「交流-素子④」の編集履歴（バックアップ）一覧はこちら

「交流-素子④」(2013/06/14 (金) 11:10:06) の最新版変更点

追加された行は緑色になります。

削除された行は赤色になります。

----
***抵抗/インダクタンス/静電容量直列接続に因る電流/電圧/偏角
-RLC直列回路に対する印加電圧瞬時値&br()$$v=\sqrt{2}V\sin\theta$$

-RLC端子間電圧瞬時値&br()$$v_{R}=\sqrt{2}V_{R}\sin(\omega t+\theta_{1})$$&br()$$v_{L}=\sqrt{2}V_{L}\sin(\omega t+\theta_{2})$$&br()$$v_{C}=\sqrt{2}V_{C}\sin(\omega t+\theta_{3})$$

-RLC素子における循環電流&br()$$i_{R}=\frac{\sqrt{2}V_{R}}{R}\sin(\omega t+\theta_{1})$$&br()$$i_{L}=\frac{\sqrt{2}V_{L}}{\omega L}\sin\left(\omega t+\theta_{2}-\frac{\pi}{2}\right)$$&br()$$i_{C}=\frac{\sqrt{2}V_{C}}{1/\omega C}\sin\left(\omega t+\theta_{3}+\frac{\pi}{2}\right)$$

-コイル/コンデンサ電圧実行値に対するインダクタンス/静電容量/抵抗印加電圧/偏角換算&br()$$i_{R}=i_{L}=i_{C}\\$$&br()$$V_{L}=\frac{\omega L}{R}V_{R},V_{C}=\frac{1}{\omega CR}V_{R}$$&br()$$\theta_{2}=\theta_{1}+\frac{\pi}{2},\theta_{3}=\theta_{1}-\frac{\pi}{2}$$

-印加電圧における合計瞬時値換算&br()$$v=v_{R}+v_{L}+v_{C}=\sqrt{2}V_{R}\sin(\omega t+\theta_{1})+\frac{\sqrt{2}\omega L}{R}\sin\left(\theta_{1}+\frac{\pi}{2}\right)+\frac{\sqrt{2}\frac{1}{\omega C}}{R}\sin\left(\theta_{1}-\frac{\pi}{2}\right)$$&br()$$=\sqrt{2}V_{R}\sin(\omega t+\theta_{1})+\frac{\sqrt{2}V_{R}\omega L}{R}\cos(\omega t+\theta_{1})-\frac{\sqrt{2}V_{R}\frac{1}{\omega C}}{R}\cos(\omega t+\theta_{1})$$&br()$$=\frac{\sqrt{2}V_{R}}{R}\left \{ R\sin(\omega t+\theta_{1})+\left ( \omega L-\frac{1}{\omega C} \right )\cos(\omega t+\theta_{1}) \right \}$$&br()$$=\frac{\sqrt{2}V_{R}}{R}\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}\sin(\omega t+\theta_{1}+\theta)$$&br()$$\theta=\tan^{-1}\frac{\left ( \omega L-\frac{1}{\omega C} \right )}{R}$$

-抵抗における電圧実行値/角度換算&br()$$\sqrt{2}V=\frac{\sqrt{2}V_{R}}{R}\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}$$&br()$$V_{R}=\frac{VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}$$&br()$$\omega t=\omega t+\theta_{1}+\theta$$&br()$$\theta=-\theta_{1}$$

-コイル/コンデンサ電圧に対する電圧実行値換算&br()$$V_{L}=\frac{\omega L}{R}V_{R}=\frac{\omega L}{R}\frac{VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}=\frac{V\omega L}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}$$&br()$$V_{C}=\frac{\frac{1}{\omega C}}{R}V_{R}=\frac{\frac{1}{\omega C}}{R}\frac{VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}=\frac{V\frac{1}{\omega C}}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}$$

-各素子における電圧実行値に因る電圧瞬時値換算&br()$$v_{R}=\frac{\sqrt{2}VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}(\omega t -\theta )$$&br()$$v_{L}=\frac{\sqrt{2}V\omega L}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}\left(\omega t -\theta +\frac{\pi}{2}\right)$$&br()$$v_{C}=\frac{\sqrt{2}V\frac{1}{\omega C}}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}\left(\omega t -\theta -\frac{\pi}{2}\right)$$

-抵抗における電流瞬時値換算&br()$$i=\frac{v_{R}}{R}=\frac{\sqrt{2}V}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}(\omega t -\theta )$$

-交流電源接続における電流/電圧相互換算&br()$$I=\frac{V}{Z}=\frac{V}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}=\frac{V}{\sqrt{R^{2}+X_{L}^{2}+X_{C}^{2}}}$$

-RLC直列接続回路におけるインピーダンス&br()$$Z=\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}=\sqrt{R^{2}+X_{L}^{2}+X_{C}^{2}}$$

-インピーダンス角&br()$$\theta=tan^{-1}\frac{\omega L-\frac{1}{\omega C}}{R}=tan^{-1}\frac{X_{L}-X_{C}}{R}$$

