Circuitry Ch01 Basic Concepts

8/2/2019 Circuitry Ch01 Basic Concepts

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Chap 1 Basic Concepts

Introduction

Charge and current

Voltage

Power and energy

Circuit elements

Applications

http://c007.ndhu.edu.tw/~pclab/

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1.1 Introduction

Electrical engineering (including electrical, electronic and

computerengineering) is concerned with systems that produce,

transmit, and measure electric signals (or energy)

Examples of such systems are communication, computer,

control systems,power, and signal-processing systems All branches of electrical engineering have electric circuits in

common

Electric circuit: An interconnection of electrical elements

Electrical elements include electric sources, resistors,

capacitors, semiconductor devices, , and wire connections


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Introduction

The objective of this course is not the study of the applications

of the circuits; the main concern is the analysis of the circuits

Electric circuit theory and electromagnetic theory are the two

fundamental theories of all branches electrical engineering

Circuit theory is a special case of electromagnetic field theory

Circuit theory is applicable if the following assumptions hold

1. Electrical effects happen instantaneously throughout a system

2. The net charge on every component in the system is always zero

3. There is no magnetic coupling between the components in a system

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Introduction

1. Electrical effects happen instantaneously throughout a system

2. The net charge on every component in the system is always zero

3. There is no magnetic coupling between the components in a system

When is assumption 1 valid? Electric signals travel at speed of light (c = 3

108 m/s), assumption

will hold if the physical system is small

System is small (0.1) relative to wavelength () of the electricsignals produced, transmitted or measured, where = c/f

For a power system f= 50Hz, 0.1= 600km

For a communication system f= 109Hz 0.1 = 3cm

Assumption 2 is charge conservation

Including magnetic circuit theory, electric circuit theory isalso helpful for circuit analysis


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A simple and a complicated electric circuits

Electric circuit of a radio receiver

Flash light

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1.2 Systems of Units


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1.3 Charge and Current

The concept ofelectric charge is the basis for describing all

electrical phenomena

Electric charge is an electrical property of the atomic particles

of which matter consists, measured in coulombs (C)

The charge on an electron e is -1.60210-19 C

One Cof charge is collectively carried by 6.241018 electrons

Electric charges exist in discrete quantities

The law of conservation of charge states that charge can

neither be created nor destroyed, only transferred. Thus, thealgebraic sum of the electric charges in a system does not

change

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Electric Current

Electrical effects are attributed to both the

separation of charges and charges in motion

The separation of charge creates an

electric force orvoltage (v)

The motion of charge creates an electric fluid orcurrent(i)

Definition: Electric current is the time rate of change of

charge, measured in amperes and expressed as

where i is current in amperes (A), q is charge

in coulombs (C), tis time in seconds (s)

Current is always assumed as rate of flow ofpositive charge

Also, 1 ampere = 1 coulomb/second

dt

dqi


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Electric Current

The charge transferred between

time t0 and tis obtained by

Although current is made up ofdiscrete moving electrons, we

consider it to be continuous as there are so many of electrons

There are several types of current:

A direct current(dc) is a current that remains constant with time

An alternating current(ac) is a current that varies sinusoidally with

time

t

t0

idtQ

direct current(dc) alternating current(ac)

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Polarity convention (reference direction)

Positive current flow Negative current flow


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Example 1.1

Practice Problem 1.1

Calculate the amount of charge represented by two million protons.

Answer: +3.20410-13 C

How much charge is represented by 4600 electrons?

Sol:

Each electron has -1.60210-19 C

4600 electrons will have -1.60210-19 4600 = -7.36910-16 C

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Example 1.2

mA413110021025i

50t

mAt4t20t45

mC/st4t5dt

d

dt

dqi

.cossin

,.At

)cossin(

)sin(

=+=+=

=+=

==

The total charge entering a terminal is given by q = 5tsin4t mC.Calculate the current at t= 0.5s.

Sol:

Practice problem 1.2

If in example 1.2, q = 10(1 - e-2t) mC, find the current at t= 0.5s.

Answer: 7.36 mA


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Example 1.3

C5.52

11)28(

2

)3(

2

1

23

2

1

22

1

=

=

=

== =

tt

dtttidtQt

Determine the total charge entering a terminal between t= 1s and t= 2s, if

the current passing the terminal is i = (3t2t)A

Sol:


The current flowing through an element is

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

Answer: 6.6667 C

>


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Voltage

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

A direct voltage (dc) is a voltage that remains constant with

time (as produced by a battery)

An alternating voltage (ac) is a voltage that varies

sinusoidally with time (as produced by a generator)

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Polarity convention (polarity reference)

baab vv =

Voltage drop between a and b is 9V

Note:

Electric current is always through an element

Electric voltage is always across the element between two points

Voltage drop between b and a is -9V


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Power and energy

It is usual to express output of a system in terms ofpoweror

energy when electrical energy is consumed

All practical devices have limitations on the amount of power

they can handle

Definition: Poweris the time rate of expending

or absorbing energy, expressed as:

wherep is power in watts (W), w is energy in

joules (J), and tis time in seconds (s)

Power is associated with the flow of charge:

where v is voltage in volts (V), i is current in amperes (A)

dt

dwp

=

vidt

dq

dq

dw

dt

dwp =

=

= (instantaneous power)

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Reference polarity and reference direction

Assignment of reference polarity forv and reference direction

fori is entirely arbitrary or random

Passive sign convention

When the current enters through the positive (voltage) terminal of an

element p = +vi If current enters through the negative terminal p = - vi

supplying powerabsorbing power


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Power and the passive sign convention

Use a positive (+) sign if current indirection of voltage drop For example,p = vi, ifp>0, power is

being delivered to the circuit inside thebox (e.g. heater)

Use a negative (-) sign if current notin direction of voltage drop For example,p = -vi, ifp


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Example 1.4

V.

