فازور: تفاوت میان نسخه‌ها

:<math>A\cdot \cos(\omega t + \theta) = A \cdot \frac{e^{i(\omega t + \theta)} + e^{-i(\omega t + \theta)}}{۲2},</math> &nbsp; &nbsp;

A_3^2 = (A_1 \cos{\theta_1}+A_2 \cos{\theta_2})^2 + (A_1 \sin{\theta_1}+A_2 \sin{\theta_2})^۲2,

:<math>\frac{d\ v_C(t)}{dt} + \frac{۱1}{RC}v_C(t) = \frac{۱1}{RC}v_S(t)</math>

<math>\frac{d\ \operatorname{Re} \{V_c \cdot e^{i\omega t}\}}{dt} + \frac{۱1}{RC}\operatorname{Re} \{V_c \cdot e^{i\omega t}\} = \frac{۱1}{RC}\operatorname{Re} \{V_s \cdot e^{i\omega t}\}</math>

:<math>i\omega V_c \cdot e^{i\omega t} + \frac{۱1}{RC}V_c \cdot e^{i\omega t} = \frac{۱1}{RC}V_s \cdot e^{i\omega t}</math>

:<math>\left(i\omega V_c + \frac{۱1}{RC}V_c = \frac{۱1}{RC}V_s\right) \cdot e^{i\omega t}</math>

:<math>i\omega V_c + \frac{۱1}{RC}V_c = \frac{۱1}{RC}V_s \quad</math>

:<math>i \omega V_c + \frac{۱1}{RC} V_c = \frac{۱1}{RC}V_s</math>

V_c = \frac{۱1}{1 + i \omega RC} \cdot (V_s) = \frac{1-i\omega R C}{1+(\omega R C)^2} \cdot (V_P e^{i\theta})\,

:<math>v_C(t) = \frac{۱1}{\sqrt{1 + (\omega RC)^2}}\cdot V_P \cos(\omega t + \theta- \phi(\omega))</math>

:<math>\ Z_C = \frac{۱1}{j\omega C},</math>

:<math>\frac{۱1}{Z_{\text{eq}}} = \frac{۱1}{Z_1} + \frac{۱1}{Z_2}</math>