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éé»ç·åçžã®å¯Ÿå°é»å§ã¯ã$\dot{E}_a, \dot{E}_b, \dot{E}_c$ãéä¿¡ç·ã®é»äœïŒæ±ããèªå°é»å§ã¯** $\dot{E}_0$ãåçžãšéä¿¡ç·éã®çžäºéé»å®¹é㯠$C_a, C_b, C_c$ãéä¿¡ç·ãšå€§å°éã®å¯Ÿå°éé»å®¹éã¯$C_0$ãšããŸãã
éé»ç·ïŒåçžïŒããéä¿¡ç·ãžæµãã黿µïŒåã³ã³ãã³ãµãæµãã黿µïŒãèããŸããåçžãšéä¿¡ç·ã®éã®é»äœå·®ã«ãåã¢ãããã¿ã³ã¹ ($j\omega C$) ãæããŸãã
$\dot{I}_a = j\omega C_a (\dot{E}_a – \dot{E}_0)$
$\dot{I}_b = j\omega C_b (\dot{E}_b – \dot{E}_0)$
$\dot{I}_c = j\omega C_c (\dot{E}_c – \dot{E}_0)$
éä¿¡ç·ãšå€§å°ã®é»äœå·®ã¯ $\dot{E}_0 – 0$ ãªã®ã§ãéä¿¡ç·ãã倧å°ãžæµãã黿µã¯ä»¥äžã®ããã«ãªããŸãã
$\dot{I}_0 = j\omega C_0 \dot{E}_0$
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$$\dot{I}_a + \dot{I}_b + \dot{I}_c = \dot{I}_0$$
ãããäžèšã®é»æµã®åŒã«çœ®ãæãããšã以äžã®ããã«ãªããŸãã
$$j\omega C_a (\dot{E}_a – \dot{E}_0) + j\omega C_b (\dot{E}_b – \dot{E}_0) + j\omega C_c (\dot{E}_c – \dot{E}_0) = j\omega C_0 \dot{E}_0$$
䞡蟺ã $j\omega$ ã§å²ããæ¬åŒ§ãå±éããŠæŽçããŠãããŸãã
$$C_a \dot{E}_a – C_a \dot{E}_0 + C_b \dot{E}_b – C_b \dot{E}_0 + C_c \dot{E}_c – C_c \dot{E}_0 = C_0 \dot{E}_0$$
$\dot{E}_0$ ãå«ãé ãå³èŸºã«ãŸãšããŸãã
$$C_a \dot{E}_a + C_b \dot{E}_b + C_c \dot{E}_c = C_0 \dot{E}_0 + C_a \dot{E}_0 + C_b \dot{E}_0 + C_c \dot{E}_0$$
$\dot{E}_0$ ã§æ¬ããŸãã
$$C_a \dot{E}_a + C_b \dot{E}_b + C_c \dot{E}_c = (C_a + C_b + C_c + C_0) \dot{E}_0$$
$\dot{E}_0$ ã«ã€ããŠè§£ããŸãã
$$\dot{E}_0 = \frac{C_a \dot{E}_a + C_b \dot{E}_b + C_c \dot{E}_c}{C_a + C_b + C_c + C_0}$$
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ã§ã¯ã$C_a = C_b = C_c = C$ ãšãªããŸãã
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$$C(\dot{E}_a + \dot{E}_b + \dot{E}_c)$$
äžçžäº€æµã®åé»å§ã®ãã¯ãã«å㯠0 ïŒ$\dot{E}_a + \dot{E}_b + \dot{E}_c = 0$ïŒã§ããããã$\dot{E}_0 = 0$ ãšãªããèªå°é害ã¯çºçããŸããã
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ç·å°çµ¡äºæ ãçºçãããšã倧ããªå°çµ¡é»æµïŒé¶çžé»æµïŒã倧å°ãåž°è·¯ãšããŠæµãããããéé»ç·ãšéä¿¡ç·ãšã®éã®çžäºã€ã³ãã¯ã¿ã³ã¹ $M$ ãéããŠéåžžã«é«ãé»å§ãéä¿¡ç·è·¯ã«çºçããŸããããããé»ç£èªå°é»å§ããšãããŸããéä¿¡ç·ã«çºçããé»ç£èªå°é»å§ã $\dot{V}_0$ ãšãããšã以äžã®åŒã«ãªããŸãã
$$\dot{V}_0 = j\omega ML (\dot{I}_a + \dot{I}_b + \dot{I}_c) = = 2\pi f M L (\dot{I}_a + \dot{I}_b + \dot{I}_c)$$
$f$ïŒé»æºåšæ³¢æ°ïŒ$\omega = 2\pi f$ïŒ
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