Fundamental Physics/Electric exponential decay

 Electric current decay circuit Configuration Formula RL series ${\displaystyle V_{L}+V_{R}=0}$ ${\displaystyle L{\frac {di}{dt}}+iR=0}$ ${\displaystyle {\frac {di}{dt}}=-{\frac {1}{T}}i}$ ${\displaystyle T={\frac {L}{R}}}$ ${\displaystyle \int {\frac {di}{i}}=-{\frac {1}{T}}\int dt}$ ${\displaystyle Lni=-{\frac {1}{T}}+c}$ ${\displaystyle i=e^{-{\frac {1}{T}}t+c}=Ae^{-{\frac {1}{T}}t}}$ ${\displaystyle A=e^{c}}$ RC series ${\displaystyle V_{C}+V_{R}=0}$ ${\displaystyle C{\frac {dv}{dt}}+{\frac {v}{R}}=0}$ ${\displaystyle {\frac {dv}{dt}}=-{\frac {1}{T}}v}$ ${\displaystyle T=RC}$ ${\displaystyle \int {\frac {dv}{v}}=-{\frac {1}{T}}\int dt}$ ${\displaystyle Lnv=-{\frac {1}{T}}+c}$ ${\displaystyle v=e^{-{\frac {1}{T}}t+c}=Ae^{-{\frac {1}{T}}t}}$ ${\displaystyle A=e^{c}}$