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The easiest way to understand electromagnetic oscillations is by an LC circuit or the combination of a capacitor and an inductor circuit. Typically, we begin with a fully charged capacitor which is then linked to an inductor by a switch. The basic circuit is shown in the figure as follows:
For this circuit, the behavior is characterized by oscillating current, charge, and voltages. This is in sharp contrast to the exponential behavior of the current, voltages, and charges for the case of RL or RC circuits. If we assume we have initially charged the capacitor to a voltage Vmax before connecting it to the inductor, we can ask what the behavior will be.
This is a case in which the energy approach for looking at the circuit is more immediately obvious than the voltage approach. This is because we can clearly see that energy is conserved for this case since capacitors and inductors involve only electric and magnetic fields which are conservative.
In dealing with specific cases of circuits, we now need to deal with one of the ever-present "difficult" issues of physics, namely: how do you decide what approach to use for solving any particular problem? This is especially true for circuits involving inductors, capacitors, and resistors because the formulas which describe the behavior of the individual circuit elements are difficult to memorize. In such cases we must memorize behaviors, not formulas.
In applying this idea to the case at hand, remember that the behavior is determined by the same considerations that were important for physics problem in Mechanics. If there are no dissipative elements, use energy conservation. In cases where dissipative elements, resistors in this case, are involved, think about the behavior in terms of the initial and long-time aspects of inductor or capacitor behavior. These kinds of considerations are essential to deriving the exact formulas. But, for a large class of problems, these same considerations allow us to dispense with the exact formulas.
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