{"id":2904,"date":"2014-04-07T21:33:29","date_gmt":"2014-04-08T01:33:29","guid":{"rendered":"http:\/\/pages.vassar.edu\/magnes\/?p=2904"},"modified":"2014-04-14T22:47:31","modified_gmt":"2014-04-15T02:47:31","slug":"project-plan-rlc-circuits","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2014\/04\/07\/project-plan-rlc-circuits\/","title":{"rendered":"Project Plan: RLC Circuits"},"content":{"rendered":"

Plan\/Goals:<\/strong><\/p>\n

In this project, I plan to study the relevant differential equations that govern RLC circuits and use Mathematica to solve them for values that are useful. The general equation governing a basic RLC circuit with a capacitor, voltage, resistor, and inductor in series, in that order is:<\/p>\n

\"LI'(t)+RI(t)+\frac{1}{C}Q(t)=V(t)\" [Equation 1] (UBC- Source 4)<\/p>\n

which, when going through a series of substitutions, becomes:<\/p>\n

\"LI''(t)+RI'(t)+\frac{1}{C}I(t)=\omega E_{0}cos(\omega t)\" [Equation 2] (UBC- Source 4)<\/p>\n

Equation 1 has six variables: L (inductance), R (resistance), C (capacitance), V (voltage), Q (charge), and I (current). When a circuit like this is set up in the lab, the values that are known are L, R, C, and V because they directly depend on the components of the circuit. Once the differential equation [2] is solved, values for current (I) and charge (Q) can be determined. I will use Mathematica to solve for the general solution to this differential equation [2], which is a second-order differential equation. Once I have the general solution, I will vary the initial conditions to determine the effect of different circuit components on the overall properties of the circuit. Following this, I will develop more series RLC circuits with components that are set up differently in terms of their component structure.<\/p>\n

Timeline (Weeks 1-5):<\/strong><\/p>\n

Week 1: I will begin by reviewing basic differential equation solving techniques for first and second order differential equations. I will also study the differential equation solving capabilities of Mathematica and review the techniques for solving second-order differential equations as they apply to RLC circuits.<\/p>\n

Week 2: I plan on solving for the general solution to Equation 2 above (using Mathematica). I will vary different initial conditions and create graphs that visualize the changes that occur.\u00a0I will also have a visual representation of the circuit.<\/p>\n

Week 3: Develop another series circuit or study a previously built one. Determine the general equation for it and begin the solution process.<\/p>\n

Week 4: Finalize the solution for the second circuit. Develop graphs for visualization purposes.<\/p>\n

Week 5: I will finalize my project by proofreading all the components and making sure everything is presentable. I will also provide constructive criticism to my peers on their projects.<\/p>\n

Sources:<\/strong><\/p>\n

1. Mathematica Cookbook by Sal Mangano<\/p>\n

2. Electronic Circuit Analysis for Scientists by James A. McCray and Thomas A. Cahill<\/p>\n

3. Dynamical Systems with Applications using Mathematica by Stephen Lynch<\/p>\n

4. The RLC Circuit- University of British Columbia- http:\/\/www.math.ubc.ca\/~feldman\/m121\/RLC.pdf<\/a><\/p>\n

5. Class Notes- Mathematics 228 (Methods of Applied Mathematics) taught by Matthew Miller<\/p>\n

Collaborators:<\/strong><\/p>\n

N\/A<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Plan\/Goals: In this project, I plan to study the relevant differential equations that govern RLC circuits and use Mathematica to solve them for values that are useful. The general equation governing a basic RLC circuit with a capacitor, voltage, resistor, and inductor in series, in that order is: [Equation 1] (UBC- Source 4) which, when […]<\/p>\n","protected":false},"author":1826,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4101,54058,188,5569,54190],"tags":[],"class_list":["post-2904","post","type-post","status-publish","format-standard","hentry","category-advanced-em","category-gagandeep","category-mathematica","category-project-plan","category-spring-2014"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2904","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/1826"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=2904"}],"version-history":[{"count":17,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2904\/revisions"}],"predecessor-version":[{"id":2999,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2904\/revisions\/2999"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=2904"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=2904"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=2904"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}