# 物理代写|电磁学代写electromagnetism代考|PHYC20014

## 物理代写|电磁学代写electromagnetism代考|Series Combination

Next, we consider an electric circuit in which two capacitors are combined in series, as shown in Fig. 4.6. That is known as a series combination of capacitors. In that combination, the left plate of capacitor 1 connects to one of the terminals of a battery (for example, the positive terminal in Fig. 4.6) and the right plate of capacitor 2 connects to the other terminal (for example, the negative terminal in Fig.4.6). Furthermore, the other two plates, from each capacitor, connect each other via a conducting wire and to nothing else, as shown in Fig. 4.6. Two capacitors connected that way form an isolated conductor that is initially uncharged and must continue to have a net charge zero.

In the following, we will analyze the combination of two capacitors in series. When the two capacitors are initially uncharged and just connect to a battery in the circuit, then the electrons transfer from the left plate of $C_1$ and into the right plate of $C_2$. That is, during the process, a negative charge (electrons) stores on the right plate of $C_2$ and the same amount of negative charge leaves the left plate of $C_2$ as electrons migrating from that plate to the conducting wire leave behind the left plate having an excess positive charge. Therefore, we can say that the negative charge leaving the left plate of $C_2$ transfers via the conducting wire and stores on the right plate of $C_1$. As a result, the right plates, when the equilibrium establishes, accumulate a charge $-Q$, and the left plates a charge $+Q$. That indicates that the charges on capacitors connected as in Fig. $4.6$ are the same.

It can be seen that the $\Delta V$ across the battery terminals is split between two capacitors:
$$\Lambda V=\wedge V_1+\wedge V_2$$
In Eq. (4.21), $\Delta V_1$ and $\Delta V_2$ are the potential across $C_1$ and $C_2$, respectively. In general, the total potential difference across any number of capacitors connected in series is the sum of the potential differences across the individual capacitors. Now, consider an equivalent capacitor, $C_{e q}$, with same effect on the circuit as the series combination of the capacitors. After it is fully charged, the equivalent capacitor must have a charge of $-Q$ on its right plate and a charge of $+Q$ on its left plate. Using the definition of capacitance to the equivalent circuit in Fig.

## 物理代写|电磁学代写electromagnetism代考|Energy Storage in the Electric Field

To transfer an amount of charge from one plate of a capacitor to the other during the process of charging the capacitor, an external work is done against the electric field. That work stores in the capacitor in the form of the potential energy. For that, let $q$ be the charge on the capacitor at some instant during the charging process when the potential difference across the capacitor is $\Delta V=q / C$. At that instant, one of the plates is carrying a charge $+q$ and the other $-q$. To transfer an increment of charge $d q$ from the plate with charge $-q$ (which is at a lower electric potential) to the plate carrying charge $+q$ (which is at a higher electric potential) an elementary work is done against the electric field:
$$d W=\Delta V d q=\frac{q}{C} d q$$
To calculate the total work required to charge the capacitor from $q=0$ to final charge $Q$, we integrate Eq. (4.27) as follows:
$$W=\int_0^Q \frac{q}{C} d q=\frac{1}{2} \frac{Q^2}{C}$$

This work done to charge the capacitor stores in the capacitor as an electric potential energy $U$. Therefore, $U=W$. Also, we can express the potential energy $U$ in the following forms:
\begin{aligned} U &=\frac{1}{2} \frac{Q^2}{C} \ &=\frac{1}{2} Q \Delta V \ &=\frac{1}{2} C(\Delta V)^2 \end{aligned}
Note that all expressions given by Eqs. (4.29)-(4.31) are equivalent; that is, they can all be used to calculate the potential energy stored in a capacitor depending on what is known. We can consider the energy stored in a capacitor as being stored in the electric field created between the plates as the capacitor is charged. This description is reasonable from the viewpoint that the electric field is proportional to the charge $Q$ stored on a capacitor. For a capacitor of two parallel plates, the potential difference is related to the electric field through a simple relationship $\Delta V=E d$.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Series Combination

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: