雖然我們可以從『馬克士威之方程組』推導出來克希荷夫的『電路定律』。事實上，克希荷夫是將歐姆的成果加以推廣得了『電流』與『電壓』兩個定律。在時間上，它早於『馬克士威之方程組』。那什麼是『電路』的呢？『電路』是由『兩端』two terminals 或『多端』的『元件』component 『連接』成『網路』 network 所構成。多個『元件』的『連接點』，稱之為『節點』，一個『節點』至少連接『兩個以上』的『元件』，祇用於『導電』的『導線』可以看成是理想之『零電阻』的『兩端元件』。一般的『電路』中，每個『元件』的『任一端點』都一定會連接到某一『節點』上，形成完整的『電流』網路。通常連結兩個『節點』的『元件』又叫做電路的『分支』 branch；連結多個『節點』形成的『封閉路徑』被稱作『網目』 mesh。在一個電路中，『元件』的『作用』與『行為』，『假設』可以用這個『元件』的『端點』之『電壓』 
和流入或流出之『電流』 
作完全的描述。
假設進入某個節點的電流符號為正，離開這個節點的電流則為負值，那麼這個節點所有元件之電流的『代數和』等於零。如果以方程式表達，對於電路中的任一節點
此處，
是某個元件 
進入【+】或離開【-】這個節點的電流，它可以是實數或相量。
克希荷夫電流定律 KCL
假使我們從『電荷量』 
的觀點來看，『克希荷夫電流定律』是講 
，也就是說，每一個『節點』上都沒有『電荷』的累積變化。這樣『電容器』滿足『電流定律』的嗎？
克希荷夫電壓定律 KVL
沿著封閉路徑，所有元件分支電壓 ── 兩節點間之電位差 ── 的代數和等於零。如果以方程式表達，對於電路的任一網目
此處，
是這個封閉路徑中的元件編號，
是元件兩端的分支電壓，可以是實數或相量。
如果我們用『電場』 
的概念來表達，『克希荷夫電壓定律』可以寫成
，此處 
是封閉路徑。假使我們從『馬克士威之方程組』中的『法拉第感應定律』來看
，也就是說任一『網目』中的『磁通量』都不隨時間變化。這樣『電感器』滿足『電壓定律』的嗎？
『真實元件』一般用『理想元件』的『電路模型』表達
由於『電壓差』才具有物理意義，所謂的『元件』的『完全的描述』中講的『端點電壓』是相對於『接地』之『參考點』而言的『電壓值』，其實它也是一種『電壓差』。對一個『兩端點』元件來說，用左圖中的『電路一』表示，它的『特性』可以用 
與 
來確定，假使『電路二』的元件，只要 
= ，就可以得到 
，即使這兩個元件的構造不同，它們在電路上的作用是『等效的』。
既然已經有了更好的『電磁學』，為什麼還要『電路學』的呢？因為『電磁學』的『馬克士威之方程組』是一組『偏微分方程式』，先不管說它能不能夠方便『求解』，在許多情況下，人們所關心的『物理量』，並不需要那麼的『詳盡』。舉例來說，一個『點亮燈泡』的簡單電路，為了避免『燈絲燒斷』，我們會關心流過『燈絲』的『總電流』大小是否會超過『額定電流』，但是我們並不在意那個『電流密度』的分佈如何，也不考慮『燈絲』的『溫度』、『形狀』或者『方向』等等，此時如果簡單的把『燈絲』看成一的『電阻』，用『歐姆定律』就得到了所要的『電流』不是更『容易』的嗎？這就是『電路學』在『工程領域』之『重要性』，它簡化了『實務』所不需要的『複雜性』與『精確性』！
─── 有人說︰在 EE 裡，人們用簡易的方法作事情 ───
─── 《【SONIC Π】電聲學導引《八》》
即使能用『廣義相對論』計算足球運動之『測地線』，怕於踢球射門沒啥好處也！
故耳為求簡明扼要談談『機械能』產生器『引擎』
Engine
An engine or motor is a machine designed to convert one form of energy into mechanical energy.[1][2] Heat engines burn a fuel to create heat which is then used to do work. Electric motors convert electrical energy intomechanical motion; pneumatic motors use compressed air; and clockwork motors in wind-up toys use elastic energy. In biological systems, molecular motors, like myosins in muscles, use chemical energy to create forces and eventually motion.
