Foundations

Voldate

Voldate represents the work per unit charge (J/C) required to move the charges from one point to the other.

Resistance

Resistance is determined by the physical dimensions and the resistivity ρ of the material of which the resistor is composed. For a bar of resistive material of length l and cross-sectional area A the resistance is given by $$R=\frac{\rho l}{A} =\frac{l}{\sigma A}$$ ρ [Ω·m] is the resistivity of the material, and σ [S/m] is the conductivity of the material.

Electric circuits

Collection

In the electric circuits,there are three parts of electric devices.Source provide the power,conductor like wire will transfer electric to the load,and the load will transform electric to other forms.

Circuit equations

An electric circuit may be described mathematically by ordinary differential equations.

All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

Equivalent circuit

Source

Two elements represents the transformation of electric energy from nonelectric energy. EMF source and current source.

电源在电路分析当中既有可能是信号源,也有可能是能量来源,我们并不用关心到底是什么,并且将他们统称为电源。且电压源与电流源不总是起电源作用,它们还有可能只是一个耗电的玩意儿

电流源,即理想电流源,是从实际电源抽象出来的一种模型,其端钮总能向外提供一定的电流而不论其两端的电压为多少,电流源具有两个基本的性质:第一,它提供的电流是定值I或是一定的时间函数I(t)与两端的电压无关。第二,电流源自身电流是确定的,而它两端的电压是任意的。

电压源,即理想电压源,是从实际电源抽象出来的一种模型,在其两端总能保持一定的电压而不论流过的电流为多少,电压源具有两个基本的性质:第一,它的端电压定值U或是一定的时间函数U(t)与流过的电流无关。第二,电压源自身电压是确定的,而流过它的电流是任意的。

Resistance

Resistance is an equivalent circuit element which represents the transformation of electric energy into nonelectric energy.
Resistance(R)\(R=\frac{du}{di}\) Conductance(g)\(g=\frac{di}{du}\)

Inductor

An ideal inductor is an energy-storage circuit element (with no loss associated with it) representing the magnetic-field effect. $$L=\frac{d\psi }{di}$$ $$i(t)=\frac{1}{L}\int u(t)dt$$

Capacitor

An ideal capacitor is an energy-storage circuit element (with no loss associated with it) representing the electric-field effect. $$C=\frac{dq}{du}$$ $$u(t)=\frac{1}{C}\int i(t)dt$$

When elements have their own signs,if the current flow is opposite to it the whole power is on the contrary.

Circuit topology

Series connection

$$R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}+R_{5}$$ $$L_{eq}=L_{1}+L_{2}+L_{3}$$ $$E_{eq}=E_{1}+E_{2}+E_{3}-E_{4}+E_{5}$$ $$g_{eq1}=g_{2}+g_{3}\qquad g_{eq2}=g_{eq1}+g_{1}$$ $$R_{eq1}=\frac{R_{2}R_{3}}{R_{2}+R_{3}}\qquad R_{eq2}=\frac{R_{1}R_{eq1}}{R_{1}+R_{eq1}}$$ $$\frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}$$ $$J_{eq}=J_{1}+J_{2}-J_{3}$$

Node & Junction

A node is a point at which two or more components or devices are connected together. The node can be called a junction point in the case of connecting of three or more wires.

Branch & Loop

A branch is a part of a circuit containing one element or several elements connected in series.Actually a element with two terminals can be seen as a branch. A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more than once.

Star and delta connections

$$\left\{ \begin{aligned} & R_a&= & \frac{R_{ab}R_{ac}}{R_{ab}+R_{ac}+R_{bc}}&\\ & R_b&= & \frac{R_{ba}R_{bc}}{R_{ab}+R_{ac}+R_{bc}}&\\ & R_c&= & \frac{R_{cb}R_{ca}}{R_{ab}+R_{ac}+R_{bc}}&\\ \end{aligned} \right. \Leftrightarrow \left\{ \begin{aligned} & R_{ab}&= & \frac{R_aR_b+R_aR_c+R_bR_c}{R_c}&\\ & R_{ac}&= & \frac{R_aR_b+R_aR_c+R_bR_c}{R_b}&\\ & R_{bc}&= & \frac{R_aR_b+R_aR_c+R_bR_c}{R_a}&\\ \end{aligned} \right.$$


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