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Author SHA1 Message Date
deadvey
3046f62ce0 Added lba to chs conversion 2025-10-26 21:39:43 +00:00
deadvey
dc410e7b4e Added fringe spacing 2025-10-26 21:11:31 +00:00
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@@ -97,6 +97,9 @@
<li>
<a class="function" href="#tribonacci_series">tribonacci_series</a>
</li>
<li>
<a class="function" href="#lba_to_chs">lba_to_chs</a>
</li>
</ul>
@@ -406,6 +409,23 @@
</span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="s2">&quot;The Tribonacci Series of the first $</span><span class="si">{n}</span><span class="s2">$ numbers is ?&quot;</span>
</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">tribSeries</span><span class="p">))</span>
</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">solution</span><span class="si">}</span><span class="s1">$&#39;</span>
</span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a>
</span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a><span class="k">def</span><span class="w"> </span><span class="nf">lba_to_chs</span><span class="p">(</span><span class="n">max_lba</span><span class="o">=</span><span class="mi">2880</span><span class="p">,</span> <span class="n">sectors_per_track</span><span class="o">=</span><span class="mi">18</span><span class="p">,</span> <span class="n">number_of_heads</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
</span><span id="L-291"><a href="#L-291"><span class="linenos">291</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot; Calculating the Cylinder, Head and Sector numbers for a given LBA</span>
</span><span id="L-292"><a href="#L-292"><span class="linenos">292</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-293"><a href="#L-293"><span class="linenos">293</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a><span class="sd"> | If the LBA of a block is $2243$ on a device with $18$ sectors per track and $2$ heads, what are the cylinder, head and sector numbers? | Cylinder: $62$, Head: $0$, Sector: $12$ |</span>
</span><span id="L-295"><a href="#L-295"><span class="linenos">295</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a> <span class="n">lba</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_lba</span><span class="p">)</span>
</span><span id="L-297"><a href="#L-297"><span class="linenos">297</span></a> <span class="n">cylinder</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">lba</span><span class="o">/</span><span class="p">(</span><span class="n">sectors_per_track</span><span class="o">*</span><span class="n">number_of_heads</span><span class="p">));</span>
</span><span id="L-298"><a href="#L-298"><span class="linenos">298</span></a> <span class="n">t</span> <span class="o">=</span> <span class="n">cylinder</span><span class="o">*</span><span class="p">(</span><span class="n">sectors_per_track</span><span class="o">*</span><span class="n">number_of_heads</span><span class="p">);</span>
</span><span id="L-299"><a href="#L-299"><span class="linenos">299</span></a> <span class="n">t</span> <span class="o">=</span> <span class="n">lba</span><span class="o">-</span><span class="n">t</span><span class="p">;</span>
</span><span id="L-300"><a href="#L-300"><span class="linenos">300</span></a> <span class="n">head</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">t</span><span class="o">/</span><span class="p">(</span><span class="n">sectors_per_track</span><span class="p">));</span>
</span><span id="L-301"><a href="#L-301"><span class="linenos">301</span></a> <span class="n">sector</span> <span class="o">=</span> <span class="n">t</span> <span class="o">-</span> <span class="p">(</span><span class="n">head</span> <span class="o">*</span> <span class="n">lba</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">;</span>
</span><span id="L-302"><a href="#L-302"><span class="linenos">302</span></a>
</span><span id="L-303"><a href="#L-303"><span class="linenos">303</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;If the LBA of a block is $</span><span class="si">{</span><span class="n">lba</span><span class="si">}</span><span class="s2">$ on a disk with $</span><span class="si">{</span><span class="n">sectors_per_track</span><span class="si">}</span><span class="s2">$ sectors per track and $</span><span class="si">{</span><span class="n">number_of_heads</span><span class="si">}</span><span class="s2">$ heads, what are the cylinder, head and sector numbers?&quot;</span>
</span><span id="L-304"><a href="#L-304"><span class="linenos">304</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Cylinder: $</span><span class="si">{</span><span class="n">cylinder</span><span class="si">}</span><span class="s2">$, Head: $</span><span class="si">{</span><span class="n">head</span><span class="si">}</span><span class="s2">$, Sector: $</span><span class="si">{</span><span class="n">sector</span><span class="si">}</span><span class="s2">$&quot;</span>
</span><span id="L-305"><a href="#L-305"><span class="linenos">305</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
@@ -1177,6 +1197,56 @@
</div>
</section>
<section id="lba_to_chs">
<input id="lba_to_chs-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
<div class="attr function">
<span class="def">def</span>
<span class="name">lba_to_chs</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">max_lba</span><span class="o">=</span><span class="mi">2880</span>, </span><span class="param"><span class="n">sectors_per_track</span><span class="o">=</span><span class="mi">18</span>, </span><span class="param"><span class="n">number_of_heads</span><span class="o">=</span><span class="mi">2</span></span><span class="return-annotation">):</span></span>
<label class="view-source-button" for="lba_to_chs-view-source"><span>View Source</span></label>
</div>
<a class="headerlink" href="#lba_to_chs"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="lba_to_chs-291"><a href="#lba_to_chs-291"><span class="linenos">291</span></a><span class="k">def</span><span class="w"> </span><span class="nf">lba_to_chs</span><span class="p">(</span><span class="n">max_lba</span><span class="o">=</span><span class="mi">2880</span><span class="p">,</span> <span class="n">sectors_per_track</span><span class="o">=</span><span class="mi">18</span><span class="p">,</span> <span class="n">number_of_heads</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
</span><span id="lba_to_chs-292"><a href="#lba_to_chs-292"><span class="linenos">292</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot; Calculating the Cylinder, Head and Sector numbers for a given LBA</span>
</span><span id="lba_to_chs-293"><a href="#lba_to_chs-293"><span class="linenos">293</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="lba_to_chs-294"><a href="#lba_to_chs-294"><span class="linenos">294</span></a><span class="sd"> | --- | --- |</span>
</span><span id="lba_to_chs-295"><a href="#lba_to_chs-295"><span class="linenos">295</span></a><span class="sd"> | If the LBA of a block is $2243$ on a device with $18$ sectors per track and $2$ heads, what are the cylinder, head and sector numbers? | Cylinder: $62$, Head: $0$, Sector: $12$ |</span>
</span><span id="lba_to_chs-296"><a href="#lba_to_chs-296"><span class="linenos">296</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="lba_to_chs-297"><a href="#lba_to_chs-297"><span class="linenos">297</span></a> <span class="n">lba</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_lba</span><span class="p">)</span>
</span><span id="lba_to_chs-298"><a href="#lba_to_chs-298"><span class="linenos">298</span></a> <span class="n">cylinder</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">lba</span><span class="o">/</span><span class="p">(</span><span class="n">sectors_per_track</span><span class="o">*</span><span class="n">number_of_heads</span><span class="p">));</span>
</span><span id="lba_to_chs-299"><a href="#lba_to_chs-299"><span class="linenos">299</span></a> <span class="n">t</span> <span class="o">=</span> <span class="n">cylinder</span><span class="o">*</span><span class="p">(</span><span class="n">sectors_per_track</span><span class="o">*</span><span class="n">number_of_heads</span><span class="p">);</span>
</span><span id="lba_to_chs-300"><a href="#lba_to_chs-300"><span class="linenos">300</span></a> <span class="n">t</span> <span class="o">=</span> <span class="n">lba</span><span class="o">-</span><span class="n">t</span><span class="p">;</span>
</span><span id="lba_to_chs-301"><a href="#lba_to_chs-301"><span class="linenos">301</span></a> <span class="n">head</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">t</span><span class="o">/</span><span class="p">(</span><span class="n">sectors_per_track</span><span class="p">));</span>
</span><span id="lba_to_chs-302"><a href="#lba_to_chs-302"><span class="linenos">302</span></a> <span class="n">sector</span> <span class="o">=</span> <span class="n">t</span> <span class="o">-</span> <span class="p">(</span><span class="n">head</span> <span class="o">*</span> <span class="n">lba</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">;</span>
