Electric Circuit Theory

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Electric Circuit Theory

Nam Ki Min

010-9419-2320

nkmin@korea.ac.kr

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Circuit Variables

Chapter 1 Nam Ki Min

010-9419-2320

nkmin@korea.ac.kr

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 Electrical Engineering

1.1 Electrical Engineering

Network theory

Electrical engineering disciplines Circuit analysis

Electromagnetics Solid-state electronics Electric machines Electric power systems Digital logic circuits Computer systems

Communication systems Electro-optics

Instrumentation systems Control systems

Signal processing system

 Electrical engineering is concerned with the generation, transmission and utilization of

electrical energy(signal) and with the transmitting and processing of information.

 Electrical engineers are involved in the analysis, design and production of electric power, radio, radar, television, computing, telecommunication, control and information systems.

 The typical curriculum of an undergraduate electrical engineering student includes the subjects listed in Table.

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1.1 Electrical Engineering 4

 Five Major Classifications of Electrical Systems

• Communication system

• Computer system

• Control system

• Power system

• Signal processing systems

Power system

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1.1 Electrical Engineering 5

Electrical engineering systems in the automobile

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 Electric Circuits

 The Size Scale of Circuits

Centimeters

Microns Meters Kilometers

 An electric circuit is an interconnection of electrical elements.

• A simple electric circuit is shown in Figure.

It consists of three basic components: a battery, a lamp, and connecting wires.

 Electric circuits are used in numerous electrical systems to accomplish different tasks.

• An electric circuit is an mathematical model that approximates the behavior of an actual electrical system.

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 Electric circuit theory is the most important course for the Electrical Engineering Student.

 Electric circuit theory and electromagnetic theory are the two fundamental theories.

 All the other subjects(branches) in your electrical engineering rely on the concepts of these theories.

Therefore, the basic electric circuit theory course is the most important course for an electrical engineering student, and always an excellent starting point for a beginning student in electrical engineering education.

 CIE 201 is … boring, but absolutely essential !!!

CIEN 201,202

CIEN 309,310 Instrumentation

CIEN 311, 312 Electronic Circuits

CIEN 231,232 Electromagnetics

CIEN 301 Control Eng.

CIEN 304 Electronic Circuits

Lab

CIEN 223, 224 Instrumentation

Lab

CIEN 207

Physical electronics

CIEN

Control Eng.

Lab

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 The SI units are based on seven defined quantities:

1.2 The International System of Units(SI)

• Length

• Mass

• Time

• Electric current

• Thermodynamic temperature

• Amount of substance

• Luminous intensity

 Derived Units

𝐹𝑜𝑟𝑐𝑒 ∶ 𝐹 = 𝑚𝑎 kg m s²

Basic or

fundamental units

 The SI derived units are obtained from some physical law defining that unit and the seven SI base units.

𝐴𝑟𝑒𝑎 ∶ 𝐴 = 𝑎 × 𝑏 m²

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 Prefixes

1.2 The International System of Units(SI)

 In many cases, the SI unit is either too small or too large to use conveniently.

 Standard prefixes corresponding to powers of 10 are then applied to the basic unit.

yocto y 10^-24 zepto z 10^-21

peta P 10¹⁵

exa E 10¹⁸

zetta Z 10²¹

yotta Y 10²⁴

 It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol.

Because multiple prefixes may not be used, in the case of the kilogram the prefix names of Table 1.3 are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g."

 With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.

 Example: 10^-6 kg = 1 mg (one milligram), but not 10^-6 kg = 1 µ kg (one microkilogram)

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1.3 Circuit Analysis: An Overview 10

 A circuit is said to be solved when the voltage across and the current in every element have been determined.

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1.4 Voltage and Current 11

 Electric Charge

• The charge is bipolar.

- Positive change: proton, +ion, hole - Negative charge: electron, -ion

• Electrons and protons are often referred to as elementary charge:

C(Coulomb)

The fundamental electric quantity

𝑒 = 1.6022 × 10

⁻¹⁹

ion - +

ion atom

electron loss electron

gain

• Charge is an electrical property of the atomic particles of which matter consists. Each atom consists of electrons, protons, and neutrons.

• The nucleus is positively charged and has the protons and neutrons.

• Electrons are negatively charged and in discrete shells.

• The presence of equal numbers of protons and electrons leaves an atom neutrally charged.

• The concept of electric charge is the underlying principle for explaining all electrical phenomena.

The following points should be noted about electric charge:

• The 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.

Charge quantization: the electric charge exists in discrete quantities, which are integral multiples of the elementary charge.

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 Electric Charge

 Electrical effects are attributed to both the separation of charge and charges in motion.

