update
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@@ -65,14 +65,13 @@
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<h2>Corriente Alterna</h2>
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</header>
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<section>
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<p></p>
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<p>Corriente alterna (abreviada CA en español y AC en inglés, de alternating current) se denomina a la corriente
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eléctrica en la que la magnitud y el sentido varían cíclicamente.</p>
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eléctrica en la que la magnitud y el sentido varían cíclicamente, significando esto que gráficamente
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pasa la mitad del tiempo en zona positiva y la otra mitad en zona negativa.</p>
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<p>La forma de oscilación de la corriente alterna más comúnmente utilizada es la oscilación senoidal (sinusoidal
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en inglés) con la que se consigue una transmisión más eficiente de la energía, a tal punto que al
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hablar de corriente alterna se sobrentiende que se refiere a la corriente alterna senoidal.</p>
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</p>
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<img class="symbol" src="images/Corriente_Alterna.png" height="240" />
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<img class="symbol" src="images/Onda_Senoidal.png" height="240" />
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<p>Sin embargo, en ciertas aplicaciones se utilizan otras formas de oscilación periódicas, tales como la
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triangular o la cuadrada.</p>
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<p>Utilizada genéricamente, la CA se refiere a la forma en la cual la electricidad llega a los hogares y
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@@ -82,7 +81,7 @@
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<p>Algunos tipos de oscilaciones periódicas tienen el inconveniente de no tener definida su expresión matemática,
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por lo que no se puede operar analíticamente con ellas. Por el contrario, la oscilación sinusoidal
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no tiene esta indeterminación matemática y presenta las siguientes ventajas:</p>
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<ol>
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<ul>
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<li>La función seno está perfectamente definida mediante su expresión analítica y gráfica. Mediante la
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teoría de los números complejos se analizan con suma facilidad los circuitos de alterna.</li>
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<li>Las oscilaciones periódicas no sinusoidales se pueden descomponer en suma de una serie de oscilaciones
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@@ -92,11 +91,181 @@
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de la energía eléctrica.</li>
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<li>Su transformación en otras oscilaciones de distinta magnitud se consigue con facilidad mediante la
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utilización de transformadores.</li>
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</ol>
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<h4>Potencia en C.A</h4>
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</ul>
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<section>
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<header class="major">
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<h3>Oscilación Senoidal</h3>
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</header>
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<p>Una señal senoidal o sinusoidal,
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<em>a(t)</em>, tensión,
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<em>v(t)</em>, y corriente,
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<em>i(t)</em>, se puede expresar matemáticamente según sus parámetros característicos, como una función
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del tiempo por medio de la siguiente ecuación:</p>
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<img class="symbol" src="images/Onda_Senoidal_Parametros.png" height="300" />
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<img class="symbol" src="images/symbols/Corriente_Alterna_03.png" height="60" />
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<p>Donde:</p>
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<ul>
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<li>
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<b>A0</b> es la amplitud en voltios (Vmax) o amperios(Imax) (también llamado valor máximo o
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de pico)</li>
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<li>
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<b>ω</b> la pulsación en radianes/segundo</li>
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<li>
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<b>t</b> el tiempo en segundos </li>
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<li>
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<b>β</b> el ángulo de fase inicial en radianes</li>
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</ul>
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<p>Dado que la velocidad angular es más interesante para matemáticos que para ingenieros, la fórmula
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anterior se suele expresar como:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_04.png" height="60" />
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<p>Donde se puede observar que
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<em>ω = 2πf</em>, y donde
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<strong>f</strong> es la frecuencia en hercios (Hz) y equivale a la inversa del período
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<em>f=1/T</em>. Los valores más empleados en la distribución son 50 Hz y 60 Hz.</p>
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</section>
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<section>
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<header class="major">
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<h3>Valores Significativos</h3>
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</header>
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<ul>
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<li>
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<strong>Valor instantáneo</strong> (
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<em>a(t)</em> ): Es el que toma la ordeada en un instante, t, determinado.</li>
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<li>
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<strong>Valor pico a pico</strong> (
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<em>App</em> ): Diferencia entre su pico o máximo positivo y su pico negativo. Dado que el valor
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máximo de sen(x) es +1 y el valor mínimo es -1, una señal sinusoidal que oscila entre +A0
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y -A0. El valor de pico a pico, escrito como AP-P, es por lo tanto (+A0)-(-A0) = 2×A0</li>
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<li>
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<strong>Valor medio</strong> (
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<em>Amed</em> ): Valor del área que forma con el eje de abscisas partido por su período. El valor
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medio se puede interpretar como el componente de continua de la oscilación sinusoidal. El
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área se considera positiva si está por encima del eje de abscisas y negativa si está por
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debajo. Como en una señal sinusoidal el semiciclo positivo es idéntico al negativo, su valor
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medio es nulo. Por eso el valor medio de una Oscilación sinusoidal se refiere a un semiciclo.