</span><span id="lba_to_chs-303"><a href="#lba_to_chs-303"><span class="linenos">303</span></a>
</span><span id="lba_to_chs-304"><a href="#lba_to_chs-304"><span class="linenos">304</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;If the LBA of a block is $</span><span class="si">{</span><span class="n">lba</span><span class="si">}</span><span class="s2">$ on a disk with $</span><span class="si">{</span><span class="n">sectors_per_track</span><span class="si">}</span><span class="s2">$ sectors per track and $</span><span class="si">{</span><span class="n">number_of_heads</span><span class="si">}</span><span class="s2">$ heads, what are the cylinder, head and sector numbers?&quot;</span>
</span><span id="lba_to_chs-305"><a href="#lba_to_chs-305"><span class="linenos">305</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Cylinder: $</span><span class="si">{</span><span class="n">cylinder</span><span class="si">}</span><span class="s2">$, Head: $</span><span class="si">{</span><span class="n">head</span><span class="si">}</span><span class="s2">$, Sector: $</span><span class="si">{</span><span class="n">sector</span><span class="si">}</span><span class="s2">$&quot;</span>
</span><span id="lba_to_chs-306"><a href="#lba_to_chs-306"><span class="linenos">306</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
<div class="docstring"><p>Calculating the Cylinder, Head and Sector numbers for a given LBA</p>
<table>
<thead>
<tr>
<th>Ex. Problem</th>
<th>Ex. Solution</th>
</tr>
</thead>
<tbody>
<tr>
<td>If the LBA of a block is $2243$ on a device with $18$ sectors per track and $2$ heads, what are the cylinder, head and sector numbers?</td>
<td>Cylinder: $62$, Head: $0$, Sector: $12$</td>
</tr>
</tbody>
</table>
</div>
</section>
</main>
<script>

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@@ -61,6 +61,9 @@
<li>
<a class="function" href="#resistivity">resistivity</a>
</li>
<li>
<a class="function" href="#fringe_spacing">fringe_spacing</a>
</li>
</ul>
@@ -85,65 +88,85 @@
<div class="pdoc-code codehilite"><pre><span></span><span id="L-1"><a href="#L-1"><span class="linenos"> 1</span></a><span class="kn">import</span><span class="w"> </span><span class="nn">random</span>
</span><span id="L-2"><a href="#L-2"><span class="linenos"> 2</span></a><span class="kn">import</span><span class="w"> </span><span class="nn">math</span>
</span><span id="L-3"><a href="#L-3"><span class="linenos"> 3</span></a>
</span><span id="L-4"><a href="#L-4"><span class="linenos"> 4</span></a><span class="k">def</span><span class="w"> </span><span class="nf">kinetic_energy</span><span class="p">(</span><span class="n">max_mass</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">max_vel</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
</span><span id="L-5"><a href="#L-5"><span class="linenos"> 5</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Kinetic Energy calculation using Ek = 0.5 * m * v^2</span>
</span><span id="L-6"><a href="#L-6"><span class="linenos"> 6</span></a>
</span><span id="L-7"><a href="#L-7"><span class="linenos"> 7</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-8"><a href="#L-8"><span class="linenos"> 8</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-9"><a href="#L-9"><span class="linenos"> 9</span></a><span class="sd"> | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |</span>
</span><span id="L-10"><a href="#L-10"><span class="linenos">10</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-11"><a href="#L-11"><span class="linenos">11</span></a> <span class="n">velocity</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_vel</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="L-12"><a href="#L-12"><span class="linenos">12</span></a> <span class="n">mass</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_mass</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="L-13"><a href="#L-13"><span class="linenos">13</span></a> <span class="n">kinetic_energy</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">mass</span> <span class="o">*</span> <span class="n">velocity</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="mi">2</span><span class="p">)</span>
</span><span id="L-14"><a href="#L-14"><span class="linenos">14</span></a>
</span><span id="L-4"><a href="#L-4"><span class="linenos"> 4</span></a><span class="c1"># Generic</span>
</span><span id="L-5"><a href="#L-5"><span class="linenos"> 5</span></a><span class="k">def</span><span class="w"> </span><span class="nf">kinetic_energy</span><span class="p">(</span><span class="n">max_mass</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">max_vel</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
</span><span id="L-6"><a href="#L-6"><span class="linenos"> 6</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Kinetic Energy calculation using Ek = 0.5 * m * v^2</span>
</span><span id="L-7"><a href="#L-7"><span class="linenos"> 7</span></a>
</span><span id="L-8"><a href="#L-8"><span class="linenos"> 8</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-9"><a href="#L-9"><span class="linenos"> 9</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-10"><a href="#L-10"><span class="linenos">10</span></a><span class="sd"> | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |</span>
</span><span id="L-11"><a href="#L-11"><span class="linenos">11</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-12"><a href="#L-12"><span class="linenos">12</span></a> <span class="n">velocity</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_vel</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="L-13"><a href="#L-13"><span class="linenos">13</span></a> <span class="n">mass</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_mass</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="L-14"><a href="#L-14"><span class="linenos">14</span></a> <span class="n">kinetic_energy</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">mass</span> <span class="o">*</span> <span class="n">velocity</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="mi">2</span><span class="p">)</span>
</span><span id="L-15"><a href="#L-15"><span class="linenos">15</span></a>
</span><span id="L-16"><a href="#L-16"><span class="linenos">16</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;What is the kinetic energy of an object of mass $</span><span class="si">{</span><span class="n">mass</span><span class="si">}</span><span class="s2"> kg$ and velocity $</span><span class="si">{</span><span class="n">velocity</span><span class="si">}</span><span class="s2"> m/s$?&quot;</span>
</span><span id="L-17"><a href="#L-17"><span class="linenos">17</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">kinetic_energy</span><span class="si">}</span><span class="s1"> J$&#39;</span>
</span><span id="L-18"><a href="#L-18"><span class="linenos">18</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="L-19"><a href="#L-19"><span class="linenos">19</span></a>
</span><span id="L-20"><a href="#L-20"><span class="linenos">20</span></a><span class="k">def</span><span class="w"> </span><span class="nf">potential_dividers</span><span class="p">(</span><span class="n">max_vin</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mi">500</span><span class="p">):</span>
</span><span id="L-21"><a href="#L-21"><span class="linenos">21</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Potential Divider question using Vout = (Vin * R2) / (R2 + R1)</span>
</span><span id="L-22"><a href="#L-22"><span class="linenos">22</span></a>
</span><span id="L-23"><a href="#L-23"><span class="linenos">23</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-24"><a href="#L-24"><span class="linenos">24</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-25"><a href="#L-25"><span class="linenos">25</span></a><span class="sd"> | In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |</span>
</span><span id="L-26"><a href="#L-26"><span class="linenos">26</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-27"><a href="#L-27"><span class="linenos">27</span></a><span class="w"> </span><span class="sd">&#39;&#39;&#39;</span>
</span><span id="L-28"><a href="#L-28"><span class="linenos">28</span></a><span class="sd"> This is what a potential divider circuit looks like:</span>
</span><span id="L-29"><a href="#L-29"><span class="linenos">29</span></a><span class="sd"> ------</span>
</span><span id="L-30"><a href="#L-30"><span class="linenos">30</span></a><span class="sd"> | R1</span>
</span><span id="L-31"><a href="#L-31"><span class="linenos">31</span></a><span class="sd"> Vi = |----o</span>
</span><span id="L-32"><a href="#L-32"><span class="linenos">32</span></a><span class="sd"> | R2 Vout</span>
</span><span id="L-33"><a href="#L-33"><span class="linenos">33</span></a><span class="sd"> |____|____o</span>
</span><span id="L-34"><a href="#L-34"><span class="linenos">34</span></a><span class="sd"> &#39;&#39;&#39;</span>
