Download View File - UET Taxila

Basic Electrical
Engineering
Lecture # 02 & 03
Circuit Elements
Course Instructor:
Engr. Sana Ziafat
Agenda
•
•
•
•
Ideal Basic Circuit Elements
Active vs Passive elements
Electrical Resistance
Kirchhoff’s Laws
Circuit Analysis Basics
•
Fundamental elements
▫
▫
▫
▫
▫
•
•
•
Voltage Source
Current Source
Resistor
Inductor
Capacitor
Kirchhoff’s Voltage and Current Laws
Resistors in Series
Voltage Division
Active vs. Passive Elements
• Active elements can generate energy
▫ Voltage and current sources
▫ Batteries
• Passive elements cannot generate energy
▫ Resistors
▫ Capacitors and Inductors (but CAN store energy)
Active and Passive Elements
• Active element
▫ a device capable of generating
electrical energy
 Voltage source
 Current source
 Power source
 Batteries
 Generators
▫ a device that needs to be
powered (biased)
 transistor
• Passive element
▫ a device that absorbs
electrical energy
 Resistor





Capacitor
Inductor
motor
light bulb
heating element
Voltage and Current
• Voltage is the difference in electric potential
between two points. To express this difference, we
b
a
label a voltage with a “+” and “-” :
1.5V
Here, V1 is the potential at “a” minus
+ V1 the potential at “b”, which is -1.5 V.
• Current is the flow of positive charge. Current has a
value and a direction, expressed by an arrow:
i1
Here, i1 is the current that flows right;
i1 is negative if current actually flows left.
• These are ways to place a frame of reference in your
analysis.
Electrical Source
• Is a one that converts electrical energy to non
electrical or vice versa.
For example;
1. Discharging battery
2. Charging battery
3. Motor
4. Generator
Ideal Voltage Source
• The ideal voltage source explicitly defines
the voltage between its terminals.
Vs


▫ Constant (DC) voltage source: Vs = 5 V
▫ Time-Varying voltage source: Vs = 10 sin(t) V
▫ Examples: batteries, wall outlet, function generator,
…
• The ideal voltage source does not provide any information
about the current flowing through it.
• The current through the voltage source is defined by the rest
of the circuit to which the source is attached. Current cannot
be determined by the value of the voltage.
• Do not assume that the current is zero!
Ideal Current Source
• The ideal current source sets the
value of the current running through it.
Is
▫ Constant (DC) current source: Is = 2 A
▫ Time-Varying current source: Is = -3 sin(t) A
• The ideal current source has known current, but unknown
voltage.
• The voltage across the current source is defined by the rest
of the circuit to which the source is attached.
• Voltage cannot be determined by the value of the current.
• Do not assume that the voltage is zero!
“IDEAL” or “Independent” Sources
• IDEAL voltage source
• IDEAL current source
▫ maintains the prescribed
voltage across its terminals
regardless of the current
drawn from it
▫ maintains the prescribed
current through its terminals
regardless of the voltage
across those terminals
LOADCurrent
+
0.012
A
LOAD
Is
1A
+
-
LOADVoltage
999.001 V DC 1MOhm
Z=A+jB
Vs
12 V
Z=A+jB
DC 1e-009Ohm
LOAD
“Controlled” or “Dependent” Sources
• A voltage or current source whose value
“depends” on the value of voltage or current
elsewhere in the circuit
• Use a diamond-shaped symbol
ECE 201 Circuit Theory I
11
Voltage-Controlled Current Source VCCS
+
Vx
-
Is
1 Mho
Is = aVx
• Is is the “output”
current
• Vx is the “reference”
voltage
• a is the multiplier
• Is = aIx
Current-Controlled Current Source CCCS
Ix
Is
1 A/A
Is=bIx
• Is is the “output”
current
• Ix is the “reference”
current
• b is the multiplier
• Is = bIx
Resistors
• A resistor is a circuit element that dissipates
electrical energy (usually as heat)
• Real-world devices that are modeled by
resistors: incandescent light bulbs, heating
elements (stoves, heaters, etc.), long wires
• Resistance is measured in Ohms (Ω)
Resistor
• The resistor has a currentvoltage relationship called
Ohm’s law:
v=iR
where R is the resistance in Ω,
i is the current in A, and v is the
voltage in V, with
reference
directions as pictured.
i
+
R
v

