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LC Circuits

[LC circuit] Let's start with a charged capacitor, connected across inductor at time t=0. The charge on the capacitor is assigned the symbol qmax. Initially there is no current in the circuit because of the inductance; however, note that the time rate of change of the current is maximum at this point. The energy present in the circuit is entirely in the form of electrical energy, stored in the electric field of the capacitor.
[LC circuit] The current begins to flow counterclockwise as the capacitor discharges itself and after some time (how long we will find out later!) half of the charge will remain on capacitor. Some of the electrical energy will have been converted into magnetic energy stored in the inductor.
[LC circuit] Eventually the capacitor will be completely discharged; the current in the circuit is now at a maximum. No energy will be stored in the capacitor (at this instant); all energy will be stored in the inductor.
[LC circuit] The current in the inductor continues to transport charge from one plate of the capacitor to the other. Energy is now being transferred back to the capacitor as current decreases and the inductor de-energizes itself. The capacitor is recharging, albeit with a different polarity than at the start.
[LC circuit] Soon the same amount of charge has been transferred to the other plate of the capacitor. The current is instantaneously zero and there is no energy stored in the inductor. The capacitor is now storing the same amount of energy in its electric field as at the start.

Of course, now the charge starts to flow back the other way...

These oscillations continue indefinitely in the absence of loss (if no resistance present).

The next question to ask is "What is the frequency of this process?"

[LC oscillation]

Concept Check

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Last updated Nov. 20, 1997.
Copyright George Watson, Univ. of Delaware, 1997.