Regime de ressonância
Um circuito eléctrico de corrente alternada esta em regime de ressonância de a impedância equivalente conter apenas a parte resistiva (não conter parte indutiva nem parte capacitiva).
Ressonância circuito em serie
A impedância do circuito e dado por ;
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-511.png)
Dissemos que o circuito esta em ressonância se a impedância for totalmente resistiva.
Ou seja
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-512.png)
Ressonância circuito em paralelo
A impedância do circuito e dado por ;
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-513.png)
A impedância equivalente não terá parte capacitiva nem indutiva (estará em ressonância) se;
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-514.png)
Exemplo de aplicação
1.Uma bobina real (com resistência e indutância) e um condensador ideal estão ligados em série. No regime de ressonância a tensão nos terminais do capacitor é de 180 V. Determine a tensão nos terminais da bobina. Considere que a tensão de alimentação vale 90 V.
Resolução
Como a bobina é real (com resistência e indutância) terá logicamente uma tensão na resistência (URB )e outra na indutância (ULB) ou seja;
A tensão n0s terminais da bobina e dada por UB =URB+jULB
Vamos determinar a tensão ULb como o circuito esta em regime de ressonância XL=Xc e como o capacitor e o indutor estão em serie a corrente também é a mesma. Dai como a tensão e a corrente e a mesma a tensão também será a mesma ULB=Uc=180V
A tensão total do circuito é dado por ;
U=URB+ULb-Uc
URB =U-ULB+Uc
URB=90-180+180
URB =90V
Agora podemos substituir ULB=180V ; URB =90V na expressão para calcular a tensão nos terminais da bobina
UB= URB +jULB
UB =90+j180
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-514.png)
UB =201,25V
Valores instantâneos
1. Calcular os valores instantâneos das correntes do circuito da figura dada.
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-514.png)
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-515.png)
Resolução
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-514.png)
Vamos separar a tensão em 3 instante.
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-514.png)
A corrente do circuito será a soma da corrente nos 3 instantes
Passo I
Vamos calcular I1 com E=15V
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-516.png)
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-520.png)
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-517.png)
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-518.png)
Passo II
