2026/05/16

sections/a-2/exp-detail.tex

@@ -0,0 +1,123 @@
+\section{実験条件・手順}
+
+\subsection{実験器具}
+
+今回の実験では以下の器具を用いた：
+
+\begin{itemize}
+    \item{ブレッドボード Sunhayato SHR-74}
+    \item{デジタルマルチメータ SANWA PC700}
+    \item{直流安定化電源 KENWOOD PR18-1.2A}
+    \item{抵抗器 $1.0 \ \text{k}\Omega \pm 5\%$, 1/4 W}
+    \item{抵抗器 $2.2 \ \text{k}\Omega \pm 5\%$, 1/4 W}
+    \item{抵抗器 $3.3 \ \text{k}\Omega \pm 5\%$, 1/4 W}
+\end{itemize}
+
+\subsection{実験1}
+
+\begin{enumerate}
+    \item{\cref{fig:cd-exp1}の回路をブレッドボード上で作成する}
+    \item{3種類の抵抗$(R = 1.0 \ \text{k}\Omega, 2.2 \ \text{k}\Omega, 3.3 \ \text{k}\Omega)$について，3つの電源電圧$(E = 3 \ \text{V}, 6 \ \text{V}, 9 \ \text{V})$}における\\電流を測定する
+\end{enumerate}
+
+\begin{figure}[tbh]
+    \centering
+    \begin{circuitikz}
+        \draw (0,3) to [cvsourceAM, l=$E$] (0,0);
+        \draw (0,3) to [rmeterwa, t=A] (3,3) to [R, l=$R$] (3,0) -- (0,0);
+        \draw (3,3) to [short, *-] ++(2,0) to [rmeterwa, t=V, straight instruments] ++(0,-3) to [short, -*] ++(-2,0);
+        \draw (0,0) node[ground]{} ++(0,-0.5);
+    \end{circuitikz}
+    \caption{Circuit Diagram of Experiment \# 1}
+    \label{fig:cd-exp1}
+\end{figure}
+
+\subsection{実験2}
+
+\begin{enumerate}
+    \item{\cref{fig:cd-exp2-a}の回路を作成し，電流$I_1, I_2, I_3$，抵抗$R_1, R_2, R_3$の端子間電圧$V_1, V_2, V_3$および電源電圧$E_1, E_2$を測定する}
+    \item{\cref{fig:cd-exp2-b}の回路を作成し，1. 同様に測定する}
+\end{enumerate}
+
+\begin{figure}[tbh]
+    \centering
+    \begin{minipage}[h]{0.90\linewidth}
+        \centering
+        \begin{circuitikz}
+            \draw (0,3) node[above]{a} to [cvsourceAM, l_={$E_1=15 \ \text{V}$}] (0,0) node[left]{f};
+            \draw (0,3) to [R, l={$R_1$}, a={$3.3 \ \text{k}\Omega$}, i_={$I_1$}] ++(3,0) node[above]{b};
+
+            \draw (6,3) node[above]{c} to [cvsourceAM, l={$E_2=3 \ \text{V}$}] (6,0) node[right]{d};
+            \draw (6,3) to [R, l_={$R_2$}, a^={$1.0 \ \text{k}\Omega$}, i={$I_2$}] ++(-3,0);
+
+            \draw (3,3) node[circ]{} to [R, l={$R_3$}, a={$2.2 \ \text{k}\Omega$}, i={$I_3$}] ++(0,-3) node[circ]{} node[below]{e};
+            \draw (6,0) to [short,-*] (0,0);
+            \draw (0,0) node[ground]{} ++(0,-0.5);
+        \end{circuitikz}
+        \subcaption{Circuit (a)}
+        \label{fig:cd-exp2-a}
+    \end{minipage}
+    \begin{minipage}[h]{0.90\linewidth}
+        \centering
+        \begin{circuitikz}
+            \draw (0,3) node[above]{a} to [cvsourceAM, l_={$E_1=15 \ \text{V}$}] (0,0) node[left]{f};
+            \draw (0,3) to [R, l={$R_1$}, a={$3.3 \ \text{k}\Omega$}, i_={$I_1$}] ++(3,0) node[above]{b};
+
