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# 电子代写|电路基础代写Circuit Fundamentals代考|CPE1140 Kirchhoff’s Laws

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## 电子代写|电路基础代写Circuit Fundamentals代考|Kirchhoff’s Laws

Ohm’s law by itself is not sufficient to analyze circuits. However, when it is coupled with Kirchhoff’s two laws, we have a sufficient, powerful set of tools for analyzing a large variety of electric circuits. Kirchhoff’s laws were first introduced in 1847 by the German physicist Gustav Robert Kirchhoff (1824-1887). These laws are formally known as Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL).

Kirchhoff’s first law is based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change.
Kirchhoff’s current law ( $\mathrm{KCL})$ states that the algebraic sum of currents entering a node (or a closed boundary) is zero.
Mathematically, KCL implies that
$$\sum_{n=1}^N i_n=0$$
where $N$ is the number of branches connected to the node and $i_n$ is the $n$th current entering (or leaving) the node. By this law, currents entering a node may be regarded as positive, while currents leaving the node may be taken as negative or vice versa.

## 电子代写|电路基础代写Circuit Fundamentals代考|Historical

Gustav Robert Kirchhoff (1824-1887), a German physicist, stated two basic laws in 1847 concerning the relationship between the currents and voltages in an electrical network. Kirchhoff’s laws, along with Ohm’s law, form the basis of circuit theory.

Born the son of a lawyer in Konigsberg, East Prussia, Kirchhoff entered the University of Konigsberg at age 18 and later became a lecturer in Berlin. His collaborative work in spectroscopy with German chemist Robert Bunsen led to the discovery of cesium in 1860 and rubidium in 1861. Kirchhoff was also credited with the Kirchhoff law of radiation. Thus, Kirchhoff is famous among engineers, chemists, and physicists.

To prove KCL, assume a set of currents $i_k(t), k=1,2, \ldots$, flow into a node. The algebraic sum of currents at the node is
$$i_T(t)=i_1(t)+i_2(t)+i_3(t)+\cdots$$
Integrating both sides of Eq. (2.14) gives
$$q_T(t)=q_1(t)+q_2(t)+q_3(t)+\cdots$$
where $q_k(t)=\int i_k(t) d t$ and $q_T(t)=\int i_T(t) d t$. But the law of conservation of electric charge requires that the algebraic sum of electric charges at the node must not change; that is, the node stores no net charge. Thus, $q_T(t)=0 \rightarrow i_T(t)=0$, confirming the validity of KCL.
Consider the node in Fig. 2.16. Applying $\mathrm{KCL}$ gives
$$i_1+\left(-i_2\right)+i_3+i_4+\left(-i_5\right)=0$$

## 电子代写|电路基础代写电路基本原理代考|基尔霍夫定律

$$\sum_{n=1}^N i_n=0$$
，其中$N$是连接到节点的分支的数量，$i_n$是进入(或离开)节点的第$n$次电流。根据这个定律，进入一个节点的电流可以被认为是正的，而离开该节点的电流可以被认为是负的，反之亦然

## 电子代写|电路基础代写Circuit Fundamentals代考|Historical

.

$$i_T(t)=i_1(t)+i_2(t)+i_3(t)+\cdots$$

$$q_T(t)=q_1(t)+q_2(t)+q_3(t)+\cdots$$

$$i_1+\left(-i_2\right)+i_3+i_4+\left(-i_5\right)=0$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。