「交流-素子⑤」の編集履歴（バックアップ）一覧はこちら

「交流-素子⑤」(2013/06/17 (月) 15:42:53) の最新版変更点

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***周波数特性
-&tooltip(周波数特性){frequency characterristics}:周波数/物理量の相互換算

-&tooltip(共振周波数){resonance frequency}:誘導性/容量性リアクタンスが同一となる周波数&br()$$\omega_{0}L=\frac{1}{\omega_{0}C}$$&br()$$\omega_{0}^{2}=\frac{1}{LC}$$&br()$$\omega_{0}=\frac{1}{\sqrt{LC}}$$&br()$$f_{0}=\frac{1}{2\pi\sqrt{LC}}$$

-先鋭度換算
--&tooltip(Q){Quality factor}:先鋭度/回路の性能判定基準&br()$$Q=\frac{V_{L}}{V}=\frac{V_{R}}{V}=\frac{\omega_{0}L}{R}=\frac{1}{\omega_{0} CR}$$

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***交流電力/力率
-交流電力における循環電流
--i[A]:電流瞬時値&br()$$i=\frac{\sqrt{2}V}{Z}\sin(\omega t-\theta)=\sqrt{2}I\sin(\omega t-\theta)$$&br()$$Z=\sqrt{R^{2}+X_{L}^{2}+X_{C}^{2}},I=\frac{V}{Z},\theta=\tan^{-1}\frac{X_{L}-X_{C}}{R}$$

-交流/消費電力
--p[W]:&tooltip(瞬時電力){instantaneous power}&br()$$p=vi=\sqrt{2}V\sin\omega t\cdot\sqrt{2}I\sin(\omega t-\theta)=2VI\sin\theta\sin(\omega t-\theta)=VI\cos\theta-VI\cos(2\omega t-\theta)$$
---三角関数参考&br()$$a=1,c=1$$&br()$$b^{2}=a^{2}+c^{2}-2ac\cos(\theta_{1}-\theta_{2})=2-2\cos(\theta_{1}-\theta_{2})$$&br()$$b^{2}=(\cos\theta_{1}-\cos\theta_{2})^{2}+(\sin\theta_{1}-\sin\theta_{2})^{2}=2-2(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2})$$&br()$$2(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2})$$&br()$$\cos(\theta_{1}-\theta_{2})=\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}$$&br()$$\cos(\theta_{1}+\theta_{2})=\cos\theta_{1}\cos\theta_{2}-\sin\theta_{1}\sin\theta_{2}$$&br()$$2\sin\theta_{1}\sin\theta_{2}=\cos(\theta_{1}-\theta_{2})-\cos(\theta_{1}+\theta_{2})$$
--P[W]:&tooltip(平均電力){mean power}/交流/消費電力&br()$$P=VI\cos\theta$$
--cosθ:力率&br()$$\cos\theta=\frac{R}{Z}$$

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***周波数特性
-&tooltip(周波数特性){frequency characterristics}:周波数/物理量の相互換算

-&tooltip(共振周波数){resonance frequency}:誘導性/容量性リアクタンスが同一となる周波数&br()$$\omega_{0}L=\frac{1}{\omega_{0}C}$$&br()$$\omega_{0}^{2}=\frac{1}{LC}$$&br()$$\omega_{0}=\frac{1}{\sqrt{LC}}$$&br()$$f_{0}=\frac{1}{2\pi\sqrt{LC}}$$

-先鋭度換算
--&tooltip(Q){Quality factor}:先鋭度/回路の性能判定基準&br()$$Q=\frac{V_{L}}{V}=\frac{V_{R}}{V}=\frac{\omega_{0}L}{R}=\frac{1}{\omega_{0} CR}$$

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***交流電力/力率
-交流電力における循環電流
--i[A]:電流瞬時値&br()$$i=\frac{\sqrt{2}V}{Z}\sin(\omega t-\theta)=\sqrt{2}I\sin(\omega t-\theta)$$&br()$$Z=\sqrt{R^{2}+X_{L}^{2}+X_{C}^{2}},I=\frac{V}{Z},\theta=\tan^{-1}\frac{X_{L}-X_{C}}{R}$$

-交流/消費電力
--p[W]:&tooltip(瞬時電力){instantaneous power}&br()$$p=vi=\sqrt{2}V\sin\omega t\cdot\sqrt{2}I\sin(\omega t-\theta)=2VI\sin\theta\sin(\omega t-\theta)=VI\cos\theta-VI\cos(2\omega t-\theta)$$
---三角関数参考&br()$$a=1,c=1$$&br()$$b^{2}=a^{2}+c^{2}-2ac\cos(\theta_{1}-\theta_{2})=2-2\cos(\theta_{1}-\theta_{2})$$&br()$$b^{2}=(\cos\theta_{1}-\cos\theta_{2})^{2}+(\sin\theta_{1}-\sin\theta_{2})^{2}=2-2(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2})$$&br()$$2(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2})$$&br()$$\cos(\theta_{1}-\theta_{2})=\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}$$&br()$$\cos(\theta_{1}+\theta_{2})=\cos\theta_{1}\cos\theta_{2}-\sin\theta_{1}\sin\theta_{2}$$&br()$$2\sin\theta_{1}\sin\theta_{2}=\cos(\theta_{1}-\theta_{2})-\cos(\theta_{1}+\theta_{2})$$
--P[W]:&tooltip(平均電力){mean power}/交流/消費電力&br()$$P=VI\cos\theta$$
--cosθ:力率&br()$$\cos\theta=\frac{R}{Z}$$

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***皮相/有効/無効電力
-&tooltip(皮相電力){apparent power}換算式
--S[VA]:皮相電力&br()$$S=VI$$

-&tooltip(有効電力){effective power}:平均電力

-&tooltip(無効電力){reactive power}換算式
--Q[var]:無効電力&br()$$Q=VI\sin\theta$$
--sinθ:無効率&br()$$\sin\theta=\frac{X}{Z}$$

-皮相/有効/無効電力相互換算&br()$$S^{2}=P^{2}+Q^{2}$$