Electricity/Electric circuit/RL circuit

/RL circuit/

RL series

$v_L+v_R=0$

$L\frac{d}{dt}i+iR=0$

$\frac{d}{dt}i=-\frac{1}{T}i$

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

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

2 port LR

$\frac{v_o}{v_i}=\frac{R}{R+j\omega L}=\frac{1}{1+j\omega T}$

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

${\omega }_o=\frac{1}{T}$

$\omega =0$ . $v_o=v_i$

${\omega }_o={\omega }_o$ . $v_o=\frac{v_i}{2}$

${\omega }_o=00$ . $v_o=0$

2 port RL

$\frac{v_o}{v_i}=\frac{j\omega L}{R+j\omega L}=\frac{j\omega T}{R+j\omega T}$

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

${\omega }_o=\frac{1}{T}$

$\omega =0$ . $v_o=0$

${\omega }_o={\omega }_o$ . $v_o=\frac{v_i}{2}$

${\omega }_o=00$ . $v_o=v_i$