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-516.png)
![](https://embuscadosaber.com/wp-content/uploads/2021/05/image-519.png)
![](data:image/png;base64,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)
Passo III
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ikuFaF0RIWwlZ5BKvengR0j4xS+FAbdXURqFXCcRAAgW8RuJy4UsYXb/uNiMknAXgU/G39q7DeWm9PgriHsJITJXHVX6Yhc+XBwicInJNALq4kLHZNj25d+faYvtgxX/6E46Zs05risTAos1S+chzqMSpfpxiHE7csxkb7jI9gFcW8H3fV93e6rBDHpm8VNUAABD5NIBdX44Gb4DELc/tiMrPIZGuFn3b/uP50hnpcP7AMAiDwmwTq4iqEk8RVZ1+VzO43GSEqEAABEFhMoCCu7vZTi2lqd6RO2gb7IAACIHAdArm42jXXuCSQoxgVVp/dirVHvQ4a10XbQp57gCMgAAIgcHYCmbi6L2bE+ipHwOusXiwhiAwGnyAAAiCQE0jE1WebYr01b2KO8BMFvXrFxuMHa5kujsesfw2L8RFATRAAgbUEEnEdveXnJwoKGW7wBMsCAQU2QAAELkdAi2txvdWJZJqkZo9nXQ4dAgYBEACBOgElrunzra4ZZ6AiS+X111Rx6/2gBARAAAQuRSCIq/oNo+y3ltxygVzfwxdalzpPECwIgMBCAkFcF7ZDdRAAARAAgQaBScTVZc7ZKgQvT9jHw1rP5jYIUJG1I5Y9fHW3TJL+dprM4vM2nZ5icbHPUpy8LMNPCJTibNVplUV3sAUCILAvgZOLKwvDlle2GMHKljl6EEsi59rIXwW24pspfs92qXxrnORvFHrtV6us5AuOgQAI7EHg5OLKITrxaemYXTMuVuiIq39mV64hSwFlD9wnCZXIHIvZp25R3Cv06eptiTP2VGfh/7pZkVNsjy0QAIHtBH5EXEmUhOgpLh1xNXVJTKPeeAE1f8uVv8ALwpuKqd2v9aucyHZ0n1zcEde0f24mP1t1WmXSBrZBAAQ2E/gJcc2FigSS1yiTz2yJoJSNmjastvLZ31Sc7D6La6NPthWGK+kzHK+JqzvuxD7e/odmdqNVp1WmrWAPBEBgHwLTi2surCkYI2SZoIo6JJCyPBVQ9VaARBSzusJuazPtM9StiWuo4P5oufQ3FoUtuyxQqdMqCwawAQIgsJnA1OJKQhFu2UkES69sob/gXxEaopevT5KAimUCK6CcnTrx4z7ztmPjUW9XElfyJ2arti3FowS6Use60yob8xe1QAAElhM4vbhSZsprn+q22IpeUlYUUSMuxeMES4tlwJfYVnf1qiyKXmjb3Sj3WY2TvFSv2PF9KnGt1PG+FNt3/UQFEACBLQROL65bguu2tULJWWm39j4Vdurz9Vgj7PuEACsgAAJ9AhcVV5c9UiasstI+rw01vtHnBnfRFARAYBOBi4rrJmZoDAIgAAJdAhDXLiJUAAEQAIHlBCCuy5mhBQiAAAh0CUBcu4hQAQRAAASWE4C4LmeGFiAAAiDQJQBx7SJCBRAAARBYTgDiupwZWoAACIBAlwDEtYsIFUAABEBgOQGI63JmaAECIAACXQIQ1y4iVAABEACB5QQgrsuZoQUIgAAIdAlAXLuIUAEEQAAElhOAuC5nhhYgAAIg0CUAce0iQgUQAAEQWE4A4rqcGVqAAAiAQJcAxLWLCBVAAARAYDkBiOtyZmgBAiAAAl0CFxNXellf8t6tZL9LDBV2IIBx2AEiTJycwLXE9fX44GtdTj7y33QP4/BN+uj7QwQuJa6vx4dfRvihQZytG4zDbCMGf9cQmERc3W1k9jJB9ZrrnnCaFwQ+nuZl2v5nUVtutPSz7Hf2Gu0ssKX9fKp+OR7z7u/3PSyvYBw+NRro59wETi6u/MbU+/t+T9/UShM9vl7aClZLpIwAPJ4srcvavp5ClIfGs+X3+z1f5taKZxlLEmKMw9BJhEqTEzi5uDJdN7nb2nl/3xoV/p6Pd9BWNus//571trbsvlRcuYOy3/OJazseLqXPFktXjnGQvLD9uwR+RFxJxOLtKN9234Wavh4xy9XDqduqMvPFy221sJKlmrjKJxai36rvU+6U44muapYYh0gGW9cj8BPiSpM4S1rtOiALqrl1zSq4wS62pSLVXp4YdBssxVFsZ330xMhnepsEXPp29HY7niJLxRHjcPQIwf55CEwvrsUJbfkKIag8+lNvSwK6R0YpfKiNuRKfWqWzHK/HU2cp2mAczjKQ8OMDBKYWV1rfi7f+ZhLLpwEInr+tfxXWW+ttSQz2EFZyQAgL7dofEm7OqH8jc62z5JDd8grGwfP42oc596a5S9oT0nfizsWVBCnc9iYiEI6bW+EPDRJlRNEf2vY+2YwvKct8cuKW+dpoa7+QkXGK7Sjk/YGv+v0mcZV+R8Z9q9+rUY2nwTJ6i3GILNKt5HzIlpbS+m