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. 2014 Feb 28;9(2):e77190. doi: 10.1371/journal.pone.0077190

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© 2014 Allison et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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We consider a capacitor, C, in parallel with an inductor, L. We consider the idealised case where there is no dissipative loss, or resistance R. The Lagrangian function can be written as , where the magnetic energy stored by the field of the inductor, denoted by , and the electrical potential energy stored in the capacitor is denoted by , and q = Cv is the coordinate, which we interpret as the electrical charge that is transferred through the circuit.

Inline graphic — We consider a capacitor, C, in parallel with an inductor, L. We consider the idealised case where there is no dissipative loss, or resistance R. The Lagrangian function can be written as , where the magnetic energy stored by the field of the inductor, denoted by , and the electrical potential energy stored in the capacitor is denoted by , and q = Cv is the coordinate, which we interpret as the electrical charge that is transferred through the circuit.