C

11520

1032

q

wv

20102tiq

3

=

==

===

An energy source forces a constant current of 2A for 10s to flow through a

lightbulb. If 2.3kJ is given off in the form of light and heat energy,

calculate the voltage drop across the bulb.

Sol:


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

Answer: (a) -15V (b) 5V

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Example 1.5

kW..cos.sin.

W.cos.sin

ms,At

Wcossin

Vsinsin)()(

W..cos)(cos

ms,AtWcos75

,cos)(

396643243216714137

1801804500p

3t

t60t604500vip

t60900t605603dt

di3vb

4853180751036075p

3tt60vip

t6015i3va

232

2

==

=

=

==

===

===

=

==

==

Find the power delivered to an element at t= 3ms if the current entering its

positive terminal is i = 5cos60t A and the voltage is (a) v = 3i and (b) v =3di/dt

Sol:


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Find the power delivered to the element in example 1.5 at t = 5ms if the

current remains the same but the voltage is (a) v = 2i and (b)

Answer: (a) 17.27W (b) 29.7W

Vidt510vt

0)( +=

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Example 1.6

WhhW

assametheisThis

kJ720J720,000

60(s/min)min/h)()h(W)(

2002100ptw

602100ptw

===

==

==

How much energy does a 100W electric bulb consume in two hours?

Sol:


A stove element draws 15A when connected to a 120V line. How long

does it take to consume 30kJ?

Answer: 16.667s


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1.6 Circuit Elements

Ideal basic circuit element

Has only 2 terminals

Is described mathematically in terms ofi and/orv

Cannot be subdivided into other elements

There are 5 ideal basic circuit elements

Voltage sources

Current sources

Resistors

Inductors

Capacitors

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Circuit Elements active & passive

Until Chapter 4, only voltage and current sources, and

resistors which require only algebraic equations are discussed

Inductors and capacitors require the solution of integral and

differential equations and will be dealt with later in this course

(Chapter 6) Active elements

Voltage and current sources (able to generate electric energy), op amps,

and BJTs, MOSFETs

Passive elements

Resistors, capacitors, and inductors (unable to generate electric energy)


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Voltage and Current Sources

An electric source is a device that can convert nonelectricenergy to electric energy, such as A discharging battery converts chemical energy to electrical energy

A generator converts mechanical energy to electrical energy

A motor converts electrical energy to mechanical energy

These sources can either deliver or absorb electric power,generally either maintaining voltage or current unchanged

An ideal voltage source is a circuit element that provides aspecified voltage regardless of the current flowing in those

terminals An ideal current source is a circuit element that provides a

specified current regardless of the voltage across thoseterminals

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Independent Sources

An independent source establishes a voltage or current in a

circuit without relying on voltages or currents elsewhere in the

circuit

Symbols for constant or time-varying voltage Symbols for constant voltage (dc)

Symbol for independent current source


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Dependent Sources

A dependent (or controlled) source establishes a voltage or currentwhose value depends on the value of a voltage or current elsewherein the circuit

Examples of ideal dependent sources: Voltage-controlled voltage source (VCVS)

Current-controlled voltage source (CCVS)

Voltage-controlled current source (VCCS)

Current-controlled current source (CCCS)

Symbol for dependent current sourceSymbol for dependent voltage source

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Dependent Sources

Dependent sources are useful in modeling elements such as

transistors, operational amplifiers and integrated circuits

A current-controlled voltage source


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Example 1.7

Calculate the power supplied or absorbed by each element?

Sol:

084860100

W8)52.0(8)2.0(8

W48)6(8

W60)5(12

W100)5(20

4321

4

3

2

1

=++=+++

===

==

==

==

pppp

Ip

p

p

p


Compute the power absorbed or supplied byeach component of the circuit?

Answer:p1 = -40W,p2 = 16W,p3 = 9W,

p4 = 15W

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Applications

Cathode-ray tube (CRT)


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Example 1.8

The electron beam in a TV picture tube carries 1015 electrons per second.

Determine the voltage needed to accelerate the electron beam to achieve

4W?

Sol:

Practice problem 1.8If an electron beam in a TV picture tube carries 1013 electrons per second

and is passing through plates maintained at a potential difference of 30kV,

calculate power in the beam?

Answer: 48mW

kV25V,.

A.

))(.(

,,C.

==

===

=

===

==

000251061

4

i

pVivp

1061

101061dt

dne

dt

dqi

neq1061e

400

4

1519

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Typical energy consumption in living


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Example 1.9

A homeowner consumes 700 kWh in January.

Base monthly charge = $12.00

First 100 kWh per month at 16 cents/kWh

Next 200 kWh per month at 10 cents/kWh

Over 300 kWh per month at 6 cents/kWh

Sol:

cents/kWh10.2

400200100$72costAveragr

$72.00chargeTotal

$24.00$0.06/kWh@kWh400Remaining

$20.00$0.10/kWh@kWh200Next

$16.00$0.16/kWh@kWh100First

$12.00chargemonthlyFirst

=++

=

=

=

=

=

=

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1.8 Problem solving procedure

Procedure for solving engineering problems in industry

1. Carefully Define the problem

2. Present everything you know about the problem

3. Establish a set ofAlternative solutions and determine the one that

promises the greatest likelihood of success4. Attempt a problem solution

5. Evaluate the solution and check for accuracy

6. Has the problem been solved Satisfactorily? If so, present the

solution; otherwise, return to step 3 and continue through the process

again


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Assignments

1.6, 1.12, 1.13, 1.20, 1.21, 1.27

Documents

Circuitry Ch01 Basic Concepts