d v ( t ) d t = − 1 T v ( t ) R {\displaystyle {\frac {dv(t)}{dt}}=-{\frac {1}{T}}v(t)R} d v ( t ) v ( t ) = − 1 T d t {\displaystyle {\frac {dv(t)}{v(t)}}=-{\frac {1}{T}}dt} ∫ d v ( t ) v ( t ) = − 1 T ∫ d t {\displaystyle \int {\frac {dv(t)}{v(t)}}=-{\frac {1}{T}}\int dt} L n v ( t ) = − 1 T t + c {\displaystyle Lnv(t)=-{\frac {1}{T}}t+c} v ( t ) = e − 1 T + c {\displaystyle v(t)=e^{-{\frac {1}{T}}+c}} v ( t ) = A e − 1 T {\displaystyle v(t)=Ae^{-{\frac {1}{T}}}} T = R C {\displaystyle T=RC}
T = R C {\displaystyle T=RC} ω o = 1 T {\displaystyle \omega _{o}={\frac {1}{T}}}
v o ( ω = 0 ) = 0 {\displaystyle v_{o}(\omega =0)=0} v o ( ω = ω o ) = 1 2 v i {\displaystyle v_{o}(\omega =\omega _{o})={\frac {1}{2}}v_{i}} v o ( ω = 0 ) = v i {\displaystyle v_{o}(\omega =0)=v_{i}}