Chapter 1 Introduction Electrical Engineering and Electronics II Scott

Main Contents 1.Recognize interrelationships of electrical engineering with other fields of science and engineering. 2. List the major subfields of electrical engineering. 3. List several important reasons for studying electrical engineering.

4. Define current, voltage, and power, including their units. 5. Calculate power and energy, as well as determine whether energy is supplied or absorbed by a circuit element. 6. State and apply basic circuit laws. 7. Solve for currents, voltages, and powers in simple circuits. Main Contents

Electrical systems have two main objectives: To gather, store, process, transport, and present information To distribute and convert energy between various forms 1.1 Overview of Electrical Engineering

Electrical Engineering Subdivisions Communication systems Computer systems Control systems Electromagnetics Electronics Photonics Power systems Signal processing

Why Study Electrical Engineering? To pass the Fundamentals of Engineering (FE) Examination So you can lead projects in your own field To be able to operate and maintain electrical systems To communicate with electrical engineering consultants

1.2 Circuits, Currents and Voltages

Electrical Circuit

i u uLuL L uRuR uCuC R C R0R0 E U R a b c d I V CC RBRB RCRC ICIC + _ U CE + _ V CC + _ U BE IBIB 国标符号

Electrical Current Electrical current is the time rate of flow of electrical charge through a conductor or circuit element. The units are amperes (A), which are equivalent to coulombs per second (C/s).

Reference Directions

Double-Subscript Notation for Currents

Direct Current Alternating Current When a current is constant with time, we say that we have direct current, abbreviated as DC. On the other hand, a current that varies with time, reversing direction periodically, is called alternating current, abbreviated as AC.

. Sinusoidal current

三角波方波

Actual direction ： 电流的实际方向为正电荷的运动方向。 Electrical Current

2 Example 1.1 Determining Current Given Charge

Voltages The voltage associated with a circuit element is the energy transferred per unit of charge that flows through the element. The units of voltage are volts (V), which are equivalent to joules per coulomb (J/C).

Voltages

Voltages’ Directions

1.3 POWER AND ENERGY Unit: Watt Unit: Watt Unit: Joule Unit: Joule

Power

Passive Reference Configuration I U a b ＋－ The current reference enters the positive polarity of the voltage.

Passive reference direction: Non passive reference direction: Function of Element 电源与负载的判别方法 i + - u b p a i + - u b p a

Calculate the power for each element. If it is a battery, is it being charged or discharged? Absorbing energy, being charged Supplying energy, being discharged

如图电路，各元件上电压、电流参考方向采用关 联参考方向。确定各元件的功率，指出哪些是电源、 哪些是负载？ 12 U5U5 345 U1U1 U2U2 U3U3 U4U4 Example Solution ： box 1 Load: Absorb Box 2 Load: Absorb

12 U5U5 345 U1U1 U2U2 U3U3 U4U4 Box3 source Box4 load Box5 source 注 意： 功率平衡！电路中所有元件的功率之和为 0 ！ 常用作对分析结果的检验准则。

E1E1 E2E2 R2R2 R1R1 R3R3 I1I1 I2I2 I3I3 c a b d N=2 L=3 B=3 支路 ——branch 节点 ——node 回路 ——loop Concepts

2Ω2Ω 4Ω4Ω 6Ω6Ω 3Ω3Ω 10V a b I N=3,B=5,L=6 Congsidering current I ， N=4,B=6,L=6 2Ω2Ω 4Ω4Ω 6Ω6Ω 3Ω3Ω 10V a Otherwise ，

1.4 KIRCHHOFF’S CURRENT LAW (KCL) The net( 网络，总的 ) current entering a node is zero. Alternatively, the sum of the currents entering a node equals the sum of the currents leaving a node.

I 1 + I 2 -I 3 =0 或 -I 1 - I 2 +I 3 =0 也可写成： I 1 + I 2 = I 3 （入） （出） U1U1 U2U2 R2R2 R1R1 R3R3 I1I1 I2I2 I3I3 c a b d

推广到广义节点上使用，任一闭合面 IAIA IBIB ICIC I AB I BC I CA A B C I C = I CA - I BC Add all three equations ： I A = I AB - I CA I B = I BC - I AB I A +I B +I C =0 【 Prove 】 I A +I B +I C =0 or ∑I=0

I 6V12V 5Ω5Ω 1Ω1Ω1Ω1Ω 5Ω5Ω 2Ω2Ω b a N 、 B 、 L= ？ I 、 U ab = ？ N=2,B=3,L=2 I=0,U ab =0

