Este material busca relacionar conceitos de indução eletromagnética com equações diferenciais aplicadas a circuitos RL.[br][br]

De acordo com Sadiku, Musa, Alexander (2014,p.261) um ímã é cercado por um campo magnético, que pode ser visualizado como linhas de força. A força eletromotriz (fem) é gerada quando um fluxo magnético passa por uma bobina ou condutor, fenômeno conhecido como indução eletromagnética. Michael Faraday e Joseph Henry descobriram que a variação do fluxo magnético em um condutor induz uma tensão nos terminais, levando à formulação da lei de Faraday.[br][br]A Lei de Faraday afirma que a tensão induzida em um circuito é proporcional à taxa de variação de fluxo magnético através do circuito, sendo:[br][br][math]v_L\left(t\right)=N\frac{d\left(\phi\right)}{d\left(t\right)}[/math] , sendo:[br][br] [math]v_L\left(t\right)[/math]: a tensão induzida em função do tempo em volts (V);[br]N: o número de espiras na bobina[br][math]\frac{d\left(\phi\right)}{d\left(t\right)}[/math] : a taxa de variação do campo magnético em webers por segundo (Wb/s).[br][br]FIG.12: Fluxo produzido externamente através de uma bobina de N espiras.[br][img]data:image/png;base64,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[/img][br]Fonte: Sadiku, Musa, Alexander (2014,261)[br][br][br]Faça você mesmo esse experimento com o simulador do Fluxo de Campo Magnético disponível pela Universidade do Colorado. Inicialmente com o ponteiro do mouse puxe a alavanca azul da torneira para a direita, altere a quantidade de espiras e identifique a variação na tensão induzida pelo fluxo do campo magnético e comportamento da lâmpada.

De acordo com a FIG.12, uma fem é induzida na bobina somente quando o fluxo magnético através da bobina varia, ou seja, isto é, [math]\frac{d\left(\phi\right)}{d\left(t\right)}\ne0[/math] , caso contrário, [math]\frac{d\left(\phi\right)}{d\left(t\right)}=0[/math] e a [math]v_L\left(t\right)=0[/math] .[br][br]A polaridade da força eletromotriz (fem) induzida e o sentido do fluxo da corrente são determinados pela Lei de Lenz, que afirma que a corrente induzida cria um fluxo que se opõe à mudança que a produziu. A Lei de Faraday é usada para determinar a magnitude da tensão induzida, enquanto a Lei de Lenz é utilizada para determinar a polaridade. (Sadiku, Musa, Alexander,2014,p.262)[br][br]Procurando entender o que seria a Indução Eletromagnética e a Lei de Faraday sugerimos o vídeo abaixo do canal de Física "Como é bom ser nerd" que trata muito bem dessa temática. No mesmo canal também sugerimos o vídeo que trata da Lei de Lenz .

No GeoGebra vamos analisar o gráfico da função [math]v_L\left(t\right)=N\frac{d\left(\phi\right)}{d\left(t\right)}[/math] que representa a Lei de Faraday, mas antes disso precisamos entender a função [math]\phi[/math] que representa o fluxo de um campo magnético, conforme apresentado no vídeo anterior, que corresponde a [math]\phi\left(t\right)=ABcos\left(t\right)[/math] , sendo [math]A[/math] a área da espira em [math]m^2[/math] e [math]B[/math] a intensidade do campo magnético em [math]T[/math] (tesla) e [math]t[/math] o ângulo em radianos da posição da espira em relação ao campo magnético. [br][br]Faça alterações nos valores de A e B e analise o comportamento gráfico da função periódica, nesse caso uma cossenóide.

No GeoGebra faça alterações nos valores reais de A, B e N para analisar o comportamento gráfico da função que representa a Lei de Faraday. Movimente o ponto sobre o gráfico para uma interpretação pontual dos valores de t e [math]v_L[/math] .

