Second Order Circuits

Second order circuits are circuits that have two energy storage elements, resultingin second-order differential equations. The circuits have to be cast in terms of irreducible elements (i.e.

combine L's and C's into one when possible).

An unforced RLC circuit

Consider an un-forced RLC circuit. We want to find $V_{C}$.

First, we can use KVL and KCL

$V_{R}+V_{L}+V_{C}=0$

$iR+L{\frac {di}{dt}}+V_{C}=0$

Next, we can use $i=C{\frac {dV_{C}}{dt}}$ to get

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