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Mediante el cálculo integral se puede demostrar que su expresión es la siguiente
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<img class="symbol" src="images/symbols/Corriente_Alterna_05.png" height="120" />
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</li>
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<li>
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<strong>Pico o cresta</strong>: Valor máximo, de signo positivo (+), que toma la oscilación sinusoidal
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del espectro electromagnético, cada medio ciclo, a partir del punto “0”. Ese valor aumenta
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o disminuye a medida que la amplitud “A” de la propia oscilación crece o decrece positivamente
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por encima del valor "0".</li>
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<li>
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<strong>Valor eficaz</strong> (
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<em>A</em> ): El valor eficaz se define como el valor de una corriente (o tensión) continua que
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produce los mismos efectos calóricos que su equivalente de alterna. Es decir que para determinada
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corriente alterna, su valor eficaz (Ief) será la corriente continua que produzca la misma
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disipación de potencia (P) en una resistencia(R). Matemáticamente, el valor eficaz de una
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magnitud variable con el tiempo, se define como la raíz cuadrada de la media de los cuadrados
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de los valores instantáneos alcanzados durante un período:
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<img class="symbol" src="images/symbols/Corriente_Alterna_06.png" height="120" /> En la literatura inglesa este valor se conoce como R.M.S. (root mean square, valor cuadrático
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medio), y de hecho en matemáticas a veces es llamado valor cuadrático medio de una función.
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En el campo industrial, el valor eficaz es de gran importancia, ya que casi todas las operaciones
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con magnitudes energéticas se hacen con dicho valor. De ahí que por rapidez y claridad se
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represente con la letra mayúscula de la magnitud que se trate (I, V, P, etc.). Matemáticamente
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se demuestra que para una corriente alterna sinusoidal el valor eficaz viene dado por la
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expresión:
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<img class="symbol" src="images/symbols/Corriente_Alterna_07.png" height="120" /> El valor A, tensión o intensidad, es útil para calcular la potencia consumida por una carga.
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Así, si una tensión de alterna, desarrolla una cierta potencia P en una carga resistiva dada,
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una tensión de continua de Vrms desarrollará la misma potencia P en la misma carga, por lo
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tanto,
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<em>Vrms x I = VCA x I</em>.
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</li>
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<li>
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<strong>Potencia en C.A</strong>:
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<img class="symbol" src="images/symbols/Corriente_Alterna_01.png" height="30" />
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<h4>Impedancia</h4>
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<img class="symbol" src="images/symbols/Corriente_Alterna_02.png" height="120" />
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</li>
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</ul>
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</section>
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<section>
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<header class="major">
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<h3>Representación Fasorial</h3>
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</header>
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<p>Una función sinusoidal puede ser representada por un número complejo cuyo argumento crece linealmente
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con el tiempo, al que se denomina fasor o representación de Fresnel, que tendrá las siguientes
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características:
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</p>
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<ul>
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<li>Girará con una velocidad angular ω.</li>
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<li>Su módulo será el valor máximo o el eficaz, según convenga.</li>
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</ul>
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<p>La razón de utilizar la representación fasorial está en la simplificación que ello supone. Matemáticamente,
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un fasor puede ser definido fácilmente por un número complejo, por lo que puede emplearse la
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teoría de cálculo de estos números para el análisis de sistemas de corriente alterna.</p>
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<p>Consideremos, a modo de ejemplo, una tensión de CA cuyo valor instantáneo sea el siguiente:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_08.png" height="120" />
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<p>Tomando como módulo del fasor su valor eficaz, la representación gráfica de la anterior tensión será
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la que se puede observar en la figura:</p>
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<img class="symbol" src="images/Fasor.png" height="180" />
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<p>y se anotará:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_09.png" height="90" />
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<p>denominadas formas polares, o bien:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_10.png" height="90" />
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<p>denominada forma binómica.</p>
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<p>Ahora, la parte práctica de todo esto se resume a lo siguiente:</p>
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<p>Suponiendo que se tiene el siguiente circuito cuya fuente es de corriente alterna;</p>
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<img class="symbol" src="images/Circuito_CA1.png" height="240" />
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<p>Donde
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<b>V = V(t) = Vm*Sen(ωt ± θ)</b>, y
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<b>ω=2πf</b>.</p>
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<p>Esto se conoce como Circuito en dominio del tiempo, pero para poder trabajar este circuito y aplicar
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las propiedades ya que está en corriente alterna debe hacerse una transformación hacia el dominio