Sobre Indutor Elétrico Sadiku, Musa, Alexander (2014,p.262) afirma que é um componente passivo que armazena energia na forma de um campo magnético. Eles são amplamente utilizados em eletrônica e sistemas de potência, como em fontes de energia, transformadores, rádios, TVs, radares e motores elétricos. Qualquer condutor de corrente elétrica tem propriedades indutivas, mas um indutor real é geralmente uma bobina cilíndrica com muitas espiras de fio condutor.[br][br]Qualquer condutor de corrente elétrica tem propriedades indutivas e pode ser considerado um indutor. Para aumentar o efeito indutivo, um indutor real é geralmente construído como uma bobina cilíndrica com muitas espiras de fio condutor, ou seja, [b]um indutor consiste em uma bobina de condutor de fio em volta de algum núcleo que pode ser o ar ou algum material magnético[/b]. (Sadiku, Musa, Alexander,2014,p.262)[br][br]FIG.13: Forma típica de um indutor[br][img]data:image/png;base64,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[/img][br]Fonte: Sadiku, Musa, Alexander (2014,p.262)[br][br]De acordo com Sadiku, Musa, Alexander (2014,p.262) quando uma corrente circula através de um indutor, verifica-se que a tensão sobre o indutor é diretamente proporcional à taxa de variação da corrente. [br][br][math]v_L\left(t\right)=L\frac{d\left(i\right)}{d\left(t\right)}[/math][br][br]Sendo [math]v_L\left(t\right)[/math] a função tensão no indutor em função do tempo t, L a constante de proporcionalidade também chamada de indutância do indutor e [math]\frac{d\left(i\right)}{d\left(t\right)}[/math] a taxa de variação instantânea da corrente no indutor. A unidade para indutância é o henry (H) em homenagem ao inventor americano Joseph Henry (1797 – 1878).[br][br][b]A indutância L é uma medida da capacidade de um indutor para apresentar oposição à variação de corrente através dele, medida em henrys (H), ou seja, a corrente não pode variar abruptamente (a tensão tenderia a infinito; o que de fato não ocorre).[br][br][/b]Para a interpretação gráfica da função [math]v_L\left(t\right)=L\frac{d\left(i\right)}{d\left(t\right)}[/math] precisamos conhecer a função [math]i\left(t\right)[/math] que será obtida pela solução de uma EDO modelada para um circuito RL (Resistor e Indutor).

