Electric Circuits
Preface
The post is the note based on the textbook Fundamentals of Electric Circuits written Charles K. Alexander and Matthew N. O. Sadiku (ISBN: 978-1-260-57079-3)
Some particular symbols are introduced to describe some properties, as listed below.
Symbol Table
| Symbol | Meaning |
|---|---|
| 🎒 | Already learned in middle school |
| ⚠ | Key point of some contents |
The post is done individually by Ryker Zhu from Nanjing
University of Information Science and Technology, published under
the license CC
BY-NC-SA.
DC Circuits
Basic Concepts
Charge & Current
Electric Charge: an electrical property of the atomic particles of which matter consists, measured in coulombs (\(C\)).
- The charge \(e\) on an electron is negative and equal in magnitude to \(1.602\times 10^{−19}C\), while a proton carries a positive charge of the same magnitude as the electron.
- The only charges that occur in nature are integral multiples of the electronic charge \(e=1.602\times 10^{−19}C\)
- Law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus, the algebraic sum of the electric charges in a system does not change.
Electric current: the time rate of change of charge, measured in amperes (\(A\)). The relationship between current \(i\), charge \(q\), and time \(t\) is: \[i\triangleq\frac{dq}{dt}\] The charge transferred between time \(t_0\) and \(t\) is obtained by integrating both sides: \[Q\triangleq\int^t_{t_0}i\,dt\]
Classification:
- Direct Current: a current that flows only in one direction and can be constant or time varying. (e.g. \(i\left(t\right)=\left|5\sin\left(377t\right)\right|\) whereas \(i\left(t\right)\) keeps positive all the time)
- Alternating Current: a current that changes direction with respect to time. (e.g. \(i\left(t\right)=5\sin\left(377t\right)\))
Convention:
- \(I\) - Constant current
- \(i\) - Current varies with respect to time
Voltage
Voltage (or potential difference): the energy required to move a unit charge from a reference point (\(−\)) to another point (\(+\)), measured in volts (\(V\)).
Power is the time rate of expending or absorbing energy, measured in watts (\(W\)). \[p\triangleq\frac{dw}{dt}\]