+            \draw (6,0) node[right]{d} to [cvsourceAM, l_={$E_2=3 \ \text{V}$}] (6,3) node[above]{c};
+            \draw (6,3) to [R, l_={$R_2$}, a^={$1.0 \ \text{k}\Omega$}, i={$I_2$}] ++(-3,0);
+
+            \draw (3,3) node[circ]{} to [R, l={$R_3$}, a={$2.2 \ \text{k}\Omega$}, i={$I_3$}] ++(0,-3) node[circ]{} node[below]{e};
+            \draw (6,0) to [short,-*] (0,0);
+            \draw (0,0) node[ground]{} ++(0,-0.5);
+        \end{circuitikz}
+        \subcaption{Circuit (b)}
+        \label{fig:cd-exp2-b}
+    \end{minipage}
+    \caption{Circuit Diagrams of Experiment \# 2}
+    \label{fig:cd-exp2}
+\end{figure}
+
+\subsection{実験3}
+
+\begin{enumerate}
+    \item{\cref{fig:cd-exp2-a}の回路を作成し，電流$I_1, I_2, I_3$，抵抗$R_1, R_2, R_3$の端子間電圧$V_1, V_2, V_3$および電源電圧$E_1, E_2$を測定する．この時，$E_2$を取り外し，短絡させる}
+    \item{$E_2$を戻し，$E_1$を取り外し，短絡させ，1. 同様に測定する}
+    \item{$E_1$を戻し，$E_1, E_2$同時に印加させ，1. 同様に測定する}
+\end{enumerate}
+
+なお今回の実験の手順3では実験2の手順1の結果を使用する．
+
+\subsection{実験4}
+
+\begin{enumerate}
+    \item{\cref{fig:cd-exp4-oc}を\cref{fig:cd-exp4-ec}の等価回路で表す時，$V_t$と$R_t$を理論的に求める}
+    \item{\cref{fig:cd-exp4-oc}の回路を作成し，負荷抵抗$R_L$の端子間電圧とそれに流れ込む電流を測定する}
+    \item{\cref{fig:cd-exp4-ec}の回路を作成し，2. 同様に測定する．なお$R_t$には$10 \ \text{k}\Omega$の可変抵抗を使い，電源電圧も理論値$V_t$に設定する}
+\end{enumerate}
+
+\begin{figure}[tbh]
+    \centering
+    \begin{minipage}[h]{0.45\linewidth}
+        \centering
+        \begin{circuitikz}
+            \draw (0,3) to [cvsourceAM, l_={$E_1 = 15 \ \text{V}$}] (0,0);
+            \draw (0,3) to [R={$R_1$}, a={$3.3 \ \text{k}\Omega$}] ++(2,0) to [R={$R_2$}, a={$2.2 \ \text{k}\Omega$}] ++(0,-3) to [short, *-*] ++(-2,0);
+            \draw (2,3) to [short, *-o] ++(1,0) node[above]{A} -- ++(1,0) to [R={$R_L$}, a={$1 \ \text{k}\Omega$}] ++(0,-3) -- ++(-1,0) node[above]{B} to [short, o-] ++(-1,0);
+            \draw (0,0) to node[ground]{} ++(0,-0.5);
+        \end{circuitikz}
+        \subcaption{Original Circuit}
+        \label{fig:cd-exp4-oc}
+    \end{minipage}
+    \begin{minipage}[h]{0.45\linewidth}
+        \centering
+        \begin{circuitikz}
+            \draw (0,3) to [cvsourceAM, l={$V_t$}] (0,0);
+            \draw (0,3) to [R={$R_t$}] ++(2,0) to [short, -o] ++(1,0) node[above]{A} -- ++(1,0) to [R={$R_L$}, a={$1 \ \text{k}\Omega$}] ++(0,-3) -- ++(-1,0) node[above]{B} to [short, o-*] ++(-3,0);
+            \draw (0,0) to node[ground]{} ++(0,-0.5);
+        \end{circuitikz}
+        \subcaption{Equivalent Circuit}
+        \label{fig:cd-exp4-ec}
+    \end{minipage}
+    \caption{Circuit Diagrams of Experiment \# 4}
+    \label{fig:cd-exp4}
+\end{figure}