Segundo Sadiku, Musa, Alexander (2014,p.269) um circuito RL contém apenas resistores e indutores, geralmente conectados em série. O objetivo é determinar a resposta do circuito, que é a corrente (i(t)) através do indutor. A corrente do indutor é escolhida como resposta para destacar que ela não pode mudar instantaneamente. Em t = 0, assume-se que o indutor tem uma corrente inicial [math]i\left(0\right)=I_0[/math].[br][br]Assim como realizamos nos cálculos do capacitor vamos iniciar com um circuito RL sem uma fonte de tensão (bateria), conforme FIG.14:[br][br]FIG.14:Circuito RL sem fonte de tensão[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAACwCAYAAABpcnDnAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABN0SURBVHhe7d0HeBVVwgbgL8XQEkogEDDUQAoQCCGUhBaKIK4KKqIIBGSpIliQX3HF39X1l6ZIR5qiVFkUUMSlr5RQ0iihBRJIAkkgkF5uyp3/nsksAosx0eQwc/leHx6ZMzePjzn3mzltztgoFiCiCmWr/ZuIKhCDRiQBg0YkAYNGJAGDZgBF8d9h6oChWBBm0krIaBg0g7CxUWA2awdkOBzeJ5KAdzS9M+fiZkwkQkIvIUcrIuNh0PTMfB0RW2ZjwsBBeOufCbDTisl4GDQ9s62Ltt2aw7HAEf5d26GSVkzGw6DpXM7REJy0bYfATo5aCRkRg6ZrJoQdDEWudyACnFlVRsba07P8MzgaegvNArugATtohsag6Zg5ORwR8fXQoXN1hP7rGFI4j2ZYDJqOmXOykKvk4PSWHcj39Ucd1pZhccJa10xIibsOO9eGqOWgFZEhMWhEErAxQiQBg0YkAYNGJAGDZiVMpnyY+RyNbnEwxEpERERi1aqv4OnpAW9vb7Rq5Q1XV1ftLD1oDJqVEEFbtGiJdlSsVq1aaNnS+/YfJycn7QzJxqCVo+TkZBw+fEQ7kispKRlhYWHa0f25ubndDp2HRws4OHByThYGrRydOnUa8+Yt0I70yd7eHs2bN0fbtj7o3r07KlVi2GRg0MqRGIzIz8/XjuQ6efIUli1boR3drWHDhrfvZC1aNOed7AFg0KzEnX00Z2fn28ESAyNOTnyW7UFj0KxEfHwCLl68qIarXr16WinpBYNGJAEnrIkkYNCIJGDQiCRg0IgkYNCIJGDQiCTg8L5OiWoRS7rEig+x4sTLyxN+fn6wt+e+c0bEoOmQyWRS10xmZGSic+dOariOHw9DQUE+pkx5EzVqVNc+SUbBoOmQWLMo7mJjx46Gre2vrfuNGzchJiYG06a9rZWQUbCPpjNpaWk4ceIkhg0belfIhEGDnkVKyk3Exl7WSsgoDHlH2759O2bNmo1HHnlEK7EelStXga+vL/7xjw+1kruJJuW+ffuQlZWplViPgoICjBgRjFGjRmkl1sOQQdu2bRsOHTqMd9+dppVYj7i4OKxZsx4zZnwMGxsbrfRXM2fORkBAZ7Rt20YrsR4rV66Co6Ojpck8RiuxHoYNmmheTZ/+nlZiPUR1/O1v7+O5555B+/Z+Wmkx0WScO3ceZs+egUqVrO9taStWiL6pYpVBYx9NZ8RdbOjQIVi9+htLE3G/OgJZWFiII0eOYf78hXjxxcFWGTJrx6DpUKtWLTFp0kSEh0dg4sTJGD9+Ivbu3YuRI4MRGBigfYqMhE1HnRMDBKI59TDs7cGmIz0wYmSVG+gYH4NGJAGDRiQBg0YkAYNGJAGDRiQBg0YkAYNGJAGDRiQBg0YkAYNGJAGDRiQBg0YkAYNGJAGDRiQBg0YkAYNGJAGDRiQBg0YkAYNG1iXrEo5FXEORdqgXDBpZlaLEHZj/ZRjytWO9YNCIJGDQiCRg0Igk4AaqpBtl30DVhF9mjsD8EBNuf4nzryMmqRKaNqqB268IsXXDgE/mItjTXiuQj0Ej3SiPnYqLohdixILGWD7/KVTRyvSATUciCRg0IgkYNCIJDBe09PQMZGVn/9r5JashhguKzGbt6I+xqemLx4OaQW8vXTbEYEh+fj6OHQ9F1JmzSE1NQ82aNdDBvz3a+7XTPnF/hedXY8q0LUj4nbqrHPA61r7dQzuiB2XRosW4mZqONj6t0aljB9Sv76qdMT7dB+3GjRRs3LQZtWs7q8Fyb9YUdnZ22lmyNpmZmTgeGo6w8AjUdna2BM4f3t5esLU1di9H10FLS0vDF8tXIahHN/UKRw8P8TrhrT9sx+nTUahRowaCh70EZ+da2lnj0XXQNn+/FdWdHPFYn95aCVk78c7uyBMnLXe1MEufDejYoT1827Yx/Hu7dRu0rKwszF+4BG+89iqqVNHT1CNVhJSUFEs/PAwnT51Go4Zu6GhpwYhugnh5vjXQbdASE5Pwz++2YNLE8VoJWRvx1btwIRpHj4eq9S3uXGKQy8hNxN+i26CJ0cVlK1bhrTdf4+CHlSkqKsLRY8exa/de9R3d/fr2UUcaxd+tlW6HcmrVqol6deuqbfX/EO33M2fO4nDIERw6HILw8Eh1wISMRVw4WzR3h7t7M7VpeCH6IuLjE7Sz1knXgyFXr17DmnUb0LtXEC5evISY2Mto0KA+6tSurQ73in6cKBOhDOjcSb0qkrHk5eXdHvwQdSqajqIJ6eDgoH3COug6aMJ332/FqdNR6pVvzF9f/q9JTHGX+/lfu9TKEv05Z2dn7QwZifgaXrwUoy5MEHe3tm181BHH2paLqjWowKCZkXF+H7Z+swJf7b2CAkcv9H0pGMOGBKFJKUdqExKuYt2Gb9H3sd6IttzRoi1NjLp1XdQ7mmh+iDta7OUrcKlTx3JH64jWrVtpP0lGduvWLXUE8sTJU3ByckSvnkHw9Ghh6BHICr+jmXZOQbdxP6Lx1J+w4RV3lGVYY9VXX6N1q5aWK5u/elxQUICYmFikZ2TAbDajSuUqaNq0CapXd1LPk0