# Fundamental Physics/Electricity/RC series

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## RC series

 RC series ${\displaystyle V_{C}+V_{R}=0}$ ${\displaystyle C{\frac {dv}{dt}}+{\frac {v}{R}}=0}$ ${\displaystyle {\frac {dv}{dt}}=-{\frac {1}{T}}v}$ ${\displaystyle T=RC}$ ${\displaystyle \int {\frac {dv}{v}}=-{\frac {1}{T}}\int dt}$ ${\displaystyle Lnv=-{\frac {1}{T}}+c}$ ${\displaystyle v=e^{-{\frac {1}{T}}t+c}=Ae^{-{\frac {1}{T}}t}}$ ${\displaystyle A=e^{c}}$