textbf{\arabic{acounter} 3-Phasen System mit unsymmetrischem Verbraucher} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$P=-335{,}44\,\watt $\\
\textbf{\arabic{acounter} Strangströme 3-Phasen System mit unsymmetrischem
Verbraucher} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{I}_C=4\,\ampere\cdot e^{j120\,\degree}=(-2+j3{,}46)\,\ampere\\
\uline{I}_{RL}=4\,\ampere\cdot e^{j113{,}1\,\degree}=(-1{,}57+j3{,}68)\,\ampere\\
\uline{I}_1=0{,}48\,\ampere\cdot e^{-j153\,\degree}\\
\uline{I}_2=3{,}66\,\ampere\cdot e^{j109{,}1\,\degree}\\
\uline{I}_3=4{,}03\,\ampere\cdot e^{j66{,}1\,\degree}\\
P=1280\,\watt $
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\textbf{\arabic{acounter} Resonanzfrequenz Zweipol} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }
$f_{res}=899\,\hertz\\
Z=37{,}5\,\ohm $\\
\textbf{\arabic{acounter} RLC-Reihenschwingkreis} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$R=10\,\ohm\\
C=3{,}47\,\micro\farad\\
L=35{,}4\,\milli\henry$\\
\textbf{\arabic{acounter} Effektivwert und Klirrfaktor} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$I_{\mu}=7{,}36\,\milli\ampere\\
k_{\mu}=27{,}7\%\\
I_0=7{,}88\,\milli\ampere\\
k_0=25{,}8\%$\\
\textbf{\arabic{acounter} Klirrfaktor} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$k_a=21{,}5\%\\
U_a=2{,}49\,\volt$\\
\textbf{\arabic{acounter} Momentanspannung} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$u_C(t=T=2\,\micro\second)=1{,}315\,\volt $\\
\textbf{\arabic{acounter} Nichtlinears Bauelement} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$k_i=19{,}61\%$\\
\textbf{\arabic{acounter} Wirkleistung Zweipol} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$P=573\,\watt$\\

%% Blatt 20
\textbf{\arabic{acounter} Ringspule} \stepcounter{bcounter}\stepcounter{acounter}\textbf{(B\arabic{bcounter}\setcounter{bsubcounter}{1}A\arabic{bsubcounter}): }
$U=37{,}73\,\milli\volt$\\
\textbf{\arabic{acounter} Netzwerk Wirk- und Blindanteil} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
$\uline{I}=5{,}25\milli\ampere\cdot e^{j18{,}5\,\degree}=(4{,}98+j1{,}67)\milli\ampere\\
\uline{I}_{\textrm{w}}=5{,}14\,\milli\ampere\cdot e^{j30\,\degree}\\
\uline{I}_b=1{,}05\,\milli\ampere\cdot e^{-j60\,\degree}\\
P_K=21{,}6\,\milli\watt\\
Q_K=4{,}4\,\milli\var\\
P_I=14{,}5\,\milli\watt\\
Q_I=-11{,}5\,\milli\var $\\
\textbf{\arabic{acounter} Gleichungen in Matrizenschreibweise} \stepcounter{acounter}\textbf{(B\arabic{bcounter}\stepcounter{bsubcounter}A\arabic{bsubcounter}): }\\
\scriptsize
\begin{align*}
&\left(
  \begin{array}{ccc}
    (0{,}8706+j1{,}6824) & (0-j2) & (-0{,}4706+j0{,}1176) \\
    (0-j2) & (0{,}5+j2{,}0) & (0{,}5+j0) \\
    (-0{,}4706-j0{,}1176) & (0{,}5+j0) & (1{,}4706+j1{,}8823) \\
  \end{array}
\right)\,\milli\siemens
\left(
  \begin{array}{c}
    \uline{U}_{10} \\
    \uline{U}_{20} \\
    \uline{U}_{30} \\
  \end{array}
\right)=
\left(
  \begin{array}{c}
    (6-j0)\\
    (13+j5)\\
    (0-j5)\\
  \end{array}
\right)\,\milli\ampere
\end{align*}\\
\clearpage
% }{}%