xZiN6zESsWfYnDSXZw9e0J39ppuHw5By6dBmPcmD5o/Cemvi5fuYKDh0JwyXKX87F0CXr26K52EQxLBK3imJTIT/ooHu5PKQvOF2plpWO5qikzZn2qFBaW7edKIzsxSgk/EadkFGkFFoW3opWT0WnKHUX0u1KVb0d6Ku7eI5UN14t/c2kHpiu9mzVX+nx0VMlTS0ovPz9fCQ0LVxYvXa7MnbdQOXjosJKdna2dLZne67RiRx2L4nAo5DLQJABdmpRtiD4vz4SqVauW89B+IWK+fRtjR47CsAGPYfCs4zCp5Sbs/WgwBr34EfbkqgVUGnmRiDhTAIc23dCldvFXqYZfe3hUKkR8eDgSS7m5opjK2blrDz77fAGios6iZ1B3vDbpFXQJDFC/AyUzRp1WaNDMyYdw+JwZdTt2RcsyDiKJtrlYYJqbW46/JXMOlLaTsPK7dxFU1YTLJ84gTV3ZbwMXF2cg4wZSctRPUinknz6IYym28OzSDfW1b5Lp/DnE5tvCxcMbdUu4Rlou8rgUE4P1lj740mUr1G7BqJHBCB7+Erw8PUrfHzNInVZo0NJDDuF0QQ34d2uHsjbXHR0d4e3liV8OHNJKgKSkZOz/9wFs3fYjvt+6TR1tPH8hWl2AWiq21eHu6Qb7awlIMtmiTtNmqKn+BhzQvEVTVGrgjuZOZmTGHMHuHT9hx46dOBqTrf4o3asQsQeOIAEN0b5DfeSnJ+Hc3pV4Z+p6ZAVMxqyp3fBb9yIxYb3th+1Ys3aDpS8Wh9GjRuIvTzxuCUYd7RNlUKo6zULskV34+SdRpzuw6+ApXJMcvgoMWjaOHwhDThU/dOnoqJWVTa+ePdRh+6/XrFPXPa5dvwE5OTlwda0Ht0cfReXKlSxBPIhZc+aqoRMVWBqmaMtVt8gBLXxaahcAMzLSs+AS2BNtHGzh1MQNV1ZNwfxwZ7RqVk39BN2jKBEHQ6Jhrl0HaZvHon/7AAxecA19Zv+M3d+8hgCtKXk/ojsw4OknMWb0y/D29sSKVV9h0+bvERcXr32i7EquU0c0rBmFpW+tRMyjreCatBpjnp6GnSl/7iHTsqi4oJkicfB4GuzbBCLgPkvXiop+/39SPB7RvLk7YmMvW9rxqejfry8e69NLfWRGTGwG9eiOJ5/or975xJKerKzS3H2KcDM+CTm2bvDy0kYrzYnYd7gITw0JKK6kvLM4F9cUjz3tiz92ibB+5luWbsHpQrgETcDHM2bh5Q5VkJeYDUdP11K3XhrUr4+BTz+l9sfqWy6e4mkN0YwMj4hUm5Kl9/t1mnXmLBJa9ETfVo3g078LGiUfR3hcKVtC5aDCgpZ/xtJ+T7KFR0BXuN7zXym6sg5zVp3Vjn7buXPnkZCQgFfGj1Xn0kKOHMPsTz/HwsVfYMkXKzDns3lYv/FbdY3chHGjLcGsrv1kyRTL1Q42TpbPi06ECZc2zcG+5m9ilE/xvn+mEwcRXrkDAj0e3D6Aepd95CAi86rBN9APlewa4IlnuqDa9d3Ysj9D+0TpiQGPrl0C1cD16N4Np05FYe68hdi1e0+pl9iVXKc5OH4oErX82sP55nnsnLcJiUFj8HwbiatPigcfy1uBcn7ek4pn027K30NMWlmxgsT9ypwXX1A+jSzQSu7P0gxUFixaqkRFndFKimVmZipXr15T4uLjlRs3UrTSsimM26JM7e2jdOwXrIwfO155Z9EvStLtWYQC5eSs/krglJ1K6QaWH0Y5yr6pnZQWHi8pqxO1wfO0H5TJ7ZopvqM3KTfKYTw9Ofm6smHjJuWDDz9WvlmzTrl585Z25v5KrNO8EOWD7l2V8bP/V3mhTQ/lnR2JZZ56+LMqYMI6A+e3L8eMDxfjQLItXFoHobNnDdgXmZCVchlRkWdx3XU0Nvz0DnxLuKCkpNzEV1+vUVfvV4wimHILYV+l0t2T6EWXsPT5wTgZvBeLB9bQCs0wm21h8Kfpy4/pKD7qOxRrHV/F1q2vo3gD4Gzs+5/eGPeDO97b9Q2C3f74L0uscRWPzogWTZPGjdCtaxc0bOimnS3J/eu08NQcDBydhDf2vY/Cd/tiwaPLsGVqG0htr6hx06HExCRl3oLF2pE8RYlfK8Fthitrkv5zWS5Urm5dpWyLL/+JcyMquhGhbP77IMW/SROlRedRyoIdZ5Q07VeVF/KB0quZuxI4/FPl5/OZxYWlJBYmRJ44qSxbvkqxdAmU/f/+RW29/HmFSuyS5xT/sZuVVMtRzv53laCgD5QjucVnZdHtomIxf/b5/EVq36tmTUlLb/ISsH/mBLy60Yz+E56BdyUTUi8exI6rvbDy6zFoXMK8EP0xGRmZCA0LQ1h4pLoZT0exGY+XZ7ktVMi5/DP+b8xr2Of+Pr6cOQQeVSLwyRPjcXbAEnw60R8uklopul69LzrDoiKee3agukpfzJmdO38B6enpd6119PJsARcXF+2nyAiuXInDth9/stRvBlq3bomO/v5Wtb3cvXQdNPGsknjKWizREZo0aYyW3l7Fz6PZ2SI7KxvRly7hwoWL6ojjiOFDDb+Jy8NAzHeKvUHEpLW9vT26d+sCv3a+qFbNeucsdR00cddau24jYmJj1WMxb6YGrU5tdYmOmLwWj8+ILcnEs0xT3pisrigh4xDPnomBD/EIlJeXB/zb+6GhW2kGPoxF10ELDQtXJy9HBg9TKyTq7FmcO3dB7b+JoIk/TRo3hqel6ejTuhV3yzKwzMwsHDx0GBGRJ9RVP6KvZvRn0O6k26CJ9YtiMOT5Qc+gcaNGWmkxsWpA3O3E4+7WUhFUTNStaFaKJ61Npnx08PdTm5VGv4jqdmZIPGVrb2/3XyETxEoQ0RdjyKyPqFux9ftfXx5hubM1wO49+yz99C8t34dU7RPGpNugifssg/TwERdYsUBcLMHKzcvDkBeex+RXJxh+r0fdNh3FG2RE03HY0BfVxadkvcRX8N6NecSicTHoZS10PRgi9m8UQ/fDhw0p5yetSQ/E3KgY/BBbzYnWi9gbRoTMGqdodB00MSCybv236r/FoIiTEzfhsQZiHm3P3v0IOXJUHdAa/PyzaNbUevbZvx+7Dyy0v+uO2FDTx6cVbqWmYsvWH5CUnKyWK2bF0mm2Vyc7y6YQUd+tRXQdHzSqxv7fgyLqVWyEK1opN2+l4sqVeLVMbBtorS0XXd/R7iReqXv23Dl1Hi09I11twwcGdNbOllYufpw8ClcmrcHEFmyK6oH4+omldaJ/Jl50IeZM69Wrq521HoYJ2p22bduGEydOYvr097SS0mLQ9GzJ0qWwtbHFuHFjtZLfY8IvM0dgfoip5Hea27phwCdzEVz8PM8DwaCRbqxYsQJmS7dg7NgxWon14KOMRBJY9R2t8PxqTJm2BQm39wFSkB4XA5OrO+re8XR35YDXsfbtHtoRPSjWfEdj05F0g01HIvpTGDQiCRg0IgkesqA5wO/l1/F4ffbPSK6HLGh2aNCuE9y52wFJxqYjkQQMGpEEDBqRBAwakQQMGpEEDBqRBAwakQQMGpEEDBqRBAwakQQMGpEEDBqRBAwakQQMGpEEDBqRBAwakQQMGpEEDBqRBAwakQQMGpEEDBqRBAwakQQMGpEEDBqRBIZ9m8xnn83Fk0/+RSsha7B37z4MHDiQr23Si0uXYhAaGqodWbejR4+ifv36aNSokVZi3Vq29IaPj492ZD0MGbSHyfTp09G1a1f069dPKyEjYh+NSAIGjUgCBo1IAgaNSAIGjUgCBo1IAgaNSAIGjUgCBo1IAgaNSAIGjUgCBo1IAgaNSAIGjUgCBo1IAj6P9gBERJ5AWHiEdlQyk8kEGxsbODg4aCUl69O7J5o0bqwdkV4waA9AWloabqWmakcls7H8o1j+Ka16deuiWrVq2hHpBYNGJAH7aEQSMGhEErDpqBNfLF+J3Nxc7ehXlStXRl5ennZ0t1q1amHE8KHaEekZg6YTN2/ehNls1o7uZGP5c/8qsrOzh7NzLe2I9IxBI5KAfTQiCRg0IgnYdNSpz+cvRGZmFqpWrYKcnOJBkmbNmmLokBfUv5OxMGg6JUYa760aOzu7Ui/FIn1h0IgqHPD/ufAAOa7w3vEAAAAASUVORK5CYII=[/img][br]Fonte: Sadiku, Musa, Alexander (2014,p.269)[br][br]Aplicando a LKT: [math]v_L+v_R=0[/math][math]\longleftrightarrow L\frac{d\left(i\right)}{d\left(t\right)}+Ri\left(t\right)=0[/math][math]\longleftrightarrow\frac{d\left(i\right)}{d\left(t\right)}+\frac{R}{L}i\left(t\right)=0[/math] uma EDO linear de primeira ordem homogênea.[br][br]Dessa forma, vamos em busca de uma função desconhecida [math]i\left(t\right)[/math], em que a sua taxa de variação em função do tempo t é proporcional a sua corrente elétrica [math]\left(\frac{d\left(i\right)}{d\left(t\right)}=-\frac{R}{L}i\left(t\right)\right)[/math]. Uma das funções que tem essa propriedade é a função exponencial.[br][br][br]Seja [math]i\left(t\right)=I_0e^{\left(-\frac{R}{L}t\right)}[/math] uma função exponencial com [math]I_0[/math] a corrente elétrica no instante t=0, ou seja, [math]i\left(0\right)=I_0[/math].[br][br][math]\longrightarrow i'\left(t\right)=-\frac{R}{L}I_0e^{\left(-\frac{R}{L}t\right)}\longleftrightarrow\frac{d\left(i\right)}{d\left(t\right)}=-\frac{R}{L}I_0e^{\left(-\frac{R}{L}t\right)}[/math] [br][br]Assim, identificamos que de fato [math]i\left(t\right)=I_0e^{\left(-\frac{R}{L}t\right)}[/math] é solução da EDO homogênea.[br][br]Outra método para se chegar a essa solução, entre diversos, trata-se do método dos coeficientes indeterminados:[br][br][math]ay''+by'+c=G\left(x\right)[/math], por se tratar de uma EDO homogênea [math]\longrightarrow G\left(x\right)=0[/math][br][br]Considere uma equação auxiliar para encontrar a solução da EDO homogênea [math]\frac{d\left(i\right)}{d\left(t\right)}+\frac{R}{L}i\left(t\right)=0[/math], sendo:[br][br] [br] [math]y+\frac{R}{L}=0\longrightarrow y=-\frac{R}{L}[/math] [math]\longrightarrow y_H\left(t\right)=ce^{\left(-\frac{R}{L}t\right)}[/math] , sendo [math]y_H\left(t\right)=i\left(t\right)[/math] e [math]I_0=c:[/math][br][br][math]i\left(t\right)=I_0e^{\left(-\frac{R}{L}t\right)}[/math] [br]Essa solução depende das condições iniciais [math]I_0[/math] no instante t=0.[br][br]Vamos identificar a representação gráfica desse tipo de EDO modelada para um circuito RL sem fonte de tensão no GeoGebra e analisar o seu comportamento gráfico da Função Corrente Elétrica de um Indutor em um Circuito RL em série no processo de fornecer energia.[br][br]Como exemplo, vamos considerar inicialmente os seguintes valores para R,L e [math]I_0[/math]:[br][math]R=10\Omega[/math] , [math]L=5H[/math] e [math]I_0=5A[/math]

