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電路學(一)

Text Book:

Fundamentals of Electric Circuits, by C. K. Alexander and M. N. O. Sadiku

Chapter 1 Basic ConceptsChapter 2 Basic LawsChapter 3 Methods of AnalysisChapter 4 Circuit TheoremsChapter 5 Operational AmplifiersChapter 6 Capacitors and InductorsChapter 7 First-Order CircuitsChapter 8 Second-Order Circuits

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評分標準

• Homework: 15%–一律用A4紙書寫，並裝訂好。遲交的作業：一周內補交成績以80%

採計，隔周起補交打對折。

‧期中考: 35%‧期末考: 35%‧隨堂小考、出席狀況: 15% • 教材密碼:• E-mail: ycchiang1970@nchu.edu.tw‧個人網頁: http://web.ee.nchu.edu.tw/~ycchiang1970 (或由系

網頁的連結), http://web.nchu.edu.tw/~ycchiang/‧實驗室網頁: http://web.ee.nchu.edu.tw/~rfem

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Introduction

• Electric Circuit– An interconnection of electrical elements.

Connecting wires

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Introduction

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Introduction

‧相關課程

物理學

電磁學

工程數學電路學

微電子學

電機機械

微波通訊

…

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Systems of Units

• International System of Unit (SI)– The General Conference on Weights and Measures (1960).

cdcandelaLuminous intensityKkelvinThermodynamic temperatureAampereElectric currentssecondTime

kgkilogramMassmmeterLength

SymbolBasic unitQuantity

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Systems of Units1815

12

9

6

3

2

1

1

2

3

Multiplier1 000 000 000 000 000 000 10

1 000 000 000 000 000 101 000 000 000 000 10

1 000 000 000 101 000 000 10

1 000 10100 10

10 100.1 10

0.01 100.001 10

0.000 001 1

6

9

12

15

18

Prefixexapetateragigamegakilohecto

dekadecicentimilli

0 micro0.000 000 001 10 nano

0.000 000 000 001 10 pico0.000 000 000 000 001 10 femto

0.000 000 000 000 000 001 10 atto

SymbolEPTGMkh

dadcm

npfa

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Charge and Current

• Charge– An electrical property of the atomic particles of which

matter consists, measured in coulombs (C).• Electronic Charge

• Coulomb– Unit for charges, 1 C charges:

• Low of conservation of charge– Charge can neither be created nor destroyed.

191.60 217733 10 (C)e

19 181 (1.60217733 10 ) 6.24 10 electrons

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Charge and Current

• Electric Current– The time rate of change of charge, measured in amperes (A).

(1.1)dqidt

1 ampere=1 coulomb / 1 second

0

(1.2)t

tQ i dt

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Charge and Current

• Direct Current (dc)– A current that remains constant with time.

• Alternating Current (ac)– A current that varies sinusoidally with time.

I i

t

t

0

0

Direct current (dc) Alternating current (ac)

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Charge and Current

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Example 1.1

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Practice Problem 1.1

• Calculate the amount of charge represented by four million protons.

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Example 1.2

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Practice Problem 1.2

• If in Example 1.2, q = (10 – 10e–2t ) mC, find the current at t = 0.5 s.

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Example 1.3

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Practice Problem 1.3

• The current flowing through an element is

Calculate the charge entering the element from t = 0 to t = 2s.

2

2 A, 0 12 A, 1

ti

t t

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Voltage

• Voltage (or Potential difference, emf)– The energy required to move a unit charge through an

element, measured in volts (V).

(1.3)abdwvdq

1 volt = 1 joule / 1 coulomb = 1 newton-meter / 1 coulomb

vab = –vba

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Voltage

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Power and Energy

•• Power

– The time rate of expending or absorbing energy, measured in watts (W).

(1.5)dwpdt

(1.6)dw dw dqp vidt dq dt

(1.7)p vi

instantaneous power

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Power and Energy

• Passive sign convention– Current enter the positive polarity of the voltage.

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Power and Energy

• Passive sign convention

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Power and Energy

• Law of conservation of power

• Energy– The capacity to do work, measured in joules (J).

– The electric power utility companies measure energy in watt-hours (Wh):

0 (1.8)p

0 0

(1.9)t t

t tw p dt vi dt

1 Wh = 3600 J

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Example 1.4

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Practice Problem 1.4

• To move charge q from point a to point b requires –30 J. Find the voltage drop vab if: (a) q = 2C, (b) q = – 6C.

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Example 1.5

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Example 1.5 (cont.)

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Practice Problem 1.5

• Find the power delivered to the element in Example 1.5 at t = 5 ms if the current remains the same but the voltage is:(a) v = 2i V,(b) 010 5 V.tv idt

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Example 1.6

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Practice Problem 1.6

• A stove element draws 15A when connected to a 240-V line. How long does it take to consume 60 kJ?

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Circuit Elements

• 2 types of elements: Passive and Active • Active elements: Voltage sources, current sources, …• 2 kinds of sources: Independent and Dependent sources

• Ideal independent source– An active element that provides a specified voltage or

current that is completely independent of other circuit elements.

• Ideal dependent (or controlled) source– An active element in which the source quantity is

controlled by another voltage or current.

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Circuit Elements

• Independent sources

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Circuit Elements

• Dependent sources

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Circuit Elements

• 4 possible types of dependent sources– A voltage-controlled voltage source (VCVS)– A current-controlled voltage source (CCVS) – A voltage-controlled current source (VCCS)– A current-controlled current source (CCCS)

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Circuit Elements

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Example 1.7

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Example 1.7 (cont.)

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Example 1.7 (cont.)

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Practice Problem 1.7

• Compute the power absorbed or supplied by each component of the circuit in Fig. 1.16.

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Applications

• TV Picture Tube

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Example 1.8

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Example 1.8 (cont.)

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Practice Problem 1.8

• If an electron beam in a TV picture tube carries 1013 electrons/ second and is passing through plates maintained at a potential difference of 30 kV, calculate the power in the beam.

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Applications

• Electricity Bills

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Example 1.9

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Example 1.9 (cont.)

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Practice Problem 1.9

• Referring to the residential rate schedule in Example 1.9, calculate the average cost per kWh if only 400 kWh are consumed in July when the family is on vacation most of the time.

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Problem Solving

1. Carefully Define the problem.2. Present everything you know about the problem.3. Establish a set of Alternative solutions and determine the one

that promises the greatest likelihood of success.4. Attempt a problem solution.5. Evaluate the solution and check for accuracy.6. Has the problem been solved Satisfactorily? If so, present the

solution; if not, then return to step 3 and continue through theprocess again.

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Example 1.10

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Example 1.10 (cont.)

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Example 1.10 (cont.)

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Example 1.10 (cont.)

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Example 1.10 (cont.)