RL Series

A circuit of 2 component a resistor and an inductor connected in series

${\displaystyle V_{L}+V_{R}=0}$

${\displaystyle L{\frac {d}{dt}}i(t)+Ri(t)=0}$

${\displaystyle {\frac {d}{dt}}i(t)=-{\frac {R}{L}}i(t)}$

${\displaystyle \int {\frac {di(t)}{i(t)}}=-\int {\frac {R}{L}}dt}$

${\displaystyle Lni(t)=-{\frac {R}{L}}t+c}$

${\displaystyle i(t)=e^{-{\frac {R}{L}}t+c}}$

${\displaystyle i(t)=Ae^{-{\frac {R}{L}}t}}$