평형3상회로*

\[ e_a=E_m\sin\omega t \]\[ e_b=E_m\sin(\omega t-120) \]\[ e_c=E_m\sin(\omega t -240)\]

\[ e_a+e_a+e_a\]\[=E_m[\sin\omega t+\sin(\omega t-120)+\sin(\omega t-240)] \] \[=E_m[\sin\omega t+(\sin\omega t\cos 120-\cos\omega t\sin120)] \] \[=E_m[\sin\omega t+(-0.5\sin\omega t-0.866\cos\omega t)\]\[+(-0.5\sin\omega t+0.866\cos\omega t)]\]\[ +(\sin\omega t\cos240-\cos\omega t\sin240)]\]\[=0\]

\[ E_a+E_b+E_c=E+\angle-120+E\angle-240\]\[=E+E(\cos(-120)+j\sin(-120))\]\[+E(\cos(-240)+j\sin(-240))\]\[=E+E(-\frac{1}{2}-j\frac{\sqrt{3}}{2})+E(-\frac{1}{2}+j\frac{\sqrt{3}}{2})=0\]