Electricity/Electric circuit/RC circuit

RC series

 * $$v_C + v_R = 0$$
 * $$C \frac{d}{dt} v + \frac{v}{R} = 0$$
 * $$\frac{d}{dt} v = - \frac{1}{T} v$$
 * $$ v = A e^{-\frac{t}{T}}$$
 * $$ T = RC$$

2 port RC

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


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

2 port CR

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


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