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del fasor. Para pasar de dominio del tiempo a dominio del fasor se deben transformar los elementos:</p>
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<p>En este caso se transformará
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<b>R = R</b> (La resistencia permanece igual),
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<b>L = XL</b> (La inductancia se transforma en reactancia inductiva), y
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<b>C = Xc</b> (La capacitancia se transforma en reactancia capacitiva), y el nuevo V será el Vef
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(Voltaje eficaz),
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<b>V = Vef = Vm / √2</b>; En este caso se conserva el angulo fasor
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<b>θ</b>.</p>
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<p>Hecho esto surge un nuevo concepto llamado Impedancia</p>
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</section>
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<section>
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<header class="major">
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<h3>Impedancia</h3>
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</header>
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<p>La impedancia (Z) es una medida de oposición que presenta un circuito a una corriente cuando se aplica
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una tensión. La impedancia extiende el concepto de resistencia a los circuitos de corriente alterna
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(CA), y posee tanto magnitud como fase, a diferencia de la resistencia, que sólo tiene magnitud.
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Cuando un circuito es alimentado con corriente continua (CC), su impedancia es igual a la resistencia,
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lo que puede ser interpretado como la impedancia con ángulo de fase cero.</p>
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<p>Forma rectangular:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_02.png" height="90" />
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<p>Forma polar:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_11.png" height="90" />
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<p>En este caso X significa Xc o XL, dependiendo del elemento que se haya transformado:</p>
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<img class="symbol" src="images/symbols/Corriente_Alterna_12.png" height="240" />
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<p>Circuito transformado:</p>
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<img class="symbol" src="images/Circuito_CA2.png" height="240" />
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<p>
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<i>Las impedancias se miden en
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<em>Ohms (Ω)</em>.</i>
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</p>
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<p>Finalmente, obtenidas las impedancias el circuito puede ser calculado exactamente como un circuito
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de corriente continua, tomando las impedancias como resistencias (es decir, se pueden aplicar
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todas las leyes, teoremas y propiedades de la corriente continua), con la particularidad de que
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se debe cumplir con ciertas propiedades particulares:</p>
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<ul>
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<li>Para la suma de impedancias: Todas las impedancias deben estar en forma rectangular.</li>
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<li>Para la multiplicación de impedancias: Todas las impedancias deben estar en la misma forma, ya
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sea rectangular o polar
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<ul>
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<li>Para la multiplicación polar se multiplican las magnitudes de Z y se suman los ángulos.</li>
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<li>En la forma rectangular hay que recordar que al ser j un numero imaginario se deben aplicar
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las respectivas propiedades</li>
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</ul>
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</li>
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<li>Para la división de impedancias: Todas las impedancias deben estar en su forma polar (Se dividen
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las magnitudes y se restan los ángulos).</li>
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</ul>
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</section>
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</section>
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</div>
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</div>
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@@ -174,6 +343,10 @@
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<img class="symbol" src="images/symbols/Bobinas_01.png" height="120" />
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<p>Y la Corriente viene dada por:</p>
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<img class="symbol" src="images/symbols/Bobinas_02.png" height="90" />
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<p>Esto quiere decir que, si por ejemplo tenemos el siguiente circuito en el cual el interruptor se cierra
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en el instante t=0, el voltaje y la corriente se comportan de la siguiente manera:</p>
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<img class="symbol" src="images/Bobina_Circuito.png" height="180" />
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<img class="symbol" src="images/Bobina_Voltaje_Corriente.png" height="270" />
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</section>
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</div>
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</div>
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@@ -338,27 +511,73 @@
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tendrá el efecto de disipar una parte de la energía en cada Oscilación, conocido como Amortiguamiento</p>
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<header>
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<h4>Circuito RLC en Serie</h4>
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<h4>Amortiguamiento</h4>
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</header>
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<img class="symbol" src="images/symbols/Circuito_RLC_Serie.svg" height="180" />
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<p>Para poder explicar funcionamiento del circuito primero es importante discutir las medidas frecuencia
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angular,
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<p>Para poder explicar funcionamiento del circuito primero es importante discutir su amortiguación y para
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eso se necesita conocer las medidas frecuencia angular,
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<b>α</b> y
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<b>ω0</b>.
