교류회로에서 R(저항)과 C(콘덴서 또는 커패시터)의 병렬 연결

1. 전류와 전압의 위상 차이

전류($I$)의 위상이 전압($V$)의 위상보다 $θ$앞선다(진상회로).

${\displaystyle \eqalign { \theta &= \tan^{-1}\left(\frac{B}{G}\right) \\ &= \tan^{-1}\left(\frac{\frac{1}{X_C}}{\frac{1}{R}}\right) \\ &= \tan^{-1}\left(\frac{R}{X_C}\right) \\ &= \tan^{-1}\left({\omega RC}\right) } }$

2. 어드미턴스 $Y[\mho]$

${\displaystyle \eqalign { \dot{Y} = G+jB &= \frac{1}{R}+j\frac{1}{X_C} \\ &= \frac{1}{R}+j\frac{1}{\frac{1}{\omega C}} \\ &= \frac{1}{R}+j\omega C[\mho] } }$

${ \displaystyle \eqalign{ \left|\dot{Y}\right| &= \sqrt{\left(\frac{1}{R}\right)^2+\left(\frac{1}{X_C}\right)^2} &= \sqrt{\left(\frac{1}{R}\right)^2+\left(\omega C\right)^2}[\mho] } }$

3. 임피던스 $Z[\Omega]$

${\displaystyle \eqalign{ \dot{Z} = \frac{1}{\dot{Y}} = \frac{1}{G+jB} &= \frac{1}{\frac{1}{R}+j\frac{1}{X_C}} \\ &= \frac{1}{\frac{1}{R}+j{\omega}C} \\ &= \frac{R}{1+j{\omega}RC}[\Omega] } }$

${\displaystyle \eqalign{ \left|\dot{Z}\right|=\frac{1}{\left|\dot{Y}\right|} &= \frac{1}{\sqrt{(\frac{1}{R})^2+(\frac{1}{X_C})^2}} \\ &= \frac{1}{\sqrt{\frac{1}{R^2}+\frac{1}{X^2_C}}} \\ &= \frac{1}{\sqrt{\frac{R^2+X^2_C}{R^2{\cdot}X^2_C}}} \\ &= \frac{R\cdot X_C}{\sqrt{R^2+X_C^2  }} \\ &= \frac{1}{\sqrt{(\frac{1}{R})^2+(\omega C)^2}}[\Omega] } }$

4. 전류 $I[\text{A}]$

${\displaystyle \eqalign{ \dot{I}=I_R+jI_C &=\frac{V}{R}+j\frac{V}{X_C} \\ &= V\left(\frac{1}{R}+j\frac{1}{\frac{1}{\omega C}}\right) \\ &= V\left(\frac{1}{R}+j\omega C\right)[A] } }$

$\left|\dot{I}\right|=V\cdot\left|\dot{Y}\right|=V\cdot\sqrt{\left(\frac{1}{R}\right)^2+\left(\omega C\right)^2}$

5. 역률 $\cos\theta$

${\displaystyle \eqalign{ \cos{\theta} = \frac{G}{\left|\dot{Y}\right|} &= \frac{\frac{1}{R}}{\sqrt{(\frac{1}{R})^2+(\frac{1}{X_C})^2}} \\ &= \frac{X_C}{\sqrt{R^2+X_C^2}} \\ &= \frac{\frac{1}{\omega C}}{\sqrt{R^2+(\frac{1}{\omega C})^2}} \\ &= \frac{1}{\sqrt{1+(\omega RC)^2}} } }$