课程名称︰普通物理学甲下 课程性质︰数学系大一必带 课程教师︰黄晖理 开课学院：理学院 开课系所︰数学系 考试日期（年月日）︰2014/05/06 考试时限（分钟）：60 试题 : 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话 似乎在课堂上听过的样子 第02话 那真是太令人绝望了 第03话 已经没什麽好期望了 第04话 被当、21都是存在的 第05话 怎麽可能会all pass 第06话 这考卷绝对有问题啊 第07话 你能面对真正的分数吗 第08话 我，真是个笨蛋 第09话 这样成绩，教授绝不会让我过的 第10话 再也不依靠考古题 第11话 最後留下的补考 第12话 我最爱的学分 --

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