</span><span id="L-35"><a href="#L-35"><span class="linenos">35</span></a> <span class="n">vin</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_vin</span><span class="p">)</span> <span class="c1"># Voltage input of cell</span>
</span><span id="L-36"><a href="#L-36"><span class="linenos">36</span></a> <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R1</span>
</span><span id="L-37"><a href="#L-37"><span class="linenos">37</span></a> <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R2</span>
</span><span id="L-38"><a href="#L-38"><span class="linenos">38</span></a> <span class="n">vout</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">vin</span> <span class="o">*</span> <span class="n">r2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">r1</span> <span class="o">+</span> <span class="n">r2</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Voltage output across R2</span>
</span><span id="L-39"><a href="#L-39"><span class="linenos">39</span></a>
</span><span id="L-40"><a href="#L-40"><span class="linenos">40</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;In a Potential Divider, if resistors R1 and R2 have resistances of $</span><span class="si">{</span><span class="n">r1</span><span class="si">}</span><span class="s2"> Ω$ and $</span><span class="si">{</span><span class="n">r2</span><span class="si">}</span><span class="s2"> Ω$ respectively, and the cell has $</span><span class="si">{</span><span class="n">vin</span><span class="si">}</span><span class="s2"> V$ What is the output potential difference across R2?&quot;</span>
</span><span id="L-41"><a href="#L-41"><span class="linenos">41</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">vout</span><span class="si">}</span><span class="s2"> V$&quot;</span>
</span><span id="L-42"><a href="#L-42"><span class="linenos">42</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="L-43"><a href="#L-43"><span class="linenos">43</span></a>
</span><span id="L-44"><a href="#L-44"><span class="linenos">44</span></a><span class="k">def</span><span class="w"> </span><span class="nf">resistivity</span><span class="p">(</span><span class="n">max_diameter_mm</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mf">0.1</span><span class="p">):</span>
</span><span id="L-45"><a href="#L-45"><span class="linenos">45</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire</span>
</span><span id="L-16"><a href="#L-16"><span class="linenos">16</span></a>
</span><span id="L-17"><a href="#L-17"><span class="linenos">17</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;What is the kinetic energy of an object of mass $</span><span class="si">{</span><span class="n">mass</span><span class="si">}</span><span class="s2"> kg$ and velocity $</span><span class="si">{</span><span class="n">velocity</span><span class="si">}</span><span class="s2"> m/s$?&quot;</span>
</span><span id="L-18"><a href="#L-18"><span class="linenos">18</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">kinetic_energy</span><span class="si">}</span><span class="s1"> J$&#39;</span>
</span><span id="L-19"><a href="#L-19"><span class="linenos">19</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="L-20"><a href="#L-20"><span class="linenos">20</span></a>
</span><span id="L-21"><a href="#L-21"><span class="linenos">21</span></a>
</span><span id="L-22"><a href="#L-22"><span class="linenos">22</span></a><span class="c1"># Electricity</span>
</span><span id="L-23"><a href="#L-23"><span class="linenos">23</span></a><span class="k">def</span><span class="w"> </span><span class="nf">potential_dividers</span><span class="p">(</span><span class="n">max_vin</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mi">500</span><span class="p">):</span>
</span><span id="L-24"><a href="#L-24"><span class="linenos">24</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Potential Divider question using Vout = (Vin * R2) / (R2 + R1)</span>
</span><span id="L-25"><a href="#L-25"><span class="linenos">25</span></a>
</span><span id="L-26"><a href="#L-26"><span class="linenos">26</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-27"><a href="#L-27"><span class="linenos">27</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-28"><a href="#L-28"><span class="linenos">28</span></a><span class="sd"> | In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |</span>
</span><span id="L-29"><a href="#L-29"><span class="linenos">29</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-30"><a href="#L-30"><span class="linenos">30</span></a><span class="w"> </span><span class="sd">&#39;&#39;&#39;</span>
</span><span id="L-31"><a href="#L-31"><span class="linenos">31</span></a><span class="sd"> This is what a potential divider circuit looks like:</span>
</span><span id="L-32"><a href="#L-32"><span class="linenos">32</span></a><span class="sd"> ------</span>
</span><span id="L-33"><a href="#L-33"><span class="linenos">33</span></a><span class="sd"> | R1</span>
</span><span id="L-34"><a href="#L-34"><span class="linenos">34</span></a><span class="sd"> Vi = |----o</span>
</span><span id="L-35"><a href="#L-35"><span class="linenos">35</span></a><span class="sd"> | R2 Vout</span>
</span><span id="L-36"><a href="#L-36"><span class="linenos">36</span></a><span class="sd"> |____|____o</span>
</span><span id="L-37"><a href="#L-37"><span class="linenos">37</span></a><span class="sd"> &#39;&#39;&#39;</span>
</span><span id="L-38"><a href="#L-38"><span class="linenos">38</span></a> <span class="n">vin</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_vin</span><span class="p">)</span> <span class="c1"># Voltage input of cell</span>
</span><span id="L-39"><a href="#L-39"><span class="linenos">39</span></a> <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R1</span>
</span><span id="L-40"><a href="#L-40"><span class="linenos">40</span></a> <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R2</span>
</span><span id="L-41"><a href="#L-41"><span class="linenos">41</span></a> <span class="n">vout</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">vin</span> <span class="o">*</span> <span class="n">r2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">r1</span> <span class="o">+</span> <span class="n">r2</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Voltage output across R2</span>
</span><span id="L-42"><a href="#L-42"><span class="linenos">42</span></a>
</span><span id="L-43"><a href="#L-43"><span class="linenos">43</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;In a Potential Divider, if resistors R1 and R2 have resistances of $</span><span class="si">{</span><span class="n">r1</span><span class="si">}</span><span class="s2"> </span><span class="se">\\</span><span class="s2">Omega$ and $</span><span class="si">{</span><span class="n">r2</span><span class="si">}</span><span class="s2"> </span><span class="se">\\</span><span class="s2">Omega$ respectively, and the cell has $</span><span class="si">{</span><span class="n">vin</span><span class="si">}</span><span class="s2"> V$ What is the output potential difference across R2?&quot;</span>
</span><span id="L-44"><a href="#L-44"><span class="linenos">44</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">vout</span><span class="si">}</span><span class="s2"> V$&quot;</span>
</span><span id="L-45"><a href="#L-45"><span class="linenos">45</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="L-46"><a href="#L-46"><span class="linenos">46</span></a>
</span><span id="L-47"><a href="#L-47"><span class="linenos">47</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-48"><a href="#L-48"><span class="linenos">48</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-49"><a href="#L-49"><span class="linenos">49</span></a><span class="sd"> | A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 Ωm$ |</span>
</span><span id="L-50"><a href="#L-50"><span class="linenos">50</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-51"><a href="#L-51"><span class="linenos">51</span></a> <span class="c1"># This question requires a lot of unit conversions and calculating the area of a circle from diameter</span>
</span><span id="L-52"><a href="#L-52"><span class="linenos">52</span></a> <span class="n">diameter_mm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_diameter_mm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random diameter in mm</span>
</span><span id="L-53"><a href="#L-53"><span class="linenos">53</span></a> <span class="n">cross_sectional_area</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="n">diameter_mm</span> <span class="o">/</span> <span class="mi">2000</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Calculate the cross sectional area using pi r²</span>
</span><span id="L-54"><a href="#L-54"><span class="linenos">54</span></a> <span class="n">length_cm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random wire length in cm</span>
