12Chapter 31: Electromagnetic Oscillations and Alternat-ing Current12.1LC CircuitsWe have now seen the three major components of standard analog circuits:the resistor, thecapacitor, and the inductor. We have looked at the properties of the three devices in isolation aswell as the properties of circuits containing the RC and LR in pairs. Lets now look at the remainingpair, the LC circuit.Before we delve into the mathematics, lets look at this circuit from an energy point of view.In previous chapters we derived the energy stored in a capacitor and an inductor.They were,respectively,UE=q22C&UBLi22When we go through the mathematics of this simple circuit we will see that energy will oscillatefrom one form of energy to the other. This situation is analogous to the simple harmonic oscillatorfrom physics 1. We usually started the harmonic oscillator with some potential energy and when wereleased it the energy was transferred to kinetic energy. After that the energy was converted backto potential and the whole process started over again. These type of simple harmonic oscillations
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