• If R is given, once you know i, it is easy to find v and vice-versa.
• Since R is never negative, a resistor always absorbs power…
Ohm’s Law
v(t) = i(t) R
- or p(t) = i2(t) R = v2(t)/R
V=IR
[+ (absorbing)]
i(t)
The
Rest of
the
Circuit
+v(t)
R
–
Open Circuit
• What if R =  ?
i(t)=0
+
The
Rest of
the
Circuit
v(t)
–
i(t)=0
• i(t) = v(t)/R = 0
Short Circuit
• What if R = 0 ?
• v(t) = R i(t) = 0
i(t)
The
Rest of
the
Circuit
+
v(t)=0
–
Basic Circuit Elements
• Resistor
▫ Current is proportional to voltage (linear)
• Ideal Voltage Source
▫ Voltage is a given quantity, current is unknown
• Wire (Short Circuit)
▫ Voltage is zero, current is unknown
• Ideal Current Source
▫ Current is a given quantity, voltage is unknown
• Air (Open Circuit)
▫ Current is zero, voltage is unknown
• Reciprocal of resistance is conductance
• Having units of Simens
• G= 1/R Simens (s)
• Power calculations at terminals of Resistor????
Wire (Short Circuit)
• Wire has a very small resistance.
• For simplicity, we will idealize wire in the
following way: the potential at all points on a
piece of wire is the same, regardless of the
current going through it.
▫ Wire is a 0 V voltage source
▫ Wire is a 0 Ω resistor
Air (Open Circuit)
• Many of us at one time, after walking on a carpet in winter,
have touched a piece of metal and seen a blue arc of light.
• That arc is current going through the air. So is a bolt of
lightning during a thunderstorm.
• However, these events are unusual. Air is usually a good
insulator and does not allow current to flow.
• For simplicity, we will idealize air in the following way: current
never flows through air (or a hole in a circuit), regardless of the
potential difference (voltage) present.
▫ Air is a 0 A current source
▫ Air is a very very big (infinite) resistor
• There can be nonzero voltage over air or a hole in a circuit!
Kirchhoff’s Laws
• The I-V relationship for a device tells us how
current and voltage are related within that
device.
• Kirchhoff’s laws tell us how voltages relate to
other voltages in a circuit, and how currents
relate to other currents in a circuit.
Kirchhoff’s Laws
• Kirchhoff’s Current Law (KCL)
▫ Algebraic sum of current a any node in a circuit is
zero
• Kirchhoff’s Voltage Law (KVL)
▫ sum of voltages around any loop in a circuit is zero
KCL (Kirchhoff’s Current Law)
i1(t)
i5(t)
i2(t)
i4(t)
i3(t)
The sum of currents entering the node is zero:
n
 i (t )  0
j 1
j
Analogy: mass flow at pipe junction
Kirchhoff’s Voltage Law (KVL)
a
b
• Suppose I add up the potential drops
+ Vab around the closed path, from “a” to “b”
to “c” and back to “a”.
+
• Since I end where I began, the total
Vbc
drop in potential I encounter along the
path must be zero: Vab + Vbc + Vca = 0
c
• It would not make sense to say, for example, “b” is 1 V lower
than “a”, “c” is 2 V lower than “b”, and “a” is 3 V lower than
“c”. I would then be saying that “a” is 6 V lower than “a”,
which is nonsense!
• We can use potential rises throughout instead of potential
drops; this is an alternative statement of KVL.
Writing KVL Equations
1
+
va

b

What does KVL
say about the
voltages along
these 3 paths?
+ v2 
+
vb
-
3
Path 1:
 va  v 2  vb  0
Path 2:
 vb  v 3  vc  0
Path 3:
 va  v2  v3  vc  0
v3
2
+
a
c
+
vc

Kirchhoff’s Current Law (KCL)
• Electrons don’t just disappear or get trapped (in
our analysis).
• Therefore, the sum of all current entering a closed
surface or point must equal zero—whatever goes
in must come out.
• Remember that current leaving a closed surface
can be interpreted as a negative current entering:
i1
is the same
statement as
-i1
KCL Equations
In order to satisfy KCL, what is the value of i?
KCL says:
24 μA + -10 μA + (-)-4 μA + -i =0
24 mA
-4 mA
18 μA – i = 0
i = 18 μA
10 mA
i
Readings
• Chapter 2: 2.1, 2.2, 2.4 (Electric Circuits)
▫ By James W. Nilson
Q&A