图示电路中，已知 I 1 =11mA ， I 4 =12mA ， I 5 =6mA 。 求 I 2 ， I 3 和 I 6 。 I1I1 R1R1 R2R2 R3R3 I2I2 I3I3 I4I4 I5I5 I6I6 Example solution ： I 3 =I 1 － I 5 =11 － 6=5 （ mA) I 2 =I 3 － I 4 =5 － 12= － 7 （ mA) I 6 =I 1 － I 2 =11 － ( － 7)=18 （ mA) I 6 =I 4 +I 5 =12+6=18 （ mA)

Series Circuits i a =i b =i c The current is identical. Series: Elements are connected end to end, no other element can be connected to their common node.

Use KCL to determine the values of the unknown currents shown in Fig Answer: i a =4A i b =-2A i c =-8A

Identify the groups of the circuit elements that are connected in series shown in Fig Answer: A 、 B ； E 、 F 、 G

1.5 KIRCHHOFF’S VOLTAGE LAW(KVL) The algebraic sum of the voltages equals zero for any closed path (loop) in an electrical circuit.

电路如图所示，已知 U AB =5V ， U BC = － 4V ， U DA = － 3V 。试求：（ 1 ） U CD ；（ 2 ） U CA U AB U DA U CD U BC A B C D + - U CA 解： （ 2 ） ABCA is not a closed loop （1）（1） U AB +U BC +U CD +U DA =0 5+ （－ 4 ） +U CD + （－ 3 ） =0 U CD =2V U AB +U BC +U CA =0 U CA = －（ U AB +U BC ）＝－ 1V Example

Parallel Circuits Two components are in parallel if both ends of one element are directly connected to the corresponding ends of the other element.

v a =v b =-v c The voltage is identical. Parallel Circuits

Use repeated application of KVL to find the values of v C 、 v e for the circuit of Fig Answer: v C =8V; v e =-2V

1.6 Introduction to Circuit Elements Conductors 导线 Voltage source 电压源 Current source 电流源 Resistors 电阻器

Conductors An unbroken line Open circuit Short circuit

Independent Voltage Source Maintains a specified voltage across its terminal, regardless of other currents or voltages of any other elements. Circle enclosing reference polarity

Voltage Sources in Series Substitute several series voltage sources for one equivalent voltage source U S1 U S2 USUS + - USUS U S1 U S2 USUS + - USUS + - Named as equivalent conversion

Ideal Circuit Elements versus Reality

Dependent/Controlled Voltage Source 2, unitless 3, unit of ohm

Independent Current Source Maintains a specified current flowing through itself, regardless of other currents or voltages of any other elements. Circle enclosing an arrow

Current Sources in Parallel Substitute several parallel current sources for a equivalent current source. IS1IS1 IS2IS2 USUS ISIS USUS IS1IS1 IS2IS2 USUS ISIS USUS

Dependent/Controlled Current Source 2, unitless3, unit of Siemens

The Summary of Dependent Sources Voltage-controlled voltage sources—VCVS Current-controlled voltage sources—CCVS Voltage-controlled current sources—VCCS Current-controlled current sources—CCCS

The voltage v across an ideal/linear resistor is proportional to the current i through the resistor. The constant of proportionality is the resistance R. R——resistance value ρ——resistivity L——length of conductor A——cross sectional area Resistors

It shows the proportional relationship between current and voltage. 0 i v Ohm’s Law Passive reference configuration

Conductance

Power of Resistor Absorbing power ： DC Power ： As a DC circuit, we use capital letters.

1.7 Introduction to Circuits

Circuit Analysis Using Arbitrary Reference v1v1 v2v2 i R =2A v 2 =5i R =10V v 1 =v 2 +10=20V 电流源功率 : P i =-2v 1 =-40W Source 电压源功率 : P v =10i R =20W Load 电阻功率 : P R =5i 2 R =20W Load P1.48 Find the current i R, the power for each element in the circuit. Which one is supplying power? Page 43

P1.50 Use KVL, KCL, and Ohm’s Law to find Vx. Page 43 Answer: Vx=17.5V

Using KVL, KCL, and Ohm’s Law to Solve a Circuit Example 1.7 Solve for the source voltage Vs in the circuit. Solution:

Homework

Page 32 Practical application 1.1 Using resistance to measure strain Finding other practical application of resistance in industry and daily life Teamwork 1