</span><span id="L-55"><a href="#L-55"><span class="linenos">55</span></a> <span class="n">resistance</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random reistance in ohms</span>
</span><span id="L-56"><a href="#L-56"><span class="linenos">56</span></a>
</span><span id="L-57"><a href="#L-57"><span class="linenos">57</span></a> <span class="n">resistivity</span> <span class="o">=</span> <span class="p">(</span><span class="n">resistance</span> <span class="o">*</span> <span class="n">cross_sectional_area</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">length_cm</span> <span class="o">/</span> <span class="mi">100</span><span class="p">)</span>
</span><span id="L-58"><a href="#L-58"><span class="linenos">58</span></a>
</span><span id="L-59"><a href="#L-59"><span class="linenos">59</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;A wire has resistance $</span><span class="si">{</span><span class="n">resistance</span><span class="o">*</span><span class="mi">1000</span><span class="si">}</span><span class="s2"> mΩ$ when it is $</span><span class="si">{</span><span class="n">length_cm</span><span class="si">}</span><span class="s2"> cm$ long with a diameter of $</span><span class="si">{</span><span class="n">diameter_mm</span><span class="si">}</span><span class="s2"> mm$. Calculate the resistivity of the wire&quot;</span>
</span><span id="L-60"><a href="#L-60"><span class="linenos">60</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">resistivity</span><span class="si">:</span><span class="s2">.2e</span><span class="si">}</span><span class="s2"> Ωm$&quot;</span>
</span><span id="L-47"><a href="#L-47"><span class="linenos">47</span></a><span class="k">def</span><span class="w"> </span><span class="nf">resistivity</span><span class="p">(</span><span class="n">max_diameter_mm</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mf">0.1</span><span class="p">):</span>
</span><span id="L-48"><a href="#L-48"><span class="linenos">48</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire</span>
</span><span id="L-49"><a href="#L-49"><span class="linenos">49</span></a>
</span><span id="L-50"><a href="#L-50"><span class="linenos">50</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-51"><a href="#L-51"><span class="linenos">51</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-52"><a href="#L-52"><span class="linenos">52</span></a><span class="sd"> | A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 \Omega m$ |</span>
</span><span id="L-53"><a href="#L-53"><span class="linenos">53</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-54"><a href="#L-54"><span class="linenos">54</span></a> <span class="c1"># This question requires a lot of unit conversions and calculating the area of a circle from diameter</span>
</span><span id="L-55"><a href="#L-55"><span class="linenos">55</span></a> <span class="n">diameter_mm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_diameter_mm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random diameter in mm</span>
</span><span id="L-56"><a href="#L-56"><span class="linenos">56</span></a> <span class="n">cross_sectional_area</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="n">diameter_mm</span> <span class="o">/</span> <span class="mi">2000</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Calculate the cross sectional area using pi r²</span>
</span><span id="L-57"><a href="#L-57"><span class="linenos">57</span></a> <span class="n">length_cm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random wire length in cm</span>
</span><span id="L-58"><a href="#L-58"><span class="linenos">58</span></a> <span class="n">resistance</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random reistance in ohms</span>
</span><span id="L-59"><a href="#L-59"><span class="linenos">59</span></a>
</span><span id="L-60"><a href="#L-60"><span class="linenos">60</span></a> <span class="n">resistivity</span> <span class="o">=</span> <span class="p">(</span><span class="n">resistance</span> <span class="o">*</span> <span class="n">cross_sectional_area</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">length_cm</span> <span class="o">/</span> <span class="mi">100</span><span class="p">)</span>
</span><span id="L-61"><a href="#L-61"><span class="linenos">61</span></a>
</span><span id="L-62"><a href="#L-62"><span class="linenos">62</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="L-62"><a href="#L-62"><span class="linenos">62</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;A wire has resistance $</span><span class="si">{</span><span class="n">resistance</span><span class="o">*</span><span class="mi">1000</span><span class="si">}</span><span class="s2"> m</span><span class="se">\\</span><span class="s2">Omega$ when it is $</span><span class="si">{</span><span class="n">length_cm</span><span class="si">}</span><span class="s2"> cm$ long with a diameter of $</span><span class="si">{</span><span class="n">diameter_mm</span><span class="si">}</span><span class="s2"> mm$. Calculate the resistivity of the wire&quot;</span>
</span><span id="L-63"><a href="#L-63"><span class="linenos">63</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">resistivity</span><span class="si">:</span><span class="s2">.2e</span><span class="si">}</span><span class="s2"> </span><span class="se">\\</span><span class="s2">Omega m$&quot;</span>
</span><span id="L-64"><a href="#L-64"><span class="linenos">64</span></a>
</span><span id="L-65"><a href="#L-65"><span class="linenos">65</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="L-66"><a href="#L-66"><span class="linenos">66</span></a>
</span><span id="L-67"><a href="#L-67"><span class="linenos">67</span></a><span class="c1"># Waves</span>
</span><span id="L-68"><a href="#L-68"><span class="linenos">68</span></a><span class="k">def</span><span class="w"> </span><span class="nf">fringe_spacing</span><span class="p">(</span><span class="n">max_screen_distance</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span> <span class="n">max_slit_spacing_mm</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
</span><span id="L-69"><a href="#L-69"><span class="linenos">69</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Calculate the fringe spacing in a double slit experiment with w=(λD)/s</span>
</span><span id="L-70"><a href="#L-70"><span class="linenos">70</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="L-71"><a href="#L-71"><span class="linenos">71</span></a><span class="sd"> | --- | --- |</span>
</span><span id="L-72"><a href="#L-72"><span class="linenos">72</span></a><span class="sd"> | A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes. | Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$ |</span>
</span><span id="L-73"><a href="#L-73"><span class="linenos">73</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="L-74"><a href="#L-74"><span class="linenos">74</span></a> <span class="n">wavelength_nm</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">380</span><span class="p">,</span><span class="mi">750</span><span class="p">)</span> <span class="c1"># Random wavelength between violet and red (nm)</span>
</span><span id="L-75"><a href="#L-75"><span class="linenos">75</span></a> <span class="n">screen_distance</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_screen_distance</span><span class="p">)</span> <span class="c1"># Random distance between screen and slits (m)</span>
</span><span id="L-76"><a href="#L-76"><span class="linenos">76</span></a> <span class="n">slit_spacing_mm</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_slit_spacing_mm</span><span class="p">)</span> <span class="c1"># Random slit spacing (mm)</span>
</span><span id="L-77"><a href="#L-77"><span class="linenos">77</span></a>
</span><span id="L-78"><a href="#L-78"><span class="linenos">78</span></a> <span class="n">fringe_spacing</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((((</span><span class="n">wavelength_nm</span> <span class="o">*</span> <span class="mi">10</span><span class="o">**-</span><span class="mi">9</span><span class="p">)</span> <span class="o">*</span> <span class="n">screen_distance</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">slit_spacing_mm</span> <span class="o">*</span> <span class="mi">10</span><span class="o">**-</span><span class="mi">3</span><span class="p">)),</span><span class="mi">5</span><span class="p">)</span>
</span><span id="L-79"><a href="#L-79"><span class="linenos">79</span></a>
</span><span id="L-80"><a href="#L-80"><span class="linenos">80</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;A laser with a wavelength of $</span><span class="si">{</span><span class="n">wavelength_nm</span><span class="si">}</span><span class="s2">nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $</span><span class="si">{</span><span class="n">screen_distance</span><span class="si">}</span><span class="s2">m$ from the slits and the slits are $</span><span class="si">{</span><span class="n">slit_spacing_mm</span><span class="si">}</span><span class="s2">mm$ apart. Calculate the spacing between the bright fringes.&quot;</span>