+q +q

+q -q

Like charges repel

Unlike charges repel

The separation of change creates an electric force(voltage).

+q

𝑣

The motion of charge creates an electric current.

• Electric force(voltage)

• Electric current

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 Definition of Voltage

 Voltage is electric potential energy per unit charge, measured in joules per coulomb (= volts).

 Voltage (or potential difference) is the energy required to move a unit charge(one coulomb of charge) from one point to the other.

 Mathematically,

Potential energy:

• Energy which results from position or configuration.

• An object may have the capacity for doing work as a result of its position in a gravitational field (gravitational potential energy), an electric field (electric potential energy), or a magnetic field (magnetic potential energy).

• It may have elastic potential energy as a result of a stretched spring or other elastic deformation.

catapult

+Q

+𝒅𝒒 𝒅𝑾

𝑣 = 𝑑𝑊

𝑑𝑞 V 1 J

1 C = 1 Volt = 1 V

 Voltage is responsible for establishing current.

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 Definition of Current

 Electric current is the amount of charge that flows past a point in a unit of time (t), measured in amperes (A).

 Mathematically,

i

 If current I = 1 A in a wire, then 1 coulomb of charge flows past any point every second.

𝑖 = 𝑑𝑞 𝑑𝑡

A

Current flow in an electric conductor

C

s = A

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 Definition of Ideal Basic Circuit Element

 An ideal basic circuit element has three attributes:

1.5 The Ideal Basic Circuit Element

• It has only two terminals, which are points of connection to other circuit components.

• It is described mathematically in terms of current and/or voltage.

• It cannot be subdivided into other elements.

 The word ‘ideal’ imply that a basic circuit element does not exist as a realizable physical component.

 The word ‘basic’ imply that the circuit element cannot be further reduced or subdivided into other elements.

 Thus the basic circuit element s form the building blocks for constructing circuits, but they themselves cannot be modeled with any other type of element.

An ideal circuit element is a mathematical model of an actual electrical component, like a battery or light bulb:

Physical representation Circuit(symbolic) representation

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1.5 The Ideal Basic Circuit Element 16

 Passive Sign Convention

• The assignment of the reference polarity for voltage and the reference direction for current are entirely arbitrary.

• However, once you have assigned the references, you must write all subsequent equations to agree with the chosen references.

• The most widely used sign conventions applied to these references is called passive sign convention.

Whenever the reference direction for the current in an element is in the direction of the reference voltage drop across the element, use a positive sign in any

expression that relates the voltage to the current.

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 Power and energy calculations are important in circuit analysis

 For practical purposes, we need to know how much power an electric device can handle.

We all know from experience that a 100-watt bulb gives more light than a 60-watt bulb.

 Therefore, although current and voltage are the two basic variables in an electric circuit, they are not sufficient by themselves.

1.6 Power and Energy

 We also know that when we pay our bills to the electric utility companies, we are paying for the electric energy consumed over a certain period of time.

 Definition of Energy

 Energy is the capacity(ability) to do work, measured in joules ( J).

• One joule is the work done when a force of one newton is applied through a distance of one meter.

 Mathematically, work can be expressed by the following equation.

𝑤𝑜𝑟𝑘 𝑤 = 𝐹 𝑑 𝑐𝑜𝑠𝜃

To do work(w), forces(F) must cause displacements(d)

The work done on the briefcase by the generator is negative, removing energy from the briefcase

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 Definition of Power

 Power is the time rate of expending or absorbing energy, measured in watts (W).

p:power in watts(W) w:energy in joules(J) t: time in second(s)

 Mathematically,

𝑝 = 𝑑𝑤 𝑑𝑡

J

s = W

 Electrical Energy

 The kilowatt-hour (kWh) is a much larger unit of energy than the joule.

 There are 3.6 x 10⁶ J in a kWh.

 The kWh is convenient for electrical appliances.

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 The electrical power associated with a basic circuit element is simply equal to the product of the voltage across the element and the current flowing through it.

𝑝 = 𝑑𝑤

𝑑𝑡 = 𝑑𝑤

𝑑𝑞 ∙ 𝑑𝑞

𝑑𝑡 = 𝑣𝑖

 Watt’s law

 Passive Sign Convention

 Passive sign convention:

(a),(d) p = +vi or vi > 0:

The current enters through the positive polarity of the voltage(through the positive terminal of an element) It implies that the element is absorbing power or power is being delivered to the circuit inside the box.

(b),(c) p = -vi or vi < 0:

The current enters through the negative polarity of the voltage(through the negative terminal of an element)

It implies that the element is releasing or supplying power or power is being extracted from the circuit inside the box.

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.