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VP13.html
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VP13 RLC and Transient Behavior
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<div id="doc" class="markdown-body container-fluid comment-enabled" data-hard-breaks="true" style="position: relative;"><h1 id="VP13-RLC-and-Transient-Behavior"><a class="anchor hidden-xs" href="#VP13-RLC-and-Transient-Behavior" title="VP13-RLC-and-Transient-Behavior"><span class="octicon octicon-link"></span></a>VP13 RLC and Transient Behavior</h1><ul>
<li><a href="pdf/VP13.pdf" target="_blank" rel="noopener">官方PDF檔</a></li>
</ul><h3 id="同學們的影片"><a class="anchor hidden-xs" href="#同學們的影片" title="同學們的影片"><span class="octicon octicon-link"></span></a>同學們的影片</h3><ul>
<li><a href="" target="_blank" rel="noopener">這部份當然是還沒有啦</a></li>
</ul><h2 id="作業繳交格式"><a class="anchor hidden-xs" href="#作業繳交格式" title="作業繳交格式"><span class="octicon octicon-link"></span></a>作業繳交格式</h2><p>請上傳一個 zip 檔（壓縮檔，請注意副檔名要是 <code>zip</code>）到 CEIBA，zip 檔內需要包含一個<strong>名稱是自己學號的資料夾</strong>，裡面包含一個名為 <code>must.py</code> 的 py 檔。而若本次作業有拍攝說明影片，請<strong>將影片連結寫在</strong> <code>video.txt</code> <strong>裡面，並一併放入學號資料夾中</strong>。</p><p>範例：（zip 檔名可以隨便取，CEIBA 系統會自己把檔名改掉）</p><pre><code>the_zip_file.zip
└── r07222060
├── must.py
└── video.txt
</code></pre><blockquote>
<h4 id="助教註"><a class="anchor hidden-xs" href="#助教註" title="助教註"><span class="octicon octicon-link"></span></a>助教註:</h4>
<p>如果你是用 JuPyter notebook 寫的，請記得將你的程式用 <code>.py</code> 格式下載下來，不要給我 <code>.ipynb</code> 或甚至 <code>.html</code>。</p>
</blockquote><h2 id="Deadline"><a class="anchor hidden-xs" href="#Deadline" title="Deadline"><span class="octicon octicon-link"></span></a>Deadline</h2><p><code>2020/05/21 THU 21:00</code></p><h2 id="Homework"><a class="anchor hidden-xs" href="#Homework" title="Homework"><span class="octicon octicon-link"></span></a>Homework</h2><p><img src="pic/VP13/RLC.png" alt="RLC" height="250"></p><p>An RLC circuit, with <img src="https://latex.codecogs.com/svg.latex?\dpi{300}&space;&space;\text{R}&space;=&space;30\&space;(\Omega)">, <img src="https://latex.codecogs.com/svg.latex?\dpi{300}&space;\&space;\text{L}&space;=&space;200\&space;(\text{mH})">, <img src="https://latex.codecogs.com/svg.latex?\dpi{300}&space;&space;\text{C}&space;=&space;20\&space;(\mu\textup{F})">. The driving voltage source is</p><img src="https://latex.codecogs.com/svg.latex?\dpi{300}&space;v(t)&space;=&space;\left\{\begin{matrix}&space;0,&space;&&space;\text{if}\&space;t&space;<&space;0&space;\\&space;36&space;\cdot&space;\sin(2\pi&space;f_d&space;t),&space;&&space;\text{if}\&space;0&space;\leq&space;t&space;<&space;12\text{T}&space;\\&space;0,&space;&&space;\text{if}\&space;12\text{T}&space;\leq&space;t&space;\end{matrix}\right." title="v(t) = \left\{\begin{matrix} 0, & \text{if}\ t < 0 \\ 36 \cdot \sin(2\pi f_d t), & \text{if}\ 0 \leq t < 12T \\ 0, & \text{if}\ 12T \leq t \end{matrix}\right." height="80"><p><br>
where <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;f_d&space;=&space;120\&space;(\text{Hz})" title="f_d = 120\ (\text{Hz})">, <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;\text{T}&space;=&space;1/f_d" title="\text{T} = 1/f_d">.</p><h3 id="1"><a class="anchor hidden-xs" href="#1" title="1"><span class="octicon octicon-link"></span></a>(1)</h3><p>Solve this circuit numerically and plot the voltage <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;v(t)" title="v(t)"> and the current <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;i(t)" title="i(t)"> as a function of <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;t" title="t"> for <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;t&space;\in&space;[0,&space;20\text{T}]" title="t \in [0, 20\text{T}]"> in <code>scene1</code> and the total energy <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;\text{E}(\text{T})" title="\text{E}(\text{T})"> stored in the system in <code>scene2</code>.