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| ***Claimed by Rishab Chawla 11/19/15***
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| ==Main Idea==
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| Consider an electrical circuit consisting of an inductor, of inductance '''L''', connected in series with a capacitor, of capacitance '''C'''. Such a circuit is known as an LC circuit, for obvious reasons.
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| ===A Mathematical Model===
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| Starting with [http://physicsbook.gatech.edu/Loop_Rule Kirchoff's Loop Rule], we have V = L * dI/dt + q/C.
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| Taking the derivative of each term, dV/dt = L(d^2*I/dt^2) + 1/C * dq/dt.
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| The voltage of the battery is constant, so that derivative vanishes. The derivative of charge is current, so that gives us a second order differential equation: 0 = L(d^2*I/dt^2) + 1/C * I
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| Rearranging, (d^2/dt^2)I = - I/(LC).
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| This can be solved by guessing and checking with a generic sine function: I = I0sin(ωt + φ)
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| (d^2/dt^2)I0sin(ωt + φ) = -I0/(LC) * sin(ωt + φ)
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| − ω^2*I0sin(ωt + φ) = -I0/(LC) * sin(ωt + φ)
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| The angular frequency is now given by '''ω = 1/sqrt(LC)'''.
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| A LC circuit is then an oscillating circuit with frequency ω/(2π) = '''1/(2π*sqrt(LC))'''.
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| ===A Computational Model===
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| How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
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| ==Examples==
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| Be sure to show all steps in your solution and include diagrams whenever possible
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| ===Simple===
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| ===Middling===
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| ===Difficult===
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| ==Connectedness==
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| #How is this topic connected to something that you are interested in?
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| #How is it connected to your major?
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| #Is there an interesting industrial application?
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| ==History==
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| Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
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| == See also ==
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| Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
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| ===Further reading===
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| Books, Articles or other print media on this topic
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| ===External links===
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| Internet resources on this topic
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| ==References==
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| This section contains the the references you used while writing this page
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| [[Category:Which Category did you place this in?]]
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