No GeoGebra faça alterações nos valores reais de [math]I_0[/math], R, C para analisar o comportamento gráfico da função que representa a Corrente Elétrica de um Indutor em um Circuito RL em série no processo de fornecer energia. Movimente o ponto sobre o gráfico para uma interpretação pontual dos valores de t e [math]i\left(t\right)[/math].

Como [math]i\left(t\right)=I_0e^{\left(-\frac{R}{L}t\right)}[/math] [math]\longrightarrow\frac{d\left(i\right)}{d\left(t\right)}=-\frac{R}{L}I_0e^{\left(-\frac{R}{L}t\right)}[/math], sabemos que [math]v_L\left(t\right)=L\frac{d\left(i\right)}{d\left(t\right)}[/math] [math]\longrightarrow v_L\left(t\right)=-RI_0e^{\left(-\frac{R}{L}t\right)}=-RI_0e^{\left(-\frac{t}{\tau}\right)}[/math][br][br]Dessa forma, como [math]v_L\left(t\right)=-v_R\left(t\right)\longrightarrow v_R\left(t\right)=RI_0e^{\left(-\frac{t}{\tau}\right)}[/math][br][br]No GeoGebra vamos analisar o comportamento gráfico das funções que envolvem tensão no indutor e no resistor de um circuito RL em série sem fonte.

