Forma de Onda de Corriente en Capacitor

flux

0:28

Para determinar la forma de onda de la corriente a partir de la forma de onda del voltaje en el capacitor, se utiliza la relación fundamental para un capacitor:
i(t)=Cdv(t)dt\Large i(t) = C \frac{dv(t)}{dt}
Donde:
  • ( C = 0.06\ \mu F ) (capacitancia del capacitor)
  • ( v(t) ) es la función de voltaje mostrada en la figura 10.102
Es decir, para obtener la forma de onda de la corriente, se debe derivar la función de voltaje respecto al tiempo y multiplicarla por 0.06 µF.
Si se requiere además hallar la corriente promedio (por ejemplo, sobre un período ( T )) se definirá:
Iavg=1T∫0Ti(t) dt=CT[v(T)−v(0)]\Large I_{avg} = \frac{1}{T}\int_0^T i(t)\, dt = \frac{C}{T}\left[v(T)-v(0)\right]
Observaciones:
  • En una señal periódica en la que el voltaje en el instante ( T ) es igual al voltaje en ( 0 ) (es decir, ( v(T) = v(0) )), la corriente promedio sobre un período completo resulta cero.
  • La forma de onda instantánea de la corriente mostrará los mismos puntos críticos y características (como discontinuidades o cambios rápidos) que la derivada de la forma de onda del voltaje.
Por lo tanto, para obtener la forma de onda específica de la corriente se debe conocer la función ( v(t) ) de la figura 10.102 y aplicar la derivación según lo anterior.
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