교류회로에서 R(저항)과 L(코일)의 병렬 연결

1. 전류와 전압의 위상 차이

전류($I$)의 위상이 전압($V$)의 위상보다 뒤진다(지상회로).

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

2. 어드미턴스 $Y[\mho]$

$\displaystyle \dot{Y}=G+jB=\frac{1}{R}+j\frac{1}{X_L}[\mho]$

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

3. 임피던스 $Z[\Omega]$

$\displaystyle \left|\dot{Z}\right| =\frac{1}{\left|\dot{Y}\right|} =\frac{1}{\sqrt{\left(\frac{1}{R}\right)^2+\left(\frac{1}{\omega L}\right)^2}} =\frac{\omega RL}{\sqrt{R^2+\left(\omega L\right)^2}}$

4. 전전류 $I[\text{A}]$

${\displaystyle \eqalign{ \dot{I} = I_R+I_L &= \frac{V}{R}+\frac{V}{jX_L} \\ \\ &= \frac{V}{R}-j\frac{V}{X_L} = I_R-jI_L \\ \\ &= V\left(\frac{1}{R}-j\frac{1}{\omega L}\right) \\ \\ &= V\left(G-jB\right)[A]\left(I_R=\frac{V}{R}, I_L=\frac{V}{jX_L}\right) } }$

$\left|\dot{I}\right|=\sqrt{{I_R^2}+{I_L^2}}=\sqrt{\left(\frac{V}{R}\right)^2+\left(\frac{V}{X_L}\right)^2}$

5. 역률 $\cos\theta$

${\displaystyle \eqalign{ \cos{\theta} &= \frac{G}{Y} &= \frac{\frac{1}{R}}{\sqrt{\left(\frac{1}{R}\right)^2+\left(\frac{1}{X_L}\right)^2}} &= \frac{X_L}{\sqrt{R^2+X_L^2}} &= \frac{1}{\sqrt{1+\left(\frac{R}{\omega L}\right)^2}} } }$