You've successfully subscribed to ムえのBLOG
Welcome back! You've successfully signed in.

Electric Circuits Lecture 1 Circuit Terminology & Kirchhoff's Law

Circuit Terminology

Charge

$$q= n * q_{e} \space where\space n \space is an \space integer$$

$$q_{e} = -1.602*10^{-19} C(coulomb)$$

Current

$$i \triangleq \frac{Net , charge , crossing , surface , in , time \space \Delta t }{\Delta t} = \frac{dq}{dt} A(Ampere)$$

Voltage (Potential)

$$V_{AB} \triangleq \frac{Energy , gained , by the ,charge , in , moving , from , A , to , B}{Quantity , of , the , charge}=\frac{d \epsilon }{dq},V,(Volt)$$

A◉----->B◉

1. 只受到电场力作用e
2. 电压是一个相对的量
1. reference of a point is the ground or a point at infinitive
3. path of motion wires/circuit components
4. $-V_{AB}-$ is independent of path

Power

$$P \triangleq \frac{Transfer, of, energy, in, time ,\Delta t}{\Delta t} = \frac{d \epsilon}{dt}, W , (Walt)$$

$$P = \frac{d\epsilon}{dt} = \frac{d \epsilon}{dq} \times \frac{dq}{dt} = i * V_{AB}$$

sign convention

Reference direction

current: arrows→

in our course , we will follow the "passive sign convention"(一直参考方向/关联参考方向)

current flows into the passive polarity of the voltage

$$P = V·i \begin{cases} p>0, power, absorbed\ p<0, power, extracted \end{cases}$$

Ideal basic circuit elements

Ideal elements
ideal Voltage source/理想电压源 Active elements ->capable of generating electric energy
ideal Current source
ideal resister Passive elements ->incapable of generating electric energy
ideal inductor
ideal capacitor
ideal operational amplifier(运算放大器) Active element

Kirchhoff's Law 基尔霍夫定律

definitions

terms explains
Node A point where two or more circuit elements are connected
Branch A path that connects two nodes
Loop Any closed path in a circuit

Kirchhoff's Current Law/KCL

The algebraic sum of all the currents flowing into or out of any node in a circuit equals to Zero

Proof

from Law of conservation of electric charge (电荷守恒公理)，

$$\sum^{n}{j=1} q{j}= 0 \ \Rightarrow\sum^{n}{j=1}\frac{dq{j}}{dt}=0 \ \Rightarrow\sum^{n}{j=1}i{j}=0$$

1. reference direction not actual direction of currents
2. in series (串联)$-i_{1}=i_{2}-$ -█i1█-->-█i2█--
3. any node -> any closed surface

Kirchhoff's Voltage Law/KVL

The algebraic sum of all the voltage (voltage drop or rise) around any loop in a circuit equals to Zero

Proof

from Law of conservation of energy charge (能量守恒公理)，

$$energy, supplied = energy , consumed$$

1. reference direction not actual direction of currents

2. in parallel $-v_{1}=v_{2}-$