sections/a-2/exp-result.tex

@@ -2,49 +2,132 @@
 
 \subsection{実験1}
 
+それぞれの抵抗の理論値と実測値を\cref{fig:v-i-r}に示す．なお，理論値には$\pm 5\%$の誤差の範囲も同時に表示している．
 
+\begin{figure}[tbh]
+    \centering
+    \input{assets/a-2/exp1}
+    \caption{Voltage v.s. Current of Differenct Resistors with Theoretical Values and Error Ranges}
+    \label{fig:v-i-r}
+\end{figure}
+
+\newpage
 
 \subsection{実験2}
 
-\subsubsection{回路1}
+\subsubsection{回路(a)}
 
-At E1 = 15.000, E2 = 3.005
+$E_1 = 15.000 \ \text{V}, \ E_2 = 3.005 \ \text{V}$の時，各抵抗での電流・電圧は\cref{tab:exp2-res1}となった：
 
-I1 = -3.28m, V1 = 10.69
-I2 = 1.31m, V2 = 1.296
-I3 = 1.98m, V3 = 4.297
+%I1 = -3.28m, V1 = 10.69
+%I2 = 1.31m, V2 = 1.296
+%I3 = 1.98m, V3 = 4.297
 
-\subsubsection{回路2}
+\begin{table}[ht]
+    \centering
+    \caption{Result of Experiment \# 2 with Circuit (a)}
+    \label{tab:exp2-res1}
+    \begin{tabular}{c|c|c}
+        \hline
+        Resistor & Voltage $[\text{V}]$ & Current $[\text{mA}]$ \\
+        \hline
+        $R_1$ & 10.69 & -3.28 \\
+        $R_2$ & 1.30 & 1.31 \\
+        $R_3$ & 4.30 & 1.98 \\
+        \hline
+    \end{tabular}
+\end{table}
 
-At E1 = 15.000, E2 = -3.007
+\subsubsection{回路(b)}
 
-I1 = 4.33m, V1 = 14.10
-I2 = -3.93m, V2 = -3.891
-I3 = -0.40m, V3 = 0.890
+$E_1 = 15.000 \ \text{V}, \ E_2 = -3.007 \ \text{V}$の時，各抵抗での電流・電圧は\cref{tab:exp2-res2}となった：
+
+%I1 = 4.33m, V1 = 14.10
+%I2 = -3.93m, V2 = -3.891
+%I3 = -0.40m, V3 = 0.890
+
+\begin{table}[ht]
+    \centering
+    \caption{Result of Experiment \# 2 with Circuit (b)}
+    \label{tab:exp2-res2}
+    \begin{tabular}{c|c|c}
+        \hline
+        Resistor & Voltage $[\text{V}]$ & Current $[\text{mA}]$ \\
+        \hline
+        $R_1$ & 14.10 & 4.33 \\
+        $R_2$ & -3.89 & -3.93 \\
+        $R_3$ & 0.89 & 0.40 \\
+        \hline
+    \end{tabular}
+\end{table}
 
 \subsection{実験3}
 
-\subsubsection{E1 only}
+\subsubsection{$E_1$のみ}
 
-At E1 = 15.000
+$E_1 = 15.000 \ \text{V}$での各抵抗にかかった電流・電圧は\cref{tab:exp3-res1}となった：
 
-I1 = 3.81m, V1 = 12.40
-I2 = 2.61m, V2 = 2.596
-I3 = 1.19m, V3 = 2.593
+%I1 = 3.81m
+%I2 = 2.61m
+%I3 = 1.19m
+%V1 = 12.40
+%V2 = 2.596
+%V3 = 2.593
 
-\subsubsection{E2 only}
+\begin{table}[ht]
+    \centering
+    \caption{Result of Experiment \# 3 with $E_1$ as Voltage Source}
+    \label{tab:exp3-res1}
+    \begin{tabular}{c|c|c}
+        \hline
+        Resistor & Voltage $[\text{V}]$ & Current $[\text{mA}]$ \\
+        \hline
+        $R_1$ & 12.40 & 3.81 \\
+        $R_2$ & 2.61 & 2.61 \\
+        $R_3$ & 2.59 & 1.19 \\
+        \hline
+    \end{tabular}
+\end{table}
 
-At E2 = 3.004
+\subsubsection{$E_2$のみ}
 
-I1 = 0.52m, V1 = -1.705
-I2 = 1.31m, V2 = -1.294
-I3 = 0.78m, V3 = 1.704
+$E_2 = 3.004 \ \text{V}$での各抵抗にかかった電流・電圧は\cref{tab:exp3-res2}となった：
 
