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

$v_L+v_R=0$

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

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

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

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

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

$I=A{e}^{-\frac{t}{T}}$

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

$e^C=IR$