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If I have a source free LC circuit with two capacitors and two inductors, will the order in which they are placed in the loop effect the current and voltage characteristics?

There is an initial voltage in the circuit.

So for example, are these two circuits equivalent?

enter image description here

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  • \$\begingroup\$ Can you draw the circuit? What is the application? \$\endgroup\$ – Martin Petrei Nov 4 '15 at 14:25
  • \$\begingroup\$ You can't bake a cake by cooking the ingredients individually then mixing together so yes, the order of things can (and usually is) very important. \$\endgroup\$ – Andy aka Nov 4 '15 at 14:30
  • \$\begingroup\$ With no source your circuit won't be doing anything and your order wont matter! ;) \$\endgroup\$ – Rohan Nov 4 '15 at 14:31
  • \$\begingroup\$ @MartinPetrei I've added an example \$\endgroup\$ – Harry Beadle Nov 4 '15 at 14:40
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    \$\begingroup\$ @LeonHeller This is part of my ug degree, so isn't rubbish. A source free LC circuit functions as a simple harmonic oscillator, without a source, but with an initial voltage. If there was a source then it would exhibit forced harmonic motion, and would be governed by a completely different equation. \$\endgroup\$ – Harry Beadle Nov 4 '15 at 15:31
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You can swap the order of components in a loop like that and you'll get the same result (even with an initial voltage), in an academic context anyway. The initial voltage say \$E\$ can be modeled via the Laplace transform as \$E/s\$ so it is still a series voltage source that you can also move around freely in that loop.

But none of these holds if the loop intersects other loops at some components.

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A circuit is a model for energy exchanges in the form of magnetic field, electric field, heat, etc.
Your circuit without energy sources, not model anything. From this point of view, no matter the location of the components.

The inductance is a measure of the amount of energy in the form of magnetic field associated with the inductor. Capacitance is a measure of the amount of energy as the electric field associated capacitor.

Both the capacitor and the inductor, are passive, energy receptors, that can only store or return, but not generate it. That is why the proposed circuit has no physical utility and therefore, no matter the order of placement of components.

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  • \$\begingroup\$ What if there is an initial voltage? The circuit's current and voltage should function as a simple harmonic oscillator? \$\endgroup\$ – Harry Beadle Nov 4 '15 at 14:53
  • \$\begingroup\$ @HarryBeadle Yes, but the answer says "source free" and I asume that's no energy in the circuit. \$\endgroup\$ – Martin Petrei Nov 4 '15 at 14:59
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    \$\begingroup\$ @HarryBeadle Since all components are in series than the sequencing does not matter even with initial conditions. \$\endgroup\$ – SunnyBoyNY Nov 4 '15 at 15:04

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