No GeoGebra faça alterações nos valores reais de [math]I_0[/math], R, C para analisar o comportamento gráfico das funções que representa a Tensão no Indutor e no Resistor em um Circuito RL em série. Clique no botão iniciar e observe o movimente dos pontos sobre os gráficos para uma interpretação pontual dos valores de t e [math]v_{L\left(t\right)}[/math] e [math]v_{R\left(t\right)}[/math].

Sejam [math]V_s[/math] a tensão na fonte (bateria), [math]v_R[/math] a tensão no resistor e [math]v_L[/math] a tensão no indutor em circuito RL em série e no instante inicial [math]t=0[/math] temos [math]i\left(0\right)=0[/math], isto é, em um circuito RL com fonte de tensão constante no momento inicial [math]\left(t=0\right)[/math] não há circulação de corrente, nesse momento o [b]indutor[/b] se comporta como um [b]circuito aberto.[/b][br][br]Aplicando a LKT: [math]v_L+v_R=V_s[/math][math]\longleftrightarrow L\frac{d\left(i\right)}{d\left(t\right)}+Ri\left(t\right)=V_s[/math][math]\longleftrightarrow\frac{d\left(i\right)}{d\left(t\right)}+\frac{R}{L}i\left(t\right)=\frac{V_s}{L}[/math] uma EDO linear de primeira ordem.[br][br]Dessa forma, vamos em busca de uma função desconhecida [math]i\left(t\right)=i_{H\left(t\right)}+i_P\left(t\right)[/math] solução geral da EDO não homogênea, sendo [math]i_H\left(t\right)[/math] a solução da EDO homogênea e [math]i_P\left(t\right)[/math] a solução particular.[br][br]Já sabemos via cálculo anterior que [math]i_H\left(t\right)=I_0e^{\left(-\frac{R}{L}t\right)}[/math] é solução da EDO homogênea.[br][br]Dessa forma vamos em busca de uma solução particular. Como [math]\frac{V_s}{L}[/math] é uma constante, pelo método dos coeficientes indeterminados, queremos uma função solução particular do tipo [math]i_P\left(t\right)=k[/math][math]\longrightarrow\frac{d\left(i\right)}{d\left(t\right)}=0[/math]:[br][br][math]\frac{d\left(i\right)}{d\left(t\right)}+\frac{R}{L}i\left(t\right)=\frac{V_s}{L}\longrightarrow0+\frac{R}{L}k=\frac{V_s}{L}\longleftrightarrow k=\frac{V_s}{R}[/math][math]\Longrightarrow i_P\left(t\right)=\frac{V_s}{R}[/math][br][br]Logo, a solução geral [math]i\left(t\right)[/math] da EDO não homogênea corresponde a: [br][math]i\left(t\right)=I_0e^{\left(-\frac{R}{L}t\right)}+\frac{V_s}{R}[/math] .[br][br]De acordo com o P.V.I (Problema de Valor Inicial):[br][math]i\left(0\right)=I_0e^{\left(-\frac{R}{L}\cdot0\right)}+\frac{V_s}{R}=0\longrightarrow I_0=-\frac{V_s}{R}[/math][br][br]Portanto a solução geral com P.V.I. será:[br][br][math]i\left(t\right)=-\frac{V_s}{R}e^{\left(-\frac{R}{L}t\right)}+\frac{V_s}{R}\longleftrightarrow i\left(t\right)=\frac{V_s}{R}\left(1-e^{\left(-\frac{R}{L}t\right)}\right)[/math][br][br]Como [math]\frac{L}{R}=\tau\longrightarrow i\left(t\right)=\frac{V_s}{R}\left(1-e^{-\frac{t}{\tau}}\right)A[/math]

No GeoGebra faça alterações nos valores reais de [math]V_s[/math], R, C para analisar o comportamento gráfico da função que representa a Corrente Elétrica de um Indutor em um Circuito RL em série no processo de armazenamento de energia. Movimente o ponto P sobre o gráfico para uma interpretação pontual dos valores de t e [math]i\left(t\right)[/math] .

Já sabemos que [math]v_L\left(t\right)=L\frac{d\left(i\right)}{d\left(t\right)}[/math] e [math]i\left(t\right)=\frac{V_s}{R}\left(1-e^{-\frac{R}{L}t}\right)\longrightarrow\frac{d\left(i\right)}{d\left(t\right)}=\frac{V_s}{R}\cdot\left(\frac{R}{L}\right)e^{\left(-\frac{R}{L}t\right)}=\frac{V_s}{L}e^{\left(-\frac{R}{L}t\right)}[/math] .[br]Portanto [math]v_L\left(t\right)=L\left(\frac{V_s}{L}e^{\left(-\frac{R}{L}t\right)}\right)=V_se^{\left(-\frac{R}{L}t\right)}=V_se^{\left(-\frac{t}{\tau}\right)}\left[V\right][/math][br][br]Pela Lei LKT: [math]V_s=v_L+v_R\longleftrightarrow v_{R\left(t\right)}=V_s-v_L\left(t\right)\longrightarrow v_R\left(t\right)=V_s-\left(V_se^{\left(-\frac{t}{\tau}\right)}\right)=V_s\left(1-e^{\left(-\frac{t}{\tau}\right)}\right)\left[V\right][/math][br][br]Dessa forma, concluímos que [math]v_{L\left(t\right)}=V_se^{\left(-\frac{t}{\tau}\right)}\left[V\right][/math] e [math]v_{R\left(t\right)}=V_s\left(1-e^{\left(-\frac{t}{\tau}\right)}\right)\left[V\right][/math][br][br]Vamos analisar a interpretação gráfica dessas funções no GeoGebra.