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<b>ω
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<sub>0</sub>
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</b>.</p>
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<p>
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<b>α</b> es la frecuencia neperiana o Atenuación, y es una medida de que tan rápido la respuesta del
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circuito morirá después de ser removido una fuente de estimulo.
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<b>ω0</b> es la frecuencia de resonancia angular. En un circuito en series estas están dadas por:</p>
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<img class="symbol" src="images/symbols/Resonancia_Atenuacion_Serie.svg" height="120" />
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<b>ω
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<sub>0</sub>
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</b> es la frecuencia de resonancia angular. En un circuito en series estas están dadas por:</p>
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<img class="symbol" src="images/symbols/Resonancia_Atenuacion_Serie.svg" height="90" />
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<p>Un Circuito RLC puede esta en 3 estados de amortiguamiento dependiendo de la relación entre estas dos
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medidas:
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</p>
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<ul>
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<li>Si
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<em>α > ω0</em>, se encuentra
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<strong>Super-Amortiguado</strong>
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||||
</li>
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||||
<li>
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Si
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<em>α = ω0</em>, se encuentra
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||||
<strong>Amortiguamiento Critico</strong>
|
||||
</li>
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||||
<li>
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||||
Si
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<em>α < ω0</em>, se encuentra
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||||
<strong>Sub-Amortiguado</strong>
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||||
</li>
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||||
</ul>
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<h5>Super-Amortiguado</h5>
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<p>Definiendo a las raíces S como:</p>
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<img class="symbol" src="images/symbols/Raices_RLC.svg" height="120" />
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||||
<img class="symbol" src="images/symbols/Raices_RLC_01.svg" height="120" />
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||||
<p>Se puede calcular la formula para la Corriente en el circuito:</p>
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||||
<img class="symbol" src="images/symbols/Corriente_RLC_Serie.svg" height="45" />
|
||||
<p>En donde los coeficientes A1 e A2 son dependientes del circuito y se calculan al realizar un sistema
|
||||
de ecuaciones con la formula resulta para el valor de la Corriente en el tiempo inicial y el que
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||||
va atener después de un tiempo infinito</p>
|
||||
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||||
<img class="symbol" src="images/symbols/Corriente_RLC_Serie_01.svg" height="45" />
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<p>En donde los coeficientes
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<strong>A
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||||
<sub>1</sub>
|
||||
</strong> e
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<strong>A
|
||||
<sub>2</sub>
|
||||
</strong> son dependientes del circuito y se calculan al realizar un sistema de ecuaciones con la formula resulta
|
||||
para el valor de la Corriente en el tiempo inicial y el que va atener después de un tiempo infinito</p>
|
||||
<h5>Amortiguamiento Critico</h5>
|
||||
<p>En este caso la formula es mas simple:</p>
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||||
<img class="symbol" src="images/symbols/Corriente_RLC_Serie_02.svg" height="45" />
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<p>Al igual que la ves pasada los coeficientes
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||||
<strong>A
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||||
<sub>1</sub>
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||||
</strong> e
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||||
<strong>A
|
||||
<sub>2</sub>
|
||||
</strong> son dependientes del circuito </p>
|
||||
<h5>Sub-Amortiguamiento</h5>
|
||||
<p>Para este caso, definiendo la raíz
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||||
<strong>ω
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||||
<sub>d</sub>
|
||||
</strong>:</p>
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||||
<img class="symbol" src="images/symbols/Raices_RLC_02.svg" height="60" />
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||||
<p>Se usa la formula:</p>
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||||
<img class="symbol" src="images/symbols/Corriente_RLC_Serie_03.svg" height="40" />
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||||
</section>
|
||||
|
||||
</div>
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||||
</div>
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</section>
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Before Width: | Height: | Size: 10 KiB After Width: | Height: | Size: 14 KiB |
Reference in New Issue
Block a user