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new solution envs for mock up exam
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exam/examClass.cls

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Solution table %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\NewDocumentEnvironment{solutiontable}{+b}{
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\table[ht]
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\captionsetup{labelfont={color=blue},textfont={color=blue}}
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\color{blue}
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#1}
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{
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\endtabularx
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\endtable
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}
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\DeclareFloatingEnvironment[autorefname=Sol.-Tab.]{solutiontable}
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\captionsetup[solutiontable]{name=Solution Table, labelfont={color=blue},textfont={color=blue}}
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\renewcommand{\thesolutiontable}{\arabic{solutiontable}}
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% Change autorefname of table to Tab.
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\addto\extrasenglish{%
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\renewcommand{\tableautorefname}{Tab.}%
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Solution figure %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\NewDocumentEnvironment{solutionfigure}{+b}{
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\figure
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\captionsetup{labelfont={color=blue},textfont={color=blue}}
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\color{blue}
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#1}
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{
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\endfigure
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}
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\DeclareFloatingEnvironment[autorefname=Sol.-Fig.]{solutionfigure}
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\captionsetup[solutionfigure]{name=Solution Figure, labelfont={color=blue},textfont={color=blue}}
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\renewcommand{\thesolutionfigure}{\arabic{solutionfigure}}
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\renewcommand{\figurename}{Fig.}
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% Change autorefname of figure to Fig.
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\addto\extrasenglish{%
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\renewcommand{\figureautorefname}{Fig.}%
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\fi
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\normalsize
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\setlength{\parskip}{1em}
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\setcounter{solutionfigure}{0}
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\setcounter{solutiontable}{0}
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}
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\titleformat*{\section}{\normalfont}

exam/summer2024/tex/task01.tex

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\subtask{The disc from Fig.~\ref{fig:faraday_disk} has a diameter of $d=\SI{60}{\cm}$ and is rotating with the circumferential speed $v_\mathrm{d} = \SI{100}{\meter\per\second}$. What is the rotational speed and angular velocity of the copper disk?}{2}
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\subtaskGerman{Die Scheibe aus Abb.~\ref{fig:faraday_disk} hat einen Durchmesser von $d=\SI{60}{\cm}$ und ihre Oberfläche rotiert mit der Umfangsgeschwindigkeit $v_\mathrm{d} = \SI{100}{\meter\per\second}$. Wie groß ist die Drehzahl $n_\mathrm{d}$ und die Winkelgeschwindigkeit $\omega_\mathrm{d}$ der Kupferscheibe?}
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\subtask{The disc from \autoref{fig:faraday_disk} has a diameter of $d=\SI{60}{\cm}$ and is rotating with the circumferential speed $v_\mathrm{d} = \SI{100}{\meter\per\second}$. What is the rotational speed and angular velocity of the copper disk?}{2}
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\subtaskGerman{Die Scheibe aus \autoref{fig:faraday_disk} hat einen Durchmesser von $d=\SI{60}{\cm}$ und ihre Oberfläche rotiert mit der Umfangsgeschwindigkeit $v_\mathrm{d} = \SI{100}{\meter\per\second}$. Wie groß ist die Drehzahl $n_\mathrm{d}$ und die Winkelgeschwindigkeit $\omega_\mathrm{d}$ der Kupferscheibe?}
2020

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\begin{solutionblock}
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The rotational speed is given by

exam/summer2024/tex/task02.tex

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\end{center}
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\end{solutionblock}
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\subtask{Now consider a DC machine with the parameters given in Tab.~\ref{tab:characteristicsDC_task2}. To which of the above connection type can the parameter set belong?}{1}
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\subtaskGerman{Betrachten Sie nun eine Gleichstrommaschine mit den Parametern aus Tab.~\ref{tab:characteristicsDC_task2}. Zu welchen der obigen Verschaltungsarten kann dieser Parametersatz gehören?}
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\subtask{Now consider a DC machine with the parameters given in \autoref{tab:characteristicsDC_task2}. To which of the above connection type can the parameter set belong?}{1}
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\subtaskGerman{Betrachten Sie nun eine Gleichstrommaschine mit den Parametern aus \autoref{tab:characteristicsDC_task2}. Zu welchen der obigen Verschaltungsarten kann dieser Parametersatz gehören?}
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\begin{table}[htb]
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\caption{Characteristics of the given DC machine.}
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\centering

exam/summer2024/tex/task03.tex

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If $\omega_\mathrm{r}=\SI{0}{\per\second}$ the mechanical rotor frequency is zero and the slip angular frequency is equal to the electrical angular frequency of the stator excitation: $\omega_\mathrm{s}= \omega_\mathrm{slip}$. Consequently, the slip ratio is equal to one ($s=\omega_\mathrm{slip}/\omega_\mathrm{s}=1$) and could be dropped from the equivalent circuit diagram.
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\end{solutionblock}
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\subtask{From now on consider a \textbf{squire cage induction machine} with the parameters from Tab.~\ref{tab:characteristicsIM_task3}. Calculate the no-load speed $n_0$. }{2}
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\subtaskGerman{Wir betrachten nun eine \textbf{Käfigläufer-Asynchronmaschine} mit den Parametern aus Tab.~\ref{tab:characteristicsIM_task3}. Berechnen Sie die Leerlaufdrehzahl $n_0$.}
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\subtask{From now on consider a \textbf{squire cage induction machine} with the parameters from \autoref{tab:characteristicsIM_task3}. Calculate the no-load speed $n_0$. }{2}
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\subtaskGerman{Wir betrachten nun eine \textbf{Käfigläufer-Asynchronmaschine} mit den Parametern aus \autoref{tab:characteristicsIM_task3}. Berechnen Sie die Leerlaufdrehzahl $n_0$.}
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\begin{table}[htb]
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\caption{Characteristics of the given induction machine.}
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\centering

exam/summer2024/tex/task04.tex

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\end{figure}
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\subtask{Determine the operating mode of the machine characterized by Fig.~\ref{fig:phasor_SM}.}{2}
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\subtaskGerman{Bestimmen Sie die Betriebsart der Maschine auf Basis von Abb.~\ref{fig:phasor_SM}.}
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\subtask{Determine the operating mode of the machine characterized by \autoref{fig:phasor_SM}.}{2}
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\subtaskGerman{Bestimmen Sie die Betriebsart der Maschine auf Basis von \autoref{fig:phasor_SM}.}
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\begin{solutionblock}
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The machine is operating as an overexcited generator, since the excitation voltage $\underline{U}_\mathrm{i}$ is leading the stator voltage $\underline{U}_\mathrm{s}$ by an angle $\theta$ and the induced voltage amplitude is larger than the stator voltage amplitude.
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\begin{solutionblock}
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The short-circuit current $\underline{I}_\mathrm{s,sc}$ is orthogonal to $\underline{U}_\mathrm{i}$ and lagging behind by $\SI{90}{\degree}$, that is, pointing towards the real axis with a length of \SI{1.33}{\cm}. The synchronous reactance is then
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$$X_\mathrm{s} = \frac{\underline{U}_\mathrm{i}}{\underline{I}_\mathrm{s,sc}} = \frac{\SI{3}{\kilo\volt}}{\SI{1.33}{\kilo\ampere}} = \SI{2.26}{\ohm}.$$
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Here, the induced voltage $\underline{U}_\mathrm{i}$ has been obtained from optical measurement of the phasor diagram and also represents the open-circuit voltage.
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Here, the induced voltage $\underline{U}_\mathrm{i}$ has been obtained from optical measurement of the phasor diagram and also represents the open-circuit voltage. The completed phasor diagram is shown in \autoref{fig:phasor_SM_final}.
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\end{solutionblock}
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The angle $\varphi$ is then
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$$\varphi = -\arccos(0.96) = \SI{-16.25}{\degree}.$$
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The power factor angle is negative as the generator operates in an over-excited mode, i.e., its reactive power is negative. The resulting complex stator current is then $$\underline{I}_\mathrm{s} = \SI{0.62}{\kilo\ampere} \cdot e^{\mathrm{j}(\SI{16.25}{\degree} + \SI{63.5}{\degree})} = \SI{0.11}{\kilo\ampere} + \mathrm{j} \SI{0.61}{\kilo\ampere}.$$
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Here, the angle $\SI{63.5}{\degree}$ is the stator voltage angle counted from the real axis.
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\end{solutionblock}
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\begin{solutionblock}
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\begin{figure}[h!]
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Here, the angle $\SI{63.5}{\degree}$ is the stator voltage angle counted from the real axis. The final solution phasor diagram is shown in \autoref{fig:phasor_SM_final}.
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\begin{solutionfigure}[ht]
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\centering
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\begin{tikzpicture}
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\coordinate (b) at (0,0);
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\pic[draw, <-, angle eccentricity=1.7, angle radius=1.25cm]{angle = a--b--d};
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\node at (0.45,1.5) {$\varphi$};
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\end{tikzpicture}
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\end{figure}
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\caption{Final phasor diagram}
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\label{fig:phasor_SM_final}
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\end{solutionfigure}
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\end{solutionblock}
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\subtask{Determine the apparent power $S$ and the reactive power $Q$.}{2}
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\subtaskGerman{Bestimmen Sie die Scheinleistung $S$ und die Blindleistung $Q$.}

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