No GeoGebra faça alterações nos valores reais de [math]V_s[/math], R, C para analisar o comportamento gráfico da função que representa as Funções Tensões no Indutor e no Resistor em um Circuito RL em série com fonte no processo de fornecimento de energia (chave aberta) . Marque as funções do indutor e do indutor e movimente os pontos A e B sobre o gráfico, clicando nos botões iniciar, parar e continuar, para uma interpretação pontual e global das funções aplicadas a esse tipo de circuito elétrico com domínio no tempo t com [math]t\ge0[/math] . Analise também a constante de tempo [math]\tau[/math] e como foram definidas as funções tensão no indutor e no resistor presentes na janela 2.

Mais detalhes no vídeo a seguir:

A seguir estudaremos as EDO lineares de segunda ordem modeladas por circuitos RLC em série com ou sem fonte (cc). [br]

SADIKU, Matthew N. O; ALEXANDER, Charles K.; MUSA, Sarhan. Análise de circuitos elétricos com aplicações. AMGH Editora, 2014.

Segundo Sadiku, Musa, Alexander (2014,p.261) um indutor é um componente elétrico que armazena energia em um campo magnético, geralmente na forma de uma bobina de fio. Ele é amplamente utilizado em circuitos analógicos, especialmente em aplicações de alta frequência, embora seja menos comum que os capacitores. Indutores são raramente usados em circuitos integrados devido à dificuldade de fabricação nos chips.[br][br]

No GeoGebra vamos analisar o gráfico da função [math]v_L\left(t\right)=N\frac{d\left(\phi\right)}{d\left(t\right)}[/math] que representa a Lei de Faraday, mas antes disso precisamos entender a função [math]\phi[/math] que representa o fluxo de um campo magnético, conforme apresentado no vídeo anterior, que corresponde a [math]\phi\left(t\right)=ABcos\left(t\right)[/math] , sendo [math]A[/math] a área da espira em [math]m^2[/math] e [math]B[/math] a intensidade do campo magnético em [math]T[/math] (tesla) e [math]t[/math] o ângulo em radianos da posição da espira em relação ao campo magnético. [br][br]Faça alterações nos valores de A e B e analise o comportamento gráfico da função periódica, nesse caso uma cossenóide.

No GeoGebra vamos analisar o gráfico da função [math]v_L\left(t\right)=N\frac{d\left(\phi\right)}{d\left(t\right)}[/math] que representa a Lei de Faraday, mas antes disso precisamos entender a função [math]\phi[/math] que representa o fluxo de um campo magnético, conforme apresentado no vídeo anterior, que corresponde a [math]\phi\left(t\right)=ABcos\left(t\right)[/math] , sendo [math]A[/math] a área da espira em [math]m^2[/math] e [math]B[/math] a intensidade do campo magnético em [math]T[/math] (tesla) e [math]t[/math] o ângulo em radianos da posição da espira em relação ao campo magnético. [br][br]Faça alterações nos valores de A e B e analise o comportamento gráfico da função periódica, nesse caso uma cossenóide.

No GeoGebra vamos analisar o gráfico da função [math]v_L\left(t\right)=N\frac{d\left(\phi\right)}{d\left(t\right)}[/math] que representa a Lei de Faraday, mas antes disso precisamos entender a função [math]\phi[/math] que representa o fluxo de um campo magnético, conforme apresentado no vídeo anterior, que corresponde a [math]\phi\left(t\right)=ABcos\left(t\right)[/math] , sendo [math]A[/math] a área da espira em [math]m^2[/math] e [math]B[/math] a intensidade do campo magnético em [math]T[/math] (tesla) e [math]t[/math] o ângulo em radianos da posição da espira em relação ao campo magnético. [br][br]Faça alterações nos valores de A e B e analise o comportamento gráfico da função periódica, nesse caso uma cossenóide.

Silva, C. R., & Boscarioli, C. (2026). Livro digital interdisciplinar com GeoGebra: aplicações de equações diferenciais a circuitos elétricos em corrente contínua. [i]Revista Do Instituto GeoGebra Internacional De São Paulo[/i], [i]15[/i](1), 007–035. https://doi.org/10.23925/2237-9657.2026.v15i1p007-035