+\begin{table}[ht]
+    \centering
+    \caption{Result of Experiment \# 3 with $E_2$ as Voltage Source}
+    \label{tab:exp3-res2}
+    \begin{tabular}{c|c|c}
+        \hline
+        Resistor & Voltage $[\text{V}]$ & Current $[\text{mA}]$ \\
+        \hline
+        $R_1$ & 1.71 & 0.52 \\
+        $R_2$ & 1.29 & 1.32 \\
+        $R_3$ & 1.70 & 0.78 \\
+        \hline
+    \end{tabular}
+\end{table}
 
 \subsection{実験4}
 
-Calculated value: R_t = \frac{R_{1} R_{2}}{R_1 + R_2} = 1320, V_t = \frac{R_{2}E_{1}}{R_1 + R_2} = 6
+%Calculated value: R_t = \frac{R_{1} R_{2}}{R_1 + R_2} = 1320, V_t = \frac{R_{2}E_{1}}{R_1 + R_2} = 6
 
-without vr: 2.595V, 2.62mA
-with vr: 
+等価回路でのパラメータの値は$V_{t} = 6 \ \text{V}, \ R_{t} = 1320 \ \Omega$となった．これらの値に元にした実験の結果を\cref{tab:exp4-res}にまとめる．
+
+\begin{table}[htb]
+    \centering
+    \caption{Voltage and Current of Load}
+    \label{tab:exp4-res}
+    \begin{tabular}{c|c|c}
+        \hline
+        Circuit & Voltage $[\text{V}]$ & Current $[\text{mA}]$ \\
+        \hline
+        Original Circuit & 2.595 & 2.62 \\
+        Replaced with Variable Resistor & 2.576 & 2.61 \\
+        \hline
+    \end{tabular}
+\end{table}
+
+%without vr: 2.595V, 2.62mA
+%with vr: 2.576V, 2.61mA 
 

sections/a-2/reflection.tex

@@ -0,0 +1 @@
+\section{考察}

sections/a-2/theory.tex

@@ -0,0 +1,50 @@
+\section{理論}
+
+\subsection{オームの法則}
+
+ある抵抗値を持つ抵抗器$R \ [\Omega]$に対し電圧$V \ [\text{V}]$を印加すると抵抗に電流$I \ [\text{A}]$が流れる．
+この時，$V, R, I$には次の関係式が成り立つ．
+
+\begin{equation}\label{equ:ohm}
+    V = RI
+\end{equation}
+
+\cref{equ:ohm}で表されるこの関係をオームの法則という．
+
+電圧は電流に比例するのでV-I図は\cref{fig:v-i-example}のようになる．
+
+\begin{figure}[tbh]
+    \centering
+    \begin{tikzpicture}[domain=0:4]
+        \draw[->] (0,0) -- (4.5,0);
+        \draw[->] (0,0) -- (0,4.5);
+
+        \foreach \x in {0,...,4} {
+            \draw (\x, 0) node[below]{\x} -- (\x, 0.1);
+            \draw (0, \x) node[left]{\x} -- (0.1, \x);
+        }
+
+        \draw plot (\x, \x) node[left=5pt]{$R = 1 \ \text{k}\Omega$};
+        \draw plot (\x, {\x/2}) node[below=10pt]{$R = 2 \ \text{k}\Omega$};
+        \node at (2.25,-0.4) [below] {Voltage [V]};
+        \node[rotate=90] at (-0.3,2.25) [above] {Current [mA]};
+    \end{tikzpicture}
+    \caption{Ohm's Law on Graph}
+    \label{fig:v-i-example}
+\end{figure}
+
+\subsection{キルヒホッフの法則}
+
+複数の抵抗・電源からなる複雑な回路はオームの法則だけでは回路を解くことはできない．
+キルヒホッフの法則はそのような回路網を計算する際に用いられる．
+
+この法則には2つの性質が定義されている．
+
+第一法則は電流則とも呼ばれ，回路中の接点の電流の入出流の関係が定義されている．
+
+第二法則は電圧則とも呼ばれ，
+
+\subsection{重ね合わせの理}
+
+\subsection{テブナンの定理}
+