課程名稱︰普通物理學甲下 課程性質︰數學系大一必帶 課程教師︰黃暉理 開課學院：理學院 開課系所︰數學系 考試日期（年月日）︰2014/05/06 考試時限（分鐘）：60 試題 : 1. A generator with an adjustable frequency of oscillation is connected to re- sistance R, inductances $L_1$ and $L_2$, and capacitances $C_1$, $C_2$ and $C_3$. (a) What is the resonant frequency f of the circuit? What happens to the resonant frequency if (b) R is increased, (c) $L_1$ is increased, and (d) $C_3$ is removed from the circuit? https://i.imgur.com/l3x3tpj.png \begin{circuitikz} \draw (0, 0) to [L, l=$L_2$] (4, 0) to (8, 0) to [C, l=$C_3$] (8, 3) to (4, 3) to [R, l=$R$] (2, 3) to [L, l=$L_1$] (0, 3) to [rmeter, t=G] (0, 0); \draw (4, 0) to [C, l=$C_1$] (4, 3); \draw (6, 0) to [C, l=$C_2$] (6, 3); \end{circuitikz} 2. Figure shows a loop model (loop L) for a diamagnetic material. (a) Sketch the magnetic field lines within and about the material due to the bar magnet. What is the direction of (b) the loop's net magnetic dipole moment μ, (c) the conventional current i in the loop (clockwise or counterclockwise, face the +x), and (d) the magnetic force on the loop? https://i.imgur.com/WGjhSbu.png \begin{tikzpicture} \draw[fill=red] (-2, -.2) rectangle (-1, .2); \draw[fill=purple] (-2, -.2) -- (-2, .2) -- (-2.5, .4) -- (-2.5, 0) -- cycle; \draw[fill=purple] (-2, .2) -- (-1, .2) -- (-1.5, .4) -- (-2.5, .4) -- cycle; \draw (-2, 0) node[anchor=west]{N}; \draw[fill=cyan] (-1, -.2) rectangle (0, .2); \draw[fill=blue] (-1, .2) -- (0, .2) -- (-.5, .4) -- (-1.5, .4) -- cycle; \draw (0, 0) node[anchor=east]{S}; \draw (0, 0) -- (3, 0) node[anchor=west]{$x$}; \draw (1, 0) -- (.6, .8) -- (.5, .8) node[anchor=east]{Axis}; \draw[fill=gray] (2, 0) ellipse(.3 and .8); \draw[fill=white] (2, 0) ellipse(.2 and .7); \draw (1.7, 0) -- (2.2, 0); \draw (2, .8) node[anchor=south]{$L$}; \end{tikzpicture} 3. The intensity I of light from an isotropic point source is determined as a function of distance r from the source. Figure gives intensity I versus the inverse square $r^{-2}$ of that distance. What is the power of the source? https://i.imgur.com/9HaQsRt.png \begin{tikzpicture} \draw[very thin] (0, 0) node[anchor=north east]{0} grid (5, 4); \draw (0, 0) -- (0, 4) node[anchor=east]{$I_s$}; \draw (0, 0) -- (5, 0); \draw (4, 0) node[anchor=north]{$r_s^{-2}$}; \draw[very thick] (0, 0) -- (5, 4); \draw (2.5, -.8) node{$r^{-2}\ (m^{-2})$}; \draw (-.8, 2) node{\rotatebox{90}{$I\ (W/m^2)$}}; \end{tikzpicture} 4. A light ray is incident at angle $\theta_1$ on a series of five transparent layers with parallel boundaries. The thickness of layer i is $L_i$, and the index of refraction is $n_i$ (i = 1, 2, ..., 5). (a) At what angle $\theta_2$ does the light emerge back into air at the right? (b) How much time $t_3$ does the light take to travel through layer 3? https://i.imgur.com/tZx0uJk.png \begin{tikzpicture} \filldraw[gray] (0, -1) rectangle (2, 3); \filldraw[lightgray] (2, -1) rectangle (3, 3); \filldraw[darkgray] (3, -1) rectangle (6, 3); \filldraw[lightgray] (6, -1) rectangle (8, 3); \filldraw[gray] (8, -1) rectangle (9, 3); \foreach \x in {0, 2, 3, 6, 8, 9}{ \draw (\x, -1) -- (\x, 3); } \draw (0, -1.2) -- (0, -1.6); \draw (2, -1.2) -- (2, -1.6); \draw[<->] (0, -1.4) -- node[midway, below]{$L_1$} (2, -1.4); \foreach \x/\w in {-1/Air, 1/1, 2.5/2, 4.5/3, 7/4, 8.5/5, 9.5/Air}{ \draw (\x, 3) node[anchor=south]{\w}; } \draw[->, very thick] ({-sqrt(3)}, -1) -- (0, 0); \draw[dashed] (-2, 0) -- (0, 0); \draw[thick] (-.6, 0) arc[start angle=180, end angle=210, radius=.6]; \draw ({(-sqrt(3)-1)/3}, {(-sqrt(3)+1)/3}) node{$\theta_1$}; \end{tikzpicture} -- 第01話 似乎在課堂上聽過的樣子 第02話 那真是太令人絕望了 第03話 已經沒什麼好期望了 第04話 被當、21都是存在的 第05話 怎麼可能會all pass 第06話 這考卷絕對有問題啊 第07話 你能面對真正的分數嗎 第08話 我，真是個笨蛋 第09話 這樣成績，教授絕不會讓我過的 第10話 再也不依靠考古題 第11話 最後留下的補考 第12話 我最愛的學分 --

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