</span><span id="L-81"><a href="#L-81"><span class="linenos">81</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Using the equation $</span><span class="se">\\</span><span class="s2">frac</span><span class="se">{{\\</span><span class="s2">lambda D</span><span class="se">}}{{</span><span class="s2">s</span><span class="se">}}</span><span class="s2">$, we get a fringe spacing of $</span><span class="si">{</span><span class="n">fringe_spacing</span><span class="si">}</span><span class="s2">m$&quot;</span>
</span><span id="L-82"><a href="#L-82"><span class="linenos">82</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
@@ -159,21 +182,21 @@
</div>
<a class="headerlink" href="#kinetic_energy"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="kinetic_energy-5"><a href="#kinetic_energy-5"><span class="linenos"> 5</span></a><span class="k">def</span><span class="w"> </span><span class="nf">kinetic_energy</span><span class="p">(</span><span class="n">max_mass</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">max_vel</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
</span><span id="kinetic_energy-6"><a href="#kinetic_energy-6"><span class="linenos"> 6</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Kinetic Energy calculation using Ek = 0.5 * m * v^2</span>
</span><span id="kinetic_energy-7"><a href="#kinetic_energy-7"><span class="linenos"> 7</span></a>
</span><span id="kinetic_energy-8"><a href="#kinetic_energy-8"><span class="linenos"> 8</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="kinetic_energy-9"><a href="#kinetic_energy-9"><span class="linenos"> 9</span></a><span class="sd"> | --- | --- |</span>
</span><span id="kinetic_energy-10"><a href="#kinetic_energy-10"><span class="linenos">10</span></a><span class="sd"> | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |</span>
</span><span id="kinetic_energy-11"><a href="#kinetic_energy-11"><span class="linenos">11</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="kinetic_energy-12"><a href="#kinetic_energy-12"><span class="linenos">12</span></a> <span class="n">velocity</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_vel</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="kinetic_energy-13"><a href="#kinetic_energy-13"><span class="linenos">13</span></a> <span class="n">mass</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_mass</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="kinetic_energy-14"><a href="#kinetic_energy-14"><span class="linenos">14</span></a> <span class="n">kinetic_energy</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">mass</span> <span class="o">*</span> <span class="n">velocity</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="mi">2</span><span class="p">)</span>
</span><span id="kinetic_energy-15"><a href="#kinetic_energy-15"><span class="linenos">15</span></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="kinetic_energy-6"><a href="#kinetic_energy-6"><span class="linenos"> 6</span></a><span class="k">def</span><span class="w"> </span><span class="nf">kinetic_energy</span><span class="p">(</span><span class="n">max_mass</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">max_vel</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
</span><span id="kinetic_energy-7"><a href="#kinetic_energy-7"><span class="linenos"> 7</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Kinetic Energy calculation using Ek = 0.5 * m * v^2</span>
</span><span id="kinetic_energy-8"><a href="#kinetic_energy-8"><span class="linenos"> 8</span></a>
</span><span id="kinetic_energy-9"><a href="#kinetic_energy-9"><span class="linenos"> 9</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="kinetic_energy-10"><a href="#kinetic_energy-10"><span class="linenos">10</span></a><span class="sd"> | --- | --- |</span>
</span><span id="kinetic_energy-11"><a href="#kinetic_energy-11"><span class="linenos">11</span></a><span class="sd"> | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |</span>
</span><span id="kinetic_energy-12"><a href="#kinetic_energy-12"><span class="linenos">12</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="kinetic_energy-13"><a href="#kinetic_energy-13"><span class="linenos">13</span></a> <span class="n">velocity</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_vel</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="kinetic_energy-14"><a href="#kinetic_energy-14"><span class="linenos">14</span></a> <span class="n">mass</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_mass</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span>
</span><span id="kinetic_energy-15"><a href="#kinetic_energy-15"><span class="linenos">15</span></a> <span class="n">kinetic_energy</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">mass</span> <span class="o">*</span> <span class="n">velocity</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="mi">2</span><span class="p">)</span>
</span><span id="kinetic_energy-16"><a href="#kinetic_energy-16"><span class="linenos">16</span></a>
</span><span id="kinetic_energy-17"><a href="#kinetic_energy-17"><span class="linenos">17</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;What is the kinetic energy of an object of mass $</span><span class="si">{</span><span class="n">mass</span><span class="si">}</span><span class="s2"> kg$ and velocity $</span><span class="si">{</span><span class="n">velocity</span><span class="si">}</span><span class="s2"> m/s$?&quot;</span>
</span><span id="kinetic_energy-18"><a href="#kinetic_energy-18"><span class="linenos">18</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">kinetic_energy</span><span class="si">}</span><span class="s1"> J$&#39;</span>
</span><span id="kinetic_energy-19"><a href="#kinetic_energy-19"><span class="linenos">19</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="kinetic_energy-17"><a href="#kinetic_energy-17"><span class="linenos">17</span></a>
</span><span id="kinetic_energy-18"><a href="#kinetic_energy-18"><span class="linenos">18</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;What is the kinetic energy of an object of mass $</span><span class="si">{</span><span class="n">mass</span><span class="si">}</span><span class="s2"> kg$ and velocity $</span><span class="si">{</span><span class="n">velocity</span><span class="si">}</span><span class="s2"> m/s$?&quot;</span>
</span><span id="kinetic_energy-19"><a href="#kinetic_energy-19"><span class="linenos">19</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">kinetic_energy</span><span class="si">}</span><span class="s1"> J$&#39;</span>
</span><span id="kinetic_energy-20"><a href="#kinetic_energy-20"><span class="linenos">20</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
@@ -208,29 +231,29 @@
</div>
<a class="headerlink" href="#potential_dividers"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="potential_dividers-21"><a href="#potential_dividers-21"><span class="linenos">21</span></a><span class="k">def</span><span class="w"> </span><span class="nf">potential_dividers</span><span class="p">(</span><span class="n">max_vin</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mi">500</span><span class="p">):</span>
</span><span id="potential_dividers-22"><a href="#potential_dividers-22"><span class="linenos">22</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Potential Divider question using Vout = (Vin * R2) / (R2 + R1)</span>
</span><span id="potential_dividers-23"><a href="#potential_dividers-23"><span class="linenos">23</span></a>
</span><span id="potential_dividers-24"><a href="#potential_dividers-24"><span class="linenos">24</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="potential_dividers-25"><a href="#potential_dividers-25"><span class="linenos">25</span></a><span class="sd"> | --- | --- |</span>
</span><span id="potential_dividers-26"><a href="#potential_dividers-26"><span class="linenos">26</span></a><span class="sd"> | In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |</span>
</span><span id="potential_dividers-27"><a href="#potential_dividers-27"><span class="linenos">27</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="potential_dividers-28"><a href="#potential_dividers-28"><span class="linenos">28</span></a><span class="w"> </span><span class="sd">&#39;&#39;&#39;</span>
</span><span id="potential_dividers-29"><a href="#potential_dividers-29"><span class="linenos">29</span></a><span class="sd"> This is what a potential divider circuit looks like:</span>
</span><span id="potential_dividers-30"><a href="#potential_dividers-30"><span class="linenos">30</span></a><span class="sd"> ------</span>
</span><span id="potential_dividers-31"><a href="#potential_dividers-31"><span class="linenos">31</span></a><span class="sd"> | R1</span>
</span><span id="potential_dividers-32"><a href="#potential_dividers-32"><span class="linenos">32</span></a><span class="sd"> Vi = |----o</span>
