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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:
Practice problem 1.3
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:
Practice problem 1.4
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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Practice problem 1.5
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:
Practice problem 1.6
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
Practice problem 1.7
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
19
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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