Continuation to: Circuit Variables EE2001 Electrical Circuits I: 13 October 2021, Wednesday Asst. Prof. Dr. M. Alparslan Zehir E-mail : [email protected] Room : M4-228 (2nd floor)
Continuation to:
Circuit Variables
EE2001 Electrical Circuits I:
13 October 2021, Wednesday
Asst. Prof. Dr. M. Alparslan Zehir
E-mail : [email protected]
Room : M4-228 (2nd floor)
2
EE2001 Course Information:Tentative Schedule:
Week Date Subjects The Related Chapter
from the Book
1 Oct. 6, 7 Introduction and Circuit Variables 1
2 Oct. 13, 14 Circuit Elements 2
3 Oct. 20, 21 Simple Resistive Circuits 3
4 Oct. 27, 28 Node Voltage Analysis 4
5 Nov. 3, 4 Mesh Current Analysis 4
6 Nov. 10, 11 Thevenin and Norton Equivalents 4
7 Nov. 17, 18 The Operational Amplifies 5
8 Midterm Week
9 Dec. 1, 2 Inductance and Capacitance 6
10 Dec. 8, 9 Response of First-Order RL and RC Circuits 7
11 Dec. 15, 16 Natural and Step Responses of RLC Circuits 8
12 Dec. 22, 23 Sinusoidal Steady-State Analysis 9
13 Dec. 29, 30 Continuation to: Sinusoidal Steady-State Analysis 9
14 Jan. 5, 6 Sinusoidal Steady-State Power Calculations 10
15 Jan 12, 13 Continuation to: Sinusoidal Steady-State Power Calculations 10
16 Jan. 19, 20 Review
Outline5. Voltage and Current
6. The Ideal Basic Circuit Element
7. Passive Sign Convention
8. Power and Energy
3
• Voltage (electric potential) is electric potential energy per unit charge:
𝑣 =𝑑𝑤
𝑑𝑞
• Electric current is the rate of charge flow:
𝑖 =𝑑𝑞
𝑑𝑡
• The voltage has a polarity and the current has a direction.
• Although in reality electrons are moving from negative terminal to positive terminal, the
current flow direction is conventionally assumed from positive terminal to negative terminal.
• Although the charge is a discrete quantity, there are enormous number of charge and the
current is treated as a continuous quantity.
• If two physically different circuit elements have the same current-voltage characteristics,
their circuit models are identical and they are identical from the point of circuit analysis.
Voltage and Current
4
5𝑣 : the voltage in volts
𝑤 : the energy in joules
𝑞 : the charge in coulombs
𝑖 : the current in amperes
𝑡 : the time in seconds
The Ideal Basic Circuit Element
5
6
• An ideal basic circuit element has three attributes:
It has only two terminals,
It is described mathematically in terms of current and/or voltage,
It can not be subdivided into other elements.
• Idel basic circuit elements form the building blocks for constructing circuit models.
Passive Sign Convention
6
7• You can assume either voltage polarity or current direction arbitrarily.
• After one of them is chosen, it dictates the assumed direction of the other parameter.
• Which means, once one of these are assigned,
the corresponding equations must be written
accordingly (consistency between the equations).
• These assumptions provide reference voltage
polarity and current directions. It has nothing
to do with actual directions.
• These assumptions are done for each element one by one, independent from the other
elements in the circuit.
• The most commonly used sign convention is the passive sign convention.
7
7
• The Passive Sign Convention: If the reference direction of the current in a circuit element
is in the direction of the reference voltage drop across the circuit element, use a
positive sign in any expression that relates the voltage to the current. Otherwise, use a
negative sign.
• Basically, positive current enters the positive
voltage terminal.
Passive Sign Convention
• An example:
8
7
+-5 V
0.5 A
+
-𝑣1
𝑖1+ -𝑣2
𝑖2
𝑖3+
-
𝑣3
+
-
𝑣4𝑖4
After calculating the values for each, the negative values mean that the related parameter is in
the inverse direction than your assumption (which is ok).
Passive Sign Convention
Power and Energy
9
8
• Power and energy calculations are also important in circuit analysis.
• These can be the output of the circuit converted to other forms.
• The circuit elements have power specifications which need to be considered in a design
process.
• Power is the time rate of energy consumption or supply.
• The power can be expressed in terms of the current and the voltage
𝒑 =𝑑𝑤
𝑑𝑡=𝑑𝑤
𝑑𝑞
𝑑𝑞
𝑑𝑡= 𝒗𝒊
• For 𝒑 > 𝟎 the circuit element absorbs power from the circuit.
• For 𝒑 < 𝟎 the circuit element delivers power to the circuit.
10
End of the topic:Circuit Variables
Any questions?Supplementary videos: Enter Youtube-> Search for ‘Alparslan Zehir’ -> Go to Playlists -> Watch ‘Electrical Circuits’ playlist
Asst. Prof. Dr. M. Alparslan Zehir
E-mail : [email protected]
Room : M4-228 (2nd floor)
From our course book*
12*James W. Nilsson, Susan A. Riedel: “Electric Circuits”, 9th Ed., Prentice Hall, New Jersey, 2011.
Developing models that provide an understanding that is imperfect but adequate
for solving practical problems lies at the heart of engineering.