</span><span id="potential_dividers-33"><a href="#potential_dividers-33"><span class="linenos">33</span></a><span class="sd"> | R2 Vout</span>
</span><span id="potential_dividers-34"><a href="#potential_dividers-34"><span class="linenos">34</span></a><span class="sd"> |____|____o</span>
</span><span id="potential_dividers-35"><a href="#potential_dividers-35"><span class="linenos">35</span></a><span class="sd"> &#39;&#39;&#39;</span>
</span><span id="potential_dividers-36"><a href="#potential_dividers-36"><span class="linenos">36</span></a> <span class="n">vin</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_vin</span><span class="p">)</span> <span class="c1"># Voltage input of cell</span>
</span><span id="potential_dividers-37"><a href="#potential_dividers-37"><span class="linenos">37</span></a> <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R1</span>
</span><span id="potential_dividers-38"><a href="#potential_dividers-38"><span class="linenos">38</span></a> <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R2</span>
</span><span id="potential_dividers-39"><a href="#potential_dividers-39"><span class="linenos">39</span></a> <span class="n">vout</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">vin</span> <span class="o">*</span> <span class="n">r2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">r1</span> <span class="o">+</span> <span class="n">r2</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Voltage output across R2</span>
</span><span id="potential_dividers-40"><a href="#potential_dividers-40"><span class="linenos">40</span></a>
</span><span id="potential_dividers-41"><a href="#potential_dividers-41"><span class="linenos">41</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;In a Potential Divider, if resistors R1 and R2 have resistances of $</span><span class="si">{</span><span class="n">r1</span><span class="si">}</span><span class="s2"> Ω$ and $</span><span class="si">{</span><span class="n">r2</span><span class="si">}</span><span class="s2"> Ω$ respectively, and the cell has $</span><span class="si">{</span><span class="n">vin</span><span class="si">}</span><span class="s2"> V$ What is the output potential difference across R2?&quot;</span>
</span><span id="potential_dividers-42"><a href="#potential_dividers-42"><span class="linenos">42</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">vout</span><span class="si">}</span><span class="s2"> V$&quot;</span>
</span><span id="potential_dividers-43"><a href="#potential_dividers-43"><span class="linenos">43</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
<div class="pdoc-code codehilite"><pre><span></span><span id="potential_dividers-24"><a href="#potential_dividers-24"><span class="linenos">24</span></a><span class="k">def</span><span class="w"> </span><span class="nf">potential_dividers</span><span class="p">(</span><span class="n">max_vin</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mi">500</span><span class="p">):</span>
</span><span id="potential_dividers-25"><a href="#potential_dividers-25"><span class="linenos">25</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Potential Divider question using Vout = (Vin * R2) / (R2 + R1)</span>
</span><span id="potential_dividers-26"><a href="#potential_dividers-26"><span class="linenos">26</span></a>
</span><span id="potential_dividers-27"><a href="#potential_dividers-27"><span class="linenos">27</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="potential_dividers-28"><a href="#potential_dividers-28"><span class="linenos">28</span></a><span class="sd"> | --- | --- |</span>
</span><span id="potential_dividers-29"><a href="#potential_dividers-29"><span class="linenos">29</span></a><span class="sd"> | In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |</span>
</span><span id="potential_dividers-30"><a href="#potential_dividers-30"><span class="linenos">30</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="potential_dividers-31"><a href="#potential_dividers-31"><span class="linenos">31</span></a><span class="w"> </span><span class="sd">&#39;&#39;&#39;</span>
</span><span id="potential_dividers-32"><a href="#potential_dividers-32"><span class="linenos">32</span></a><span class="sd"> This is what a potential divider circuit looks like:</span>
</span><span id="potential_dividers-33"><a href="#potential_dividers-33"><span class="linenos">33</span></a><span class="sd"> ------</span>
</span><span id="potential_dividers-34"><a href="#potential_dividers-34"><span class="linenos">34</span></a><span class="sd"> | R1</span>
</span><span id="potential_dividers-35"><a href="#potential_dividers-35"><span class="linenos">35</span></a><span class="sd"> Vi = |----o</span>
</span><span id="potential_dividers-36"><a href="#potential_dividers-36"><span class="linenos">36</span></a><span class="sd"> | R2 Vout</span>
</span><span id="potential_dividers-37"><a href="#potential_dividers-37"><span class="linenos">37</span></a><span class="sd"> |____|____o</span>
</span><span id="potential_dividers-38"><a href="#potential_dividers-38"><span class="linenos">38</span></a><span class="sd"> &#39;&#39;&#39;</span>
</span><span id="potential_dividers-39"><a href="#potential_dividers-39"><span class="linenos">39</span></a> <span class="n">vin</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_vin</span><span class="p">)</span> <span class="c1"># Voltage input of cell</span>
</span><span id="potential_dividers-40"><a href="#potential_dividers-40"><span class="linenos">40</span></a> <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R1</span>
</span><span id="potential_dividers-41"><a href="#potential_dividers-41"><span class="linenos">41</span></a> <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">)</span> <span class="c1"># Resistance of R2</span>
</span><span id="potential_dividers-42"><a href="#potential_dividers-42"><span class="linenos">42</span></a> <span class="n">vout</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">vin</span> <span class="o">*</span> <span class="n">r2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">r1</span> <span class="o">+</span> <span class="n">r2</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Voltage output across R2</span>
</span><span id="potential_dividers-43"><a href="#potential_dividers-43"><span class="linenos">43</span></a>
</span><span id="potential_dividers-44"><a href="#potential_dividers-44"><span class="linenos">44</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;In a Potential Divider, if resistors R1 and R2 have resistances of $</span><span class="si">{</span><span class="n">r1</span><span class="si">}</span><span class="s2"> </span><span class="se">\\</span><span class="s2">Omega$ and $</span><span class="si">{</span><span class="n">r2</span><span class="si">}</span><span class="s2"> </span><span class="se">\\</span><span class="s2">Omega$ respectively, and the cell has $</span><span class="si">{</span><span class="n">vin</span><span class="si">}</span><span class="s2"> V$ What is the output potential difference across R2?&quot;</span>
</span><span id="potential_dividers-45"><a href="#potential_dividers-45"><span class="linenos">45</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">vout</span><span class="si">}</span><span class="s2"> V$&quot;</span>
</span><span id="potential_dividers-46"><a href="#potential_dividers-46"><span class="linenos">46</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
@@ -245,7 +268,7 @@
</thead>
<tbody>
<tr>
<td>In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2?</td>
<td>In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2?</td>
<td>$4 V$</td>
</tr>
</tbody>
@@ -265,25 +288,25 @@
</div>
<a class="headerlink" href="#resistivity"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="resistivity-45"><a href="#resistivity-45"><span class="linenos">45</span></a><span class="k">def</span><span class="w"> </span><span class="nf">resistivity</span><span class="p">(</span><span class="n">max_diameter_mm</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mf">0.1</span><span class="p">):</span>
</span><span id="resistivity-46"><a href="#resistivity-46"><span class="linenos">46</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire</span>
</span><span id="resistivity-47"><a href="#resistivity-47"><span class="linenos">47</span></a>
</span><span id="resistivity-48"><a href="#resistivity-48"><span class="linenos">48</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="resistivity-49"><a href="#resistivity-49"><span class="linenos">49</span></a><span class="sd"> | --- | --- |</span>
</span><span id="resistivity-50"><a href="#resistivity-50"><span class="linenos">50</span></a><span class="sd"> | A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 Ωm$ |</span>
</span><span id="resistivity-51"><a href="#resistivity-51"><span class="linenos">51</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="resistivity-52"><a href="#resistivity-52"><span class="linenos">52</span></a> <span class="c1"># This question requires a lot of unit conversions and calculating the area of a circle from diameter</span>
