Practical Electronics/Series RL

A circuit of two components R and L connected in series

Natural Response of the cicuit can be obtained by setting the differential equation of the circuit to zero

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

${\displaystyle L{\frac {dI}{dt}}+IR=0}$

${\displaystyle {\frac {dI}{dt}}=-{\frac {1}{T}}I}$

${\displaystyle \int {\frac {dI}{I}}=-{\frac {1}{T}}\int dt}$

${\displaystyle LnI=-{\frac {1}{T}}+C}$

${\displaystyle I=e^{(-{\frac {1}{T}}+C)}}$

${\displaystyle I=Ae^{-{\frac {t}{T}}}}$

${\displaystyle T={\frac {L}{R}}}$

${\displaystyle e^{C}=IR}$