</p><h3 id="2"><a class="anchor hidden-xs" href="#2" title="2"><span class="octicon octicon-link"></span></a>(2)</h3><p>You will see a transient behavior of the current <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;i(t)" title="i(t)"> before it reaches a steady-state oscillation around <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;t&space;=&space;9\text{T}" title="t = 9\text{T}">. Find <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;I" title="I">, the amplitude of the oscillating current, and <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;\phi" title="\phi"> the phase constant of the oscillating current relative to the voltage source during the 9-th period. Compare them to the theoretical values.</p><h3 id="3"><a class="anchor hidden-xs" href="#3" title="3"><span class="octicon octicon-link"></span></a>(3)</h3><p>After the voltage is turned off at <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;t&space;=&space;12&space;\text{T}" title="t = 12 \text{T}">, you will see both the current and the total energy decays. Find the time <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;t" title="t"> such that the energy decays to 10% of the energy at the time the voltage is just turned off, i.e., <img src="https://latex.codecogs.com/svg.latex?\dpi{150}&space;\text{E}(t)&space;=&space;0.1\text{E}(t=12\text{T})" title="\text{E}(t) = 0.1\text{E}(t=12\text{T})">.</p><h3 id="Template-codes"><a class="anchor hidden-xs" href="#Template-codes" title="Template-codes"><span class="octicon octicon-link"></span></a>Template codes</h3><pre><code class="python hljs"><span class="hljs-keyword">from</span> vpython <span class="hljs-keyword">import</span> *
fd = <span class="hljs-number">120</span> <span class="hljs-comment"># 120 Hz</span>
<span class="hljs-comment"># ===== Add your parameters here =====</span>
t = <span class="hljs-number">0</span>
dt = <span class="hljs-number">1.0</span> / (fd*<span class="hljs-number">5000</span>) <span class="hljs-comment"># 5000 simulation points per cycle</span>
scene1 = graph(align=<span class="hljs-string">'left'</span>, xtitle=<span class="hljs-string">'t'</span>, ytitle=<span class="hljs-string">'i(A) blue, v(100V) red'</span>, background=vector(<span class="hljs-number">0.6</span>, <span class="hljs-number">0.9</span>, <span class="hljs-number">0.6</span>))
scene2 = graph(align=<span class="hljs-string">'left'</span>, xtitle=<span class="hljs-string">'t'</span>, ytitle=<span class="hljs-string">'Energy(J)'</span>, background=vector(<span class="hljs-number">0.6</span>, <span class="hljs-number">0.9</span>, <span class="hljs-number">0.6</span>))
i_t = gcurve(color=color.blue, graph=scene1)
v_t = gcurve(color=color.red, graph=scene1)
E_t = gcurve(color=color.red, graph=scene2)
<span class="hljs-comment"># ===== Your codes here =====</span>
</code></pre>
<h2 id="Grading-Policy"><a class="anchor hidden-xs" href="#Grading-Policy" title="Grading-Policy"><span class="octicon octicon-link"></span></a>Grading Policy</h2>
<ul>
<li>The i(t) and v(t) plots are roughly correct. (20%)</li>
<li>The E(t) plot is roughly correct. (20%)</li>
<li>The theoretical values of the current amplitude and the phase constant are roughly correct. (20%)</li>
<li>The simulation results of the current amplitude and the phase constant are roughly correct. (20%)</li>
<li>The answer of the part (3) (the time such that energy decays to 10% ...) is roughly correct. (20%)</li>
</ul>
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