</span><span id="resistivity-53"><a href="#resistivity-53"><span class="linenos">53</span></a> <span class="n">diameter_mm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_diameter_mm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random diameter in mm</span>
</span><span id="resistivity-54"><a href="#resistivity-54"><span class="linenos">54</span></a> <span class="n">cross_sectional_area</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="n">diameter_mm</span> <span class="o">/</span> <span class="mi">2000</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Calculate the cross sectional area using pi r²</span>
</span><span id="resistivity-55"><a href="#resistivity-55"><span class="linenos">55</span></a> <span class="n">length_cm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random wire length in cm</span>
</span><span id="resistivity-56"><a href="#resistivity-56"><span class="linenos">56</span></a> <span class="n">resistance</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random reistance in ohms</span>
</span><span id="resistivity-57"><a href="#resistivity-57"><span class="linenos">57</span></a>
</span><span id="resistivity-58"><a href="#resistivity-58"><span class="linenos">58</span></a> <span class="n">resistivity</span> <span class="o">=</span> <span class="p">(</span><span class="n">resistance</span> <span class="o">*</span> <span class="n">cross_sectional_area</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">length_cm</span> <span class="o">/</span> <span class="mi">100</span><span class="p">)</span>
</span><span id="resistivity-59"><a href="#resistivity-59"><span class="linenos">59</span></a>
</span><span id="resistivity-60"><a href="#resistivity-60"><span class="linenos">60</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;A wire has resistance $</span><span class="si">{</span><span class="n">resistance</span><span class="o">*</span><span class="mi">1000</span><span class="si">}</span><span class="s2"> mΩ$ when it is $</span><span class="si">{</span><span class="n">length_cm</span><span class="si">}</span><span class="s2"> cm$ long with a diameter of $</span><span class="si">{</span><span class="n">diameter_mm</span><span class="si">}</span><span class="s2"> mm$. Calculate the resistivity of the wire&quot;</span>
</span><span id="resistivity-61"><a href="#resistivity-61"><span class="linenos">61</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">resistivity</span><span class="si">:</span><span class="s2">.2e</span><span class="si">}</span><span class="s2"> Ωm$&quot;</span>
<div class="pdoc-code codehilite"><pre><span></span><span id="resistivity-48"><a href="#resistivity-48"><span class="linenos">48</span></a><span class="k">def</span><span class="w"> </span><span class="nf">resistivity</span><span class="p">(</span><span class="n">max_diameter_mm</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_resistance</span><span class="o">=</span><span class="mf">0.1</span><span class="p">):</span>
</span><span id="resistivity-49"><a href="#resistivity-49"><span class="linenos">49</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire</span>
</span><span id="resistivity-50"><a href="#resistivity-50"><span class="linenos">50</span></a>
</span><span id="resistivity-51"><a href="#resistivity-51"><span class="linenos">51</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="resistivity-52"><a href="#resistivity-52"><span class="linenos">52</span></a><span class="sd"> | --- | --- |</span>
</span><span id="resistivity-53"><a href="#resistivity-53"><span class="linenos">53</span></a><span class="sd"> | A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 \Omega m$ |</span>
</span><span id="resistivity-54"><a href="#resistivity-54"><span class="linenos">54</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="resistivity-55"><a href="#resistivity-55"><span class="linenos">55</span></a> <span class="c1"># This question requires a lot of unit conversions and calculating the area of a circle from diameter</span>
</span><span id="resistivity-56"><a href="#resistivity-56"><span class="linenos">56</span></a> <span class="n">diameter_mm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_diameter_mm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random diameter in mm</span>
</span><span id="resistivity-57"><a href="#resistivity-57"><span class="linenos">57</span></a> <span class="n">cross_sectional_area</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="n">diameter_mm</span> <span class="o">/</span> <span class="mi">2000</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Calculate the cross sectional area using pi r²</span>
</span><span id="resistivity-58"><a href="#resistivity-58"><span class="linenos">58</span></a> <span class="n">length_cm</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_length_cm</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random wire length in cm</span>
</span><span id="resistivity-59"><a href="#resistivity-59"><span class="linenos">59</span></a> <span class="n">resistance</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_resistance</span><span class="p">),</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Random reistance in ohms</span>
</span><span id="resistivity-60"><a href="#resistivity-60"><span class="linenos">60</span></a>
</span><span id="resistivity-61"><a href="#resistivity-61"><span class="linenos">61</span></a> <span class="n">resistivity</span> <span class="o">=</span> <span class="p">(</span><span class="n">resistance</span> <span class="o">*</span> <span class="n">cross_sectional_area</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">length_cm</span> <span class="o">/</span> <span class="mi">100</span><span class="p">)</span>
</span><span id="resistivity-62"><a href="#resistivity-62"><span class="linenos">62</span></a>
</span><span id="resistivity-63"><a href="#resistivity-63"><span class="linenos">63</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span><span id="resistivity-63"><a href="#resistivity-63"><span class="linenos">63</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;A wire has resistance $</span><span class="si">{</span><span class="n">resistance</span><span class="o">*</span><span class="mi">1000</span><span class="si">}</span><span class="s2"> m</span><span class="se">\\</span><span class="s2">Omega$ when it is $</span><span class="si">{</span><span class="n">length_cm</span><span class="si">}</span><span class="s2"> cm$ long with a diameter of $</span><span class="si">{</span><span class="n">diameter_mm</span><span class="si">}</span><span class="s2"> mm$. Calculate the resistivity of the wire&quot;</span>
</span><span id="resistivity-64"><a href="#resistivity-64"><span class="linenos">64</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">resistivity</span><span class="si">:</span><span class="s2">.2e</span><span class="si">}</span><span class="s2"> </span><span class="se">\\</span><span class="s2">Omega m$&quot;</span>
</span><span id="resistivity-65"><a href="#resistivity-65"><span class="linenos">65</span></a>
</span><span id="resistivity-66"><a href="#resistivity-66"><span class="linenos">66</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
@@ -298,8 +321,57 @@
</thead>
<tbody>
<tr>
<td>A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire</td>
<td>$6.14e-07 Ωm$</td>
<td>A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire</td>
<td>$6.14e-07 \Omega m$</td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="fringe_spacing">
<input id="fringe_spacing-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
<div class="attr function">
<span class="def">def</span>
<span class="name">fringe_spacing</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">max_screen_distance</span><span class="o">=</span><span class="mi">30</span>, </span><span class="param"><span class="n">max_slit_spacing_mm</span><span class="o">=</span><span class="mi">100</span></span><span class="return-annotation">):</span></span>
<label class="view-source-button" for="fringe_spacing-view-source"><span>View Source</span></label>
</div>
<a class="headerlink" href="#fringe_spacing"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="fringe_spacing-69"><a href="#fringe_spacing-69"><span class="linenos">69</span></a><span class="k">def</span><span class="w"> </span><span class="nf">fringe_spacing</span><span class="p">(</span><span class="n">max_screen_distance</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span> <span class="n">max_slit_spacing_mm</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
</span><span id="fringe_spacing-70"><a href="#fringe_spacing-70"><span class="linenos">70</span></a><span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Calculate the fringe spacing in a double slit experiment with w=(λD)/s</span>
