1. Electrical Engineering and Industrial Electronics
Teacher：WANG YuPeng

2. Chapter 2 Introduction to Fundamentals of Electric Circuits
Main Contents：
♦ Charge, Current, and Kirchhoff’s Current Law
♦ Voltage and Kirchhoff’s Voltage Law
♦ Ideal Voltage and Current Sources
♦ Electric Power and Passive Sign Convention

3. The Aim Of This Chapter？

4. This chapter presents the fundamental laws of circuit analysis and serves as the foundation for the study of electrical circuits.

5. • Application of Kirchhoff’s and Ohm’s laws to elementary resistive
circuits.
• Power computation for a circuit element.
• Use of the passive sign convention in determining voltage and current
directions.
• Solution of simple voltage and current divider circuits.
• Assigning node voltages and mesh currents in an electrical circuit.
• Writing the circuit equations for a linear resistive circuit by applying
Kirchhoff’s voltage law and Kirchhoff’s current law.

6. 2.1 CHARGE, CURRENT, AND KIRCHHOFF’S CURRENT LAW
The fundamental electric quantity is charge, and the smallest amount of charge that exists is the charge carried by an electron, equal to
(2.1)

7. The other charge-carrying particle in an atom, the proton, is assigned a positive sign, and the same magnitude. The charge of a proton is
(2.2)
Charles Coulomb (1736–1806). Photo courtesy of French Embassy, Washington,D.C.

8. Electric current is defined as the time rate of change of charge passing through a predetermined area. Typically, this area is the cross-sectional area of a metal wire.
(2.3)

9. If we consider the effect of the enormous number of elementary charges actually flowing, we can write this relationship in differential form:
(2.4)
The units of current are called amperes (A), where 1 ampere=1 coulomb/second

10. EXAMPLE 2.1 Charge and Current in a Conductor
Problem
Find the total charge in a cylindrical conductor (solid wire) and compute the current flowing in the wire.
Solution
Known Quantities: Conductor geometry, charge density, charge carrier velocity.
Find: Total charge of carriers, Q; current in the wire, I .
Schematics, Diagrams, Circuits, and Given Data:
Conductor length: L = 1 m.
Conductor diameter:
Charge density:
Charge of one electron:
Charge carrier velocity:
Assumptions: None.

11. Analysis: To compute the total charge in the conductor, we first determine the volume of the conductor:
Volume = Length × Cross-sectional area
Next, we compute the number of carriers (electrons) in the conductor and the total charge:
Number of carriers = Volume × Carrier density

12. Charge = number of carriers × charge/carrier
To compute the current, we consider the velocity of the charge carriers, and the charge density per unit length of the conductor :
Current = Carrier charge density per unit length × Carrier velocity

13. Kirchhoff’s current law (KCL):
Kirchhoff’s current law states that because charge cannot be created but must be conserved, the sum of the currents at a node must equal zero (in an electrical circuit, a node is the junction of two or more conductors). Formally:
i = Current flowing
in closed circuit
Kirchhoff’s current law (KCL):
(2.5)
Figure 2.2 A simple electrical circuit

14. In applying KCL, one usually defines currents entering a node as being negative and currents exiting the node as being positive. Thus, the resulting expression for node 1 of the circuit of Figure 2.3 is:
Figure 2.3 Illustration of Kirchhoff’s current law

15. EXAMPLE 2.2 Kirchhoff’s Current Law Applied to an Automotive Electrical Harness
Problem
The following figure shows an automotive battery connected to a variety of circuits in an automobile. The circuits include headlights, taillights, starter motor, fan, power locks, and dashboard panel. The battery must supply enough current to independently satisfy the requirements of each of the “load” circuits.

16. Automotive wiring harness

17. Figure 2.4 (b) equivalent electrical circuit
Solution
Known Quantities: Components of electrical harness: headlights, taillights, starter motor, fan, power locks, and dashboard panel.
Find: Expression relating battery current to load currents.
By using KCL, we can obtain

18. 2.2 VOLTAGE AND KIRCHHOFF’S VOLTAGE LAW
The total work per unit charge associated with the motion of charge between two points is called voltage. Voltage is measured in units of volts (a joule per coulomb).
(2.6)

19. Kirchhoff’s voltage law, or KVL:
The directed sum of the electrical potential differences (voltage) around any closed network is zero.
(2.7)
where the vn are the individual voltages around the closed circuit
The principle underlying KVL means that no energy is lost or created in an electric circuit.

