# Source Free RLC Circuit **An RLC circuit without a source.** The analysis of a *source free* RLC circuit is the same as finding the [[Second Order Circuit#Natural or transient response|natural or transient]] response of a general [[second order circuit]]. The circuit is driven by the initial energy stored in the [[capacitor]] and [[inductor]]. ## Series RLC circuit In a *series* RLC circuit, the second order differential equation is in terms of its *current*. The *damping factor* and *natural frequency* are given by $\alpha=\frac{R}{2L}\qquad \omega_{0}=\frac{1}{\sqrt{LC}}$ ![[RLCSourceFreeSeriesCircuit.svg|550]] ## Parallel RLC circuit In a *parallel* RLC circuit, the differential equation is in terms of the *voltage* across the components. The *damping factor* and *natural frequency* are given by $\alpha=\frac{1}{2RC}\qquad \omega_{0}=\frac{1}{\sqrt{LC}}$ ![[RLCSourceFreeParallelCircuit.svg|550]]