Outline
1. Introduction to Circuit Elements
2. Voltage and Current Sources
3. Electrical Resistance (Ohm’s Law)
13
There are five ideal circuit elements:
• Voltage sources
• Current sources
• Resistors
• Inductors
• Capacitors
First we will learn,
• Voltage sources
• Current sources
• Resistors
Introduction to Circuit Elements
14
1
Why?
Many practical system can be modelled with them
Relative simplicity, algebraic equations
Active elements: can generate electrical energy
Passive elements: cannot generate electrical energy
• An electrical source is a device which is capable of converting non-electric (other type of)
energy to electric energy and vice versa (e.g. battery, dynamo).
• They either deliver or absorb electric power, maintaining either voltage or current. This
behavior led to the development of the ideal voltage source and ideal current source as
basic circuit elements.
• An ideal voltage source maintains a specified voltage across its terminals
regardless of the current flowing in those terminals.
• An ideal current source maintains a specified current through its terminals
regardless of the voltage across those terminals.
Voltage and Current Sources
16
2
• The circuit symbols for independent sources:
Voltage and Current Sources
17
2
Ideal independent
voltage source
Ideal independent
current source
Value of the supplied voltage
and
the reference polarity
Value of the supplied current
and
the reference direction
• There are also dependent sources.
• The value of a dependent source depends on the value of the current or voltage
somewhere else in the circuit.
• The value of the dependent source can be specified only when the value of the voltage or
current it depends on is known.
• Dependent sources are also known as controlled sources.
• There are four possible types of dependent sources.
Voltage and Current Sources
18
2
• The circuit symbols
for dependent sources:
Voltage and Current Sources
19
2
Voltage-controlled voltage source Voltage-controlled current source
Current-controlled voltage source Current-controlled current source
µ is a dimensionless
multiplying constant
𝝆 has the dimension
volts per ampere
𝜶 has the dimension
amperes per volt
𝜷 is a dimensionless
multiplying constant
Electrical Resistance (Ohm’s Law)
23
3
• Resistance is the ability of materials to impede the flow of current.
• Resistor is the circuit element used to model this behavior.
• Moving electrons that make up electric current interacts with and being resisted by the
atomic structure of the material. Through this interactions some amount of electrical energy
is converted into thermal energy and dissipated in the form of heat.
• This may be undesirable in many applications. On the other hand, several electrical
devices take advantage of resistance such as stoves, irons, space heaters, water heaters.
• Materials such as copper and aluminum have very small resistances (they are good
conductors). Usually they are not modeled as a resistor in the circuit.
Resistor symbol
Electrical Resistance (Ohm’s Law)
24
3
• The current-voltage characteristics of resistors obey Ohm’s Law, using the passive sign
convention:
Resistor symbol with an example value
Riv Riv
• The SI unit for resistance is Ohm (Ω) (1Ω = 1V/1A).
• This model of ideal resistor assumes a constant resistance. In reality resistance can vary
(e.g. depending on the temperature).
6 Ω
Electrical Resistance (Ohm’s Law)
25
3Flashback to passive sign convention (a topic covered in the past weeks):
• You can assume either voltage polarity or current direction arbitrarily.
• After one of them is chosen, it dictates the assumed direction of the other parameter.
• Which means, once one of these are assigned,
the corresponding equations must be written
accordingly (consistency between the equations).
• These assumptions provide reference voltage
polarity and current directions. It has nothing
to do with actual directions.
• These assumptions are done for each element one by one, independent from the other
elements in the circuit.
• The most commonly used sign convention is the passive sign convention.
Electrical Resistance (Ohm’s Law)
26
3
Flashback to passive sign convention (a topic covered in the past weeks):
• The Passive Sign Convention: If the reference direction of the current in a circuit element
is in the direction of the reference voltage drop across the circuit element, use a
positive sign in any expression that relates the voltage to the current. Otherwise, use a
negative sign.
• Basically, positive current enters the positive
voltage terminal.
Flashback to passive sign convention (a topic covered in the past weeks):
• An example:
Electrical Resistance (Ohm’s Law)
27
3
+-5 V
0.5 A
+
-𝑣1
𝑖1+ -𝑣2
𝑖2
𝑖3+
-
𝑣3
+
-
𝑣4𝑖4
After calculating the values for each, the negative values mean that the related parameter is in
the inverse direction than your assumption (which is ok).
Electrical Resistance (Ohm’s Law)
28
3
• The reciprocal of resistance is conductance:
• The SI unit for conductance is Siemens (S).
• Sometimes it is also referred to as Mho ().
RG
1
Electrical Resistance (Ohm’s Law)
29
3
• Calculation of the power dissipated by a resistor (always positive, always absorbs power):
R
vi
R
vi
Riv Riv
vip vip
Rip 2
R
vp
2
Rip 2
R
vp
2
iiRp )( iiRp )(
Electrical Resistance (Ohm’s Law)
30
3
• Power equations using conductance:
G
ip
2
Gvp 2
iG
ip )1
(R
vR
R
vp )(
vGG
vGp )1
(
G
Gvp
22
31
End of the Lesson (13.10.21)
Any questions?Supplementary videos: Enter Youtube-> Search for ‘Alparslan Zehir’ -> Go to Playlists -> Watch ‘Electrical Circuits’ playlist
Asst. Prof. Dr. M. Alparslan Zehir
E-mail : [email protected]
Room : M4-228 (2nd floor)