4/O0/Tc1/NY3G+Ddov97rz0dTHom8L+aQ2ea6ltrN6KxIqbyM1zZRycTUlbiLFzty+EAGeUDWrbP0EnzqrOoFDF3UB41AaeCcc4aI9OK+G5qOd+GLOlrr/4jF3cYgaY1THJR1KU1bwGYg77zvXvD4anzAY8VYui4Z1cRUtaDDDCWAbVzIRYRibIAACbQJukmsBzISzYGJoPg6ITMG0PWR9EPO/Vm/98UQ0vaFU9Fbx6cbttSuNz1/YtM7VIyTf7ub5d7oLrbUpiGs5cN3NSB3dAnsgAAKSQCVBseIgMzrZprZdmI9dkSnbKglaueaGo17IUn2z35GETHAln27cbXHNfCqFaf2ni2KBu6ifi2t3cNsGo20fBK95ND5ryh9tXXVrDcM1ba7Kd23cezD2NtLZbOdf/VYz97gyH/08pt9sDN9ZpOuyqbHu3E8brNyvZYkq9pV8BuJOM2SKwmbrPT4+XKrrhs35WNOvTFyrVy4PhAeqZnAlbjQDgYsRcKKY/VahEpgGku58JPsiA+b6qZhzF768VszV9vnki5NcEuFjLFxr+QzGzTw46RsNnMYniHDlAuAhJeLarhzA+hMgOzFChX02WMiv8LkPsX2sXIH3khj3oZpaqcy1UXGV5gbnYyljc2ackI0lTFEEewzb9rx4srjRhcA8MnkLF4T9+KRxlxJIm7nyk0iSrdp2Pkcdrvjo2yTiOg6578xeg6Ciu9jOGoZr2lwM6+Zw92DsbYQsyDtlhVJknIO+9uejf6Y6iBcb9n5ExeCCj3/aGAKP/fhoca1onM9kWxcEZ0css/CFIfiskWlxLQ6sCzJlPzKYuivsgQAISAKlDKp0TLYp/2IKP0rEt9nlOVuyrQVN9/TRvcKyRMnf0rHo50jcK8W14B/12+KnxNUJZnrV9FcQmTLzekWquDFKbIEACPQIpNlSum/b+/kX5trIfBypw5ksC3LP2QPL/bJGljWmPNJ9/xuQcXlyLO6SzpWOxYjTMYglQ+Lqrgg+5c3SXKf2co0lAxH7wxYIgMAoAS8YPLfyeVWa2APzMbFL9pVtXqflW9vaZxD10YAW1As+NAQ+iUPFkImr6Tupn8Xt3XNiKm/xaz5I1jrxVDYKnFTmugALqoIACHyEgJvchbn7kd7P3cm52UwirhWI6iqlryqLTwprq3D1oqtrlsk763zl0ldT3XNeR14J+cq50Xfd5b57xfhlDAVmyoORsePHb1TDyo7sW/Nj1pwFxttFbapZT51TS/zSfeyz57JWCGuJ5vnZnFxc/S2R+YZz22tezISsCGRp2OIxP5GzthXBiA3NVq2OOS5nC01mua9sfHunHD+JE19QrFAV/e+NnRAue3tYF2n9mp06v9E3PNTrJWPW8evbo4P+z03g5OLK8PpXKbtmXJzkZMNMmkwg2TYVu78ExoLBJXYSvoz4JW2luHDd9HOkDrWpT/TU4uf3y/GTAIlMu5bxB3cLY5e1SWyGtv5Ll4S/KFb8RllW6y3wS/qAbRAoEfgRcaUJLCZ8FmlHXE19EkOlzUZwrdjShFOT2wuBfeDZ3ZamomzFnASoWcd0mtnOHP/egVr8qQDZ/Rb7grimf+eWLm6KsQ+7dpypJPxsFh2+mKn7VK+X+Nrrn/3AJwgUCPyEuGbCaAMlEeQ1ueQzm8hJ5iQnLW+bz+fLGKZ9sstKTBNQZnLU90gdU63sNxn48g/HTG7wtvmM8YtbeBtrXciMAXPhSy5cNjw5PsIeh27tFo5zufls8bN3Mtk4i8Z+M6/X8Ss3gSMgUCQwvbi2JliM2EyY1kRjAfEN1GNpQqCtnmaTviAeo3VaPkXnP77VjN+uJQsxzWJN3S3wsTaEcGY2kotdapL2qU2LX2azZMTbCc9wU78tvyo2cBgECgSmFlcSgXhLbiZx+pqXEHBbXK2YcCYa2viNbBLTBBSZmJ3EXmxC3UadYFb6nnZ6ov0QE/vkxJK5K3ZZXWpTEFfJzFahuwEWbKrP29xn/qnHnsq1MFq/WHyVX516wQ9jMvUzdwNHQKBK4PTiSplpeLTGZpE+s7AnflLGkykL10yoapkWC93Uldn+pfgmfYciOYlrdWwHeoLrPs+0NxJ/kukJztWxMyFa8UvvCgrH5dizoKdC6ogRU3k+1Pxq1Cv0H8bWdYL/QWCYwOnFdTiStRWtCPYzpRHzr4eY0CMNfqzOWeM/q18/NvwIJyFwYXGNWRmyk+SswC4IgMBmAhcW183sYAAEQAAEqgQgrlU0KAABEACB9QT+AR6YJOLJazmsAAAAAElFTkSuQmCC)
Finalmente tendo as três correntes
![](data:image/png;base64,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)
A corrente em função do tempo será dado por;
![](data:image/png;base64,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)
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