V L + V R = 0 {\displaystyle V_{L}+V_{R}=0} L d i d t + i R = 0 {\displaystyle L{\frac {di}{dt}}+iR=0} d i d t = − 1 T i {\displaystyle {\frac {di}{dt}}=-{\frac {1}{T}}i} T = L R {\displaystyle T={\frac {L}{R}}} ∫ d i i = − 1 T ∫ d t {\displaystyle \int {\frac {di}{i}}=-{\frac {1}{T}}\int dt} L n i = − 1 T + c {\displaystyle Lni=-{\frac {1}{T}}+c} i = e − 1 T t + c = A e − 1 T t {\displaystyle i=e^{-{\frac {1}{T}}t+c}=Ae^{-{\frac {1}{T}}t}} A = e c {\displaystyle A=e^{c}}