----
***抵抗/インダクタンス/静電容量直列接続に因る電流/電圧/偏角
-RLC直列回路に対する印加電圧瞬時値&br()$$v=\sqrt{2}V\sin\theta$$

-RLC端子間電圧瞬時値&br()$$v_{R}=\sqrt{2}V_{R}\sin(\omega t+\theta_{1})$$&br()$$v_{L}=\sqrt{2}V_{L}\sin(\omega t+\theta_{2})$$&br()$$v_{C}=\sqrt{2}V_{C}\sin(\omega t+\theta_{3})$$

-RLC素子における循環電流&br()$$i_{R}=\frac{\sqrt{2}V_{R}}{R}\sin(\omega t+\theta_{1})$$&br()$$i_{L}=\frac{\sqrt{2}V_{L}}{\omega L}\sin\left(\omega t+\theta_{2}-\frac{\pi}{2}\right)$$&br()$$i_{C}=\frac{\sqrt{2}V_{C}}{1/\omega C}\sin\left(\omega t+\theta_{3}+\frac{\pi}{2}\right)$$

-コイル/コンデンサ電圧実行値に対するインダクタンス/静電容量/抵抗印加電圧/偏角換算&br()$$i_{R}=i_{L}=i_{C}\\$$&br()$$V_{L}=\frac{\omega L}{R}V_{R},V_{C}=\frac{1}{\omega CR}V_{R}$$&br()$$\theta_{2}=\theta_{1}+\frac{\pi}{2},\theta_{3}=\theta_{1}-\frac{\pi}{2}$$

-印加電圧における合計瞬時値換算&br()$$v=v_{R}+v_{L}+v_{C}=\sqrt{2}V_{R}\sin(\omega t+\theta_{1})+\frac{\sqrt{2}\omega L}{R}\sin\left(\theta_{1}+\frac{\pi}{2}\right)+\frac{\sqrt{2}\frac{1}{\omega C}}{R}\sin\left(\theta_{1}-\frac{\pi}{2}\right)$$&br()$$=\sqrt{2}V_{R}\sin(\omega t+\theta_{1})+\frac{\sqrt{2}V_{R}\omega L}{R}\cos(\omega t+\theta_{1})-\frac{\sqrt{2}V_{R}\frac{1}{\omega C}}{R}\cos(\omega t+\theta_{1})$$&br()$$=\frac{\sqrt{2}V_{R}}{R}\left \{ R\sin(\omega t+\theta_{1})+\left ( \omega L-\frac{1}{\omega C} \right )\cos(\omega t+\theta_{1}) \right \}$$&br()$$=\frac{\sqrt{2}V_{R}}{R}\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}\sin(\omega t+\theta_{1}+\theta)$$&br()$$\theta=\tan^{-1}\frac{\left ( \omega L-\frac{1}{\omega C} \right )}{R}$$

-抵抗における電圧実行値/角度換算&br()$$\sqrt{2}V=\frac{\sqrt{2}V_{R}}{R}\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}$$&br()$$V_{R}=\frac{VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}$$&br()$$\omega t=\omega t+\theta_{1}+\theta$$&br()$$\theta=-\theta_{1}$$

-コイル/コンデンサ電圧に対する電圧実行値換算&br()$$V_{L}=\frac{\omega L}{R}V_{R}=\frac{\omega L}{R}\frac{VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}=\frac{V\omega L}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}$$&br()$$V_{C}=\frac{\frac{1}{\omega C}}{R}V_{R}=\frac{\frac{1}{\omega C}}{R}\frac{VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}=\frac{V\frac{1}{\omega C}}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}$$

-各素子における電圧実行値に因る電圧瞬時値換算&br()$$v_{R}=\frac{\sqrt{2}VR}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}(\omega t -\theta )$$&br()$$v_{L}=\frac{\sqrt{2}V\omega L}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}\left(\omega t -\theta +\frac{\pi}{2}\right)$$&br()$$v_{C}=\frac{\sqrt{2}V\frac{1}{\omega C}}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}\left(\omega t -\theta -\frac{\pi}{2}\right)$$

-抵抗における電流瞬時値換算&br()$$i=\frac{v_{R}}{R}=\frac{\sqrt{2}V}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}(\omega t -\theta )$$

-交流電源接続における電流/電圧相互換算&br()$$I=\frac{V}{Z}=\frac{V}{\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}}=\frac{V}{\sqrt{R^{2}+X_{L}^{2}+X_{C}^{2}}}$$

-RLC直列接続回路におけるインピーダンス&br()$$Z=\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}=\sqrt{R^{2}+X_{L}^{2}+X_{C}^{2}}$$

-インピーダンス角&br()$$\theta=tan^{-1}\frac{\omega L-\frac{1}{\omega C}}{R}=tan^{-1}\frac{X_{L}-X_{C}}{R}$$
--電気的特性
---誘導性:電圧位相に対し電流位相が遅相
---同相:電圧/電流位相が同一
---容量性:電圧位相に対し電流位相が進相