# Practical Electronics/Parallel RLC

## Summary

Network Symbol Series RLC Parallel RLC
Network
Impedance Z ${\displaystyle Z=(j\omega )^{2}+(j\omega ){\frac {R}{L}}+{\frac {1}{LC}}}$  ${\displaystyle Z=(j\omega )^{2}+(j\omega ){\frac {1}{RC}}+{\frac {1}{LC}}}$
Roots λ λ = ${\displaystyle -\zeta \pm {\sqrt {\zeta ^{2}-\omega _{o}^{2}}}}$  λ = ${\displaystyle -\zeta \pm {\sqrt {\zeta ^{2}-\omega _{o}^{2}}}}$
I(t) Aeλ1t + Beλ2t Aeλ1t + Beλ2t Aeλ1t + Beλ2t
Damping Factor ${\displaystyle \zeta }$  ${\displaystyle \zeta ={R \over 2L}}$  ${\displaystyle \zeta ={1 \over 2RC}}$
Resonant Frequency ${\displaystyle \omega _{o}}$  ${\displaystyle \omega _{o}={1 \over {\sqrt {LC}}}}$  ${\displaystyle \omega _{o}={1 \over {\sqrt {LC}}}}$
Band Width ${\displaystyle \Delta \omega =2\zeta }$  ${\displaystyle {R \over L}}$  ${\displaystyle {1 \over CR}}$
Quality factor ${\displaystyle Q={\omega _{o} \over \Delta \omega }={\omega _{o} \over 2\zeta }}$  ${\displaystyle Q={L \over R{\sqrt {LC}}}={1 \over R}{\sqrt {L \over C}}}$  ${\displaystyle Q={CR \over {\sqrt {LC}}}={R}{\sqrt {C \over L}}}$