Electricity/Electric 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

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


 * $$\omega=0$$ . $$v_o=0$$
 * $$\omega_o=\omega_o$$ . $$v_o=\frac{v_i}{2}$$
 * $$\omega_o=00$$ . $$v_o=v_i$$