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on_electronics_._note [2016/07/20 21:31] nikolaj |
on_electronics_._note [2016/07/23 15:23] nikolaj |
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| $[R]=\dfrac{1}{[q_x]^2}$ | $[R]=\dfrac{1}{[q_x]^2}$ | ||
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| + | == Field theory == | ||
| + | On a very encompassing level, we should maybe view all those problems as question of the dynamics of charge collections, making for a charge density (making up $q_x$) under external forces (contributing to the voltages in the system). The charges interact, or put differently, the charge density self-interacts. | ||
| == Models for devices == | == Models for devices == | ||
| + | >$G = a_R + a_C \dfrac{\partial}{\partial t} + a_L \int{\mathrm d}t$ | ||
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| An capacitor are two ends of a conducting line that hold charges with a some voltage between them. Ideally, i.e. in the simplest case, we double the voltage if we double the charges - thus the number $C:=\frac{q_x}{U}$ is a constant. The factor $\frac{1}{C}$ says how strongly $U$ rises in reaction to a rise of $q_x$. Expressing that rise in terms of the time dependent incoming charge current, $q_x\propto \int^t I(t)$, we find $G{\sim}C\dfrac{\partial}{\partial t}$. | An capacitor are two ends of a conducting line that hold charges with a some voltage between them. Ideally, i.e. in the simplest case, we double the voltage if we double the charges - thus the number $C:=\frac{q_x}{U}$ is a constant. The factor $\frac{1}{C}$ says how strongly $U$ rises in reaction to a rise of $q_x$. Expressing that rise in terms of the time dependent incoming charge current, $q_x\propto \int^t I(t)$, we find $G{\sim}C\dfrac{\partial}{\partial t}$. | ||