</span><span id="fringe_spacing-71"><a href="#fringe_spacing-71"><span class="linenos">71</span></a><span class="sd"> | Ex. Problem | Ex. Solution |</span>
</span><span id="fringe_spacing-72"><a href="#fringe_spacing-72"><span class="linenos">72</span></a><span class="sd"> | --- | --- |</span>
</span><span id="fringe_spacing-73"><a href="#fringe_spacing-73"><span class="linenos">73</span></a><span class="sd"> | A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes. | Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$ |</span>
</span><span id="fringe_spacing-74"><a href="#fringe_spacing-74"><span class="linenos">74</span></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="fringe_spacing-75"><a href="#fringe_spacing-75"><span class="linenos">75</span></a> <span class="n">wavelength_nm</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">380</span><span class="p">,</span><span class="mi">750</span><span class="p">)</span> <span class="c1"># Random wavelength between violet and red (nm)</span>
</span><span id="fringe_spacing-76"><a href="#fringe_spacing-76"><span class="linenos">76</span></a> <span class="n">screen_distance</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_screen_distance</span><span class="p">)</span> <span class="c1"># Random distance between screen and slits (m)</span>
</span><span id="fringe_spacing-77"><a href="#fringe_spacing-77"><span class="linenos">77</span></a> <span class="n">slit_spacing_mm</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_slit_spacing_mm</span><span class="p">)</span> <span class="c1"># Random slit spacing (mm)</span>
</span><span id="fringe_spacing-78"><a href="#fringe_spacing-78"><span class="linenos">78</span></a>
</span><span id="fringe_spacing-79"><a href="#fringe_spacing-79"><span class="linenos">79</span></a> <span class="n">fringe_spacing</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((((</span><span class="n">wavelength_nm</span> <span class="o">*</span> <span class="mi">10</span><span class="o">**-</span><span class="mi">9</span><span class="p">)</span> <span class="o">*</span> <span class="n">screen_distance</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">slit_spacing_mm</span> <span class="o">*</span> <span class="mi">10</span><span class="o">**-</span><span class="mi">3</span><span class="p">)),</span><span class="mi">5</span><span class="p">)</span>
</span><span id="fringe_spacing-80"><a href="#fringe_spacing-80"><span class="linenos">80</span></a>
</span><span id="fringe_spacing-81"><a href="#fringe_spacing-81"><span class="linenos">81</span></a> <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;A laser with a wavelength of $</span><span class="si">{</span><span class="n">wavelength_nm</span><span class="si">}</span><span class="s2">nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $</span><span class="si">{</span><span class="n">screen_distance</span><span class="si">}</span><span class="s2">m$ from the slits and the slits are $</span><span class="si">{</span><span class="n">slit_spacing_mm</span><span class="si">}</span><span class="s2">mm$ apart. Calculate the spacing between the bright fringes.&quot;</span>
</span><span id="fringe_spacing-82"><a href="#fringe_spacing-82"><span class="linenos">82</span></a> <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Using the equation $</span><span class="se">\\</span><span class="s2">frac</span><span class="se">{{\\</span><span class="s2">lambda D</span><span class="se">}}{{</span><span class="s2">s</span><span class="se">}}</span><span class="s2">$, we get a fringe spacing of $</span><span class="si">{</span><span class="n">fringe_spacing</span><span class="si">}</span><span class="s2">m$&quot;</span>
</span><span id="fringe_spacing-83"><a href="#fringe_spacing-83"><span class="linenos">83</span></a> <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
</span></pre></div>
<div class="docstring"><p>Calculate the fringe spacing in a double slit experiment with w=(λD)/s</p>
<table>
<thead>
<tr>
<th>Ex. Problem</th>
<th>Ex. Solution</th>
</tr>
</thead>
<tbody>
<tr>
<td>A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes.</td>
<td>Using the equation $\frac{{\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$</td>
</tr>
</tbody>
</table>

2
docs/search.js
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2
mathgenerator/_gen_list.py
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@@ -136,4 +136,6 @@ gen_list = [
("kinetic_energy", "physics"),
("potential_dividers", "physics"),
("resistivity", "physics"),
("fringe_spacing", "physics"),
("lba_to_chs", "computer_science"),
]

17
mathgenerator/computer_science.py
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@@ -286,3 +286,20 @@ def tribonacci_series(min_length=1, max_length=80):
problem = "The Tribonacci Series of the first ${n}$ numbers is ?"
solution = ', '.join(map(str, tribSeries))
return problem, f'${solution}$'
def lba_to_chs(max_lba=2880, sectors_per_track=18, number_of_heads=2):
r""" Calculating the Cylinder, Head and Sector numbers for a given LBA
| Ex. Problem | Ex. Solution |
| --- | --- |
| If the LBA of a block is $2243$ on a device with $18$ sectors per track and $2$ heads, what are the cylinder, head and sector numbers? | Cylinder: $62$, Head: $0$, Sector: $12$ |
"""
lba = random.randint(0, max_lba)
cylinder = math.floor(lba/(sectors_per_track*number_of_heads));
t = cylinder*(sectors_per_track*number_of_heads);
t = lba-t;
head = math.floor(t/(sectors_per_track));
sector = t - (head * lba) + 1;
problem = f"If the LBA of a block is ${lba}$ on a disk with ${sectors_per_track}$ sectors per track and ${number_of_heads}$ heads, what are the cylinder, head and sector numbers?"
solution = f"Cylinder: ${cylinder}$, Head: ${head}$, Sector: ${sector}$"
return problem, solution

32
mathgenerator/physics.py
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@@ -1,6 +1,7 @@
import random
import math
# Generic
def kinetic_energy(max_mass=1000, max_vel=100):
r"""Kinetic Energy calculation using Ek = 0.5 * m * v^2
@@ -17,12 +18,14 @@ def kinetic_energy(max_mass=1000, max_vel=100):
solution = f'${kinetic_energy} J$'
return problem, solution
# Electricity
def potential_dividers(max_vin=50, max_resistance=500):
r"""Potential Divider question using Vout = (Vin * R2) / (R2 + R1)
| Ex. Problem | Ex. Solution |
| --- | --- |
| In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |
| In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |
"""
'''
This is what a potential divider circuit looks like:
@@ -37,7 +40,7 @@ def potential_dividers(max_vin=50, max_resistance=500):
r2 = random.randint(0, max_resistance) # Resistance of R2
vout = round((vin * r2) / (r1 + r2),2) # Voltage output across R2
problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} Ω$ and ${r2} Ω$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?"
problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} \\Omega$ and ${r2} \\Omega$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?"
solution = f"${vout} V$"
return problem, solution
@@ -46,7 +49,7 @@ def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):
| Ex. Problem | Ex. Solution |
| --- | --- |
| A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 Ωm$ |
| A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 \Omega m$ |
"""
# This question requires a lot of unit conversions and calculating the area of a circle from diameter
diameter_mm = round(random.uniform(0, max_diameter_mm),2) # Random diameter in mm
@@ -56,10 +59,29 @@ def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):
resistivity = (resistance * cross_sectional_area) / (length_cm / 100)
problem = f"A wire has resistance ${resistance*1000} mΩ$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire"
solution = f"${resistivity:.2e} Ωm$"
problem = f"A wire has resistance ${resistance*1000} m\\Omega$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire"
solution = f"${resistivity:.2e} \\Omega m$"
return problem, solution
# Waves
def fringe_spacing(max_screen_distance=30, max_slit_spacing_mm=100):
r"""Calculate the fringe spacing in a double slit experiment with w=(λD)/s
| Ex. Problem | Ex. Solution |
| --- | --- |
| A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes. | Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$ |
"""
wavelength_nm = random.randint(380,750) # Random wavelength between violet and red (nm)
screen_distance = random.randint(0, max_screen_distance) # Random distance between screen and slits (m)
slit_spacing_mm = random.randint(0, max_slit_spacing_mm) # Random slit spacing (mm)
fringe_spacing = round((((wavelength_nm * 10**-9) * screen_distance) / (slit_spacing_mm * 10**-3)),5)
problem = f"A laser with a wavelength of ${wavelength_nm}nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is ${screen_distance}m$ from the slits and the slits are ${slit_spacing_mm}mm$ apart. Calculate the spacing between the bright fringes."
solution = f"Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of ${fringe_spacing}m$"
return problem, solution