20. By KVL, we know
vab = −vba or
v1 = v2
The work generated by the battery is equal to the energy dissipated in the light bulb in order to sustain the current flow and to convert the electric energy to heat and light.
Figure 2.5 Voltages around a circuit

21. Source: Elements that provide energy
Symbolic Representation
Source: Elements that provide energy
Load: Elements that dissipate energy
Figure 2.7 Sources and
loads in an electrical circuit

22. EXAMPLE 2.3 Kirchhoff’s Voltage Law—Electric Vehicle Battery Pack
Problem
Figure (a) depicts the battery pack in the Smokin’ Buckeye electric race car. In this example we apply KVL to the series connection of V batteries that make up the battery supply for the electric vehicle.

23. The application of KVL to the equivalent circuit, we get
Thus, the electric drive is nominally supplied by a 31 × 12 = 372-V battery pack. In reality, the voltage supplied by lead-acid batteries varies depending on the state of charge of the battery.
Figure 2.8 Electric vehicle battery pack: illustration of KVL

24. 2.3 IDEAL VOLTAGE AND CURRENT SOURCES
Ideal Sources
Intuitively, an ideal source is a source that can provide an arbitrary amount of energy.
Ideal sources are divided into two types: voltage sources and current sources.
Ideal Voltage Sources
An ideal voltage source is an electrical device that will generate a prescribed voltage at its terminals.
The ability of an ideal voltage source to generate its output voltage is not affected by the current it must supply to the other circuit elements.

25. ★ The output voltage of an ideal source can be a function of time.
★ By convention the direction of positive current flow out of a voltage source is out of the positive terminal.
General symbol for ideal voltage source. vs (t) may be constant (DC source).
A special case: DC voltagesource (ideal battery)
A special case: sinusoidal
voltage source, vs(t) = V cos ωt
Figure 2.9 Ideal voltage sources

26. Figure 2.10 Various representations of an electrical system.
Symbolic (circuit) Representation
Physical representation
Figure 2.10 Various representations of an electrical system.

27. Ideal Current Sources
An ideal current source is a device that can generate a prescribed current independent of the circuit it is connected to.
An ideal current source provides a prescribed current to any circuit connected to it. The voltage generated by the source is determined by the circuit connected to it.
Figure 2.11 Symbol for ideal
current source

28. Dependent (Controlled) Sources
There exists another category of sources, however, whose output (current or voltage) is a function of some other voltage or current in a circuit. These are called dependent (or controlled) sources.

29. Thank you!

30. 2.4 ELECTRIC POWER AND SIGN CONVENTION
The definition of voltage as work per unit charge lends itself very conveniently to the introduction of power. Recall that power is defined as the work done per unit time. Thus, the power, P, either generated or dissipated by a circuit element can be represented by the following relationship:
(2.9)

31. The electrical power generated by an active element, or that dissipated or stored by a passive element, is equal to the product of the voltage across the element and the current flowing through it.
(2.10)

32. Figure 2.13 The passive sign convention
It is important to realize that, just like voltage, power is a signed quantity, and that it is necessary to make a distinction between positive and negative power. This distinction can be understood with reference to Figure 2.13, in which a sourceand a load are shown side by side.
Power dissipated == v (–i) = (–v) i = –vi
Power generated = vi
Power dissipated = vi
Power generated == v (–i) = (–v) i = –vi
Figure 2.13 The passive sign convention

33. To avoid confusion with regard to the sign of power, the electrical engineering community uniformly adopts the passive sign convention, which simply states that the power dissipated by a load is a positive quantity (or, conversely, that the power generated by a source is a positive quantity).
Another way of phrasing the same concept is to state that if current flows from a higher to a lower voltage (+ to −), the power is dissipated and will be a positive quantity.

34. It is important to note also that the actual numerical values of voltages and currents do not matter: once the proper reference directions have been established and the passive sign convention has been applied consistently, the answer will be correct regardless of the reference direction chosen. The following examples illustrate this point.

35. The Passive Sign Convention
1. Choose an arbitrary direction of current flow.
2. Label polarities of all active elements (voltage and current sources).
3. Assign polarities to all passive elements (resistors and other loads); for passive
elements, current always flows into the positive terminal.
4. Compute the power dissipated by each element according to the following rule: If positive
current flows into the positive terminal of an element, then the power dissipated is
positive (i.e., the element absorbs power); if the current leaves the positive terminal of an
element, then the power dissipated is negative (i.e., the element delivers power).

36. Thank you!