Terminology
The word engine derives from Old French engin, from the Latin ingenium–the root of the word ingenious. Pre-industrial weapons of war, such as catapults, trebuchets and battering rams, were called siege engines, and knowledge of how to construct them was often treated as a military secret. The word gin, as in cotton gin, is short for engine. Most mechanical devices invented during the industrial revolution were described as engines—the steam engine being a notable example. However, the original steam engines, such as those by Thomas Savery, were not mechanical engines but pumps. In this manner, a fire engine in its original form was merely a water pump, with the engine being transported to the fire by horses.
In modern usage, the term engine typically describes devices, like steam engines and internal combustion engines, that burn or otherwise consume fuel to perform mechanical work by exerting a torque or linear force (usually in the form of thrust). Devices converting heat energy into motion are commonly referred to simply as engines.[3] Examples of engines which exert a torque include the familiar automobile gasoline and diesel engines, as well as turboshafts. Examples of engines which produce thrust include turbofans androckets.
When the internal combustion engine was invented, the term motor was initially used to distinguish it from the steam engine—which was in wide use at the time, powering locomotives and other vehicles such as steam rollers. The term motor derives from the Latin verb moto which means to set in motion, or maintain motion. Thus a motor is a device that imparts motion.
Motor and engine later came to be used largely interchangeably in casual discourse. However, technically, the two words have different meanings. An engine is a device that burns or otherwise consumes fuel, changing its chemical composition, whereas a motor is a device driven by electricity, air, or hydraulic pressure, which does not change the chemical composition of its energy source.[4][5] However, rocketry uses the term rocket motor, even though they consume fuel.
A heat engine may also serve as a prime mover—a component that transforms the flow or changes in pressure of a fluid into mechanical energy.[6] An automobile powered by an internal combustion engine may make use of various motors and pumps, but ultimately all such devices derive their power from the engine. Another way of looking at it is that a motor receives power from an external source, and then converts it into mechanical energy, while an engine creates power from pressure (derived directly from the explosive force of combustion or other chemical reaction, or secondarily from the action of some such force on other substances such as air, water, or steam).[7]
之一的電動馬達
Electric motor
An electric motor uses electrical energy to produce mechanical energy, usually through the interaction of magnetic fields and current-carrying conductors. The reverse process, producing electrical energy from mechanical energy, is accomplished by a generator ordynamo. Traction motors used on vehicles often perform both tasks. Electric motors can be run as generators and vice versa, although this is not always practical. Electric motors are ubiquitous, being found in applications as diverse as industrial fans, blowers and pumps, machine tools, household appliances, power tools, and disk drives. They may be powered by direct current (for example a battery powered portable device or motor vehicle), or by alternating current from a central electrical distribution grid. The smallest motors may be found in electric wristwatches. Medium-size motors of highly standardized dimensions and characteristics provide convenient mechanical power for industrial uses. The very largest electric motors are used for propulsion of large ships, and for such purposes as pipeline compressors, with ratings in the thousands of kilowatts. Electric motors may be classified by the source of electric power, by their internal construction, and by their application.
The physical principle of production of mechanical force by the interactions of an electric current and a magnetic field was known as early as 1821. Electric motors of increasing efficiency were constructed throughout the 19th century, but commercial exploitation of electric motors on a large scale required efficient electrical generators and electrical distribution networks.
To reduce the electric energy consumption from motors and their associated carbon footprints, various regulatory authorities in many countries have introduced and implemented legislation to encourage the manufacture and use of higher efficiency electric motors. A well-designed motor can convert over 90% of its input energy into useful power for decades.[23] When the efficiency of a motor is raised by even a few percentage points, the savings, in kilowatt hours (and therefore in cost), are enormous. The electrical energy efficiency of a typical industrial induction motor can be improved by: 1) reducing the electrical losses in the stator windings (e.g., by increasing the cross-sectional area of the conductor, improving the winding technique, and using materials with higher electrical conductivities, such as copper), 2) reducing the electrical losses in the rotor coil or casting (e.g., by using materials with higher electrical conductivities, such as copper), 3) reducing magnetic losses by using better quality magnetic steel, 4) improving the aerodynamicsof motors to reduce mechanical windage losses, 5) improving bearings to reduce friction losses, and 6) minimizing manufacturing tolerances. For further discussion on this subject, see Premium efficiency.)
By convention, electric engine refers to a railroad electric locomotive, rather than an electric motor.
『動力模型』，就直接進入『電路學』吧。