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file mode 100644 index 0000000..e7e8c26 --- /dev/null +++ b/Electro/mixto_capacitores.svg @@ -0,0 +1,5 @@ + + ++-2432166412c1c2c3c4c6c5 \ No newline at end of file diff --git a/Electro/parcial2.md b/Electro/parcial2.md new file mode 100644 index 0000000..5678659 --- /dev/null +++ b/Electro/parcial2.md @@ -0,0 +1,164 @@ +--- +title: Resumen Parcial 2 Teoria +--- + +# Temas +- Cirtuito RC +- Capacitores +- Teoria de electromagnetismo +- Ejs de kircho(ff) +- convertir forma polar a rectangular + +# Clase 9 - Descripcion del capacitor + +La capacidad es una relacion Q/V que establece la carga que contiene y la tension entre sus placas. + + +$C = \frac{Q}{V}$ + + +$V = \frac{Q}{C}$ + + +$Q = C * V$ + +## Capacitor Placas Planas Paralelas + +Consta de dos placas metálicas planas paralelas de área A, separadas una distancia d. Entre las placas se coloca un dieléctrico de permitividad $\varepsilon$ . Resultando su capacidad: + +$C = \varepsilon \frac{A}{d}$ + +## Medir Capacitores en Serie +tenemos que tener en cuenta que + +$\frac{1}{C_r} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + ...$ + + +${C_r} = ( \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + ... )^{-1}$ + +ejemplo: +![](./capacitores.png) + +## Medir Capacitores En Paralelo +En este caso hay que sumar los dos capacitores porque actuan como un capacitor más grande + +$C_r = C_1 + C_2$ + +ejemplo: +![](./enparalelo.svg) + +## Aplicaciones +Son utilizados como filtros para frecuencias y tambien para almacenar energia. Por ejemplo los flashes fotograficos lo utilizan. + +tambien son utilizados en temporizadores y alarmas. + +Pero un uso el cual estamos más en contacto todos los dias es el de las pantallas tactiles. + +# Cuentas +## Capacitores en serie +si tenemos un circuito donde la fuente es de 120V y hay 3 capasitores en serie de: + +- 4 $\mu$ f +- 6 $\mu$ f +- 2 $\mu$ f + +### Capacidad Equivalente +$\frac{1}{C_e} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$ + +$\frac{1}{C_e} = \frac{1}{4} + \frac{1}{6} + \frac{1}{2}$ + +$C_e = 1.0909 \mu f$ + +Luego hay que pasarlo a microfaradio a faradio por lo que pasaria a ser: + +$1.09*10^-6 F = 1.0909 \mu f$ + +### Carga total +$q = \Delta V * C_e$ + +$q = 120V * 1.09*10^-6 F$ + +$q = 1.308^{-4} C$ + +### Energia del sistema +$W = \frac{1}{2} * q * \Delta V$ + +$W = \frac{1}{2} * 1.308^{-4} * 120V$ + +$W = 7.848^{-3} J$ + +## Capacitores en Paralelo +si tenemos un circuito donde la fuente es de 120V y hay 3 capasitores en paralelo de: + +- 4 $\mu$ f +- 6 $\mu$ f +- 2 $\mu$ f + +### Capacidad Equivalente + +$C_e = C_1 + C_2 + C_3$ + +$C_e = 4 + 6 + 2$ + +$C_e = 12 \mu f$ + +$C_e = 1.2*10^{-5}f$ + +### Carga total +$q = \Delta V * C_e$ + +$q = 120V * 1.2*10^{-5}$ + +$q = 1.44*10^{-3} C$ + +### Energia en el sistema +$W = \frac{1}{2} * q * \Delta V$ + +$W = \frac{1}{2} * 1.44*10^{-3} * 120V$ + +$W = 0.0864 J$ + +## Asociacion Mixta +![](./mixto_capacitores.svg) + +Primero tenemos que hacer la relacion entre los capacitores que estan en serie. Vamos a empezar con el $C_5$ y $C_6$ + +$C_{56} = (\frac{1}{12} + \frac{1}6{})^{-1} = 4 \mu f$ + +Ahora sumamos con el del capacitor 4 + +$C_{456} = C_4 + C_{56}$ + +$C_{456} = 4 \mu f + 4 \mu f = 8 \mu f$ + +ahora con esto resueto podemos calcular todo en serie + +$C_{123456} = (\frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \frac{1}{C_{456}})$ + +$C_{123456} = (\frac{1}{32} + \frac{1}{24} + \frac{1}{16} + \frac{1}{8})^{-1} = 3.84 \mu f = 3.84*10^{-6} F$ + +Luego calculamos la carga total: + +$q = \Delta V * C_e$ + +$q = 120V * 3.84*10^{-6} F$ + +$q = 4.608*10^{-4}C$ + +Luego calculamos las diferencias locales V1, V2 y V3 + +### V1 +$V_1 = \frac{4.608*10^{-4}C}{3.2*10^{-5}}$ +$V_1 = 14.4V$ + +### V2 +$V_2 = \frac{4.608*10^{-4}C}{2.4*10^{-5}}$ +$V_2 = 19.2V$ + +### V3 +$V_3 = \frac{4.608*10^{-4}C}{1.6*10^{-5}}$ +$V_3 = 28.8V$ + +### $V_{456}$ +$V_{465} = \frac{4.608*10^{-4}C}{8*10^{-6}}$ +$V_{456} = 57.6V$