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Electrical Circuits
Electrical Circuits
 Nearly all branches of electrical engineering are
fundamentally based on circuit theory.
 The only subject in electrical engineering that is
more fundamental than circuit theory is
electromagnetic field theory, which deals with the
physics of electromagnetic fields and waves.
Electrical Circuits
Electrical Circuits
 The Ideal Basic Circuit Element
 Has Only two terminal
 It is described mathematically in terms of current and/or
voltage
 It cannot be subdivided into other elements
 An electrical circuit may be defined as two or more
Basic Circuit Elements interconnected by
conductors.
Electrical Circuits
 In electrical circuits, there are numerous types of
electrical components such as resistors. capacitors.
inductors, diodes, transistors, transformers,
batteries, lamps. fuses, switches, and motors.
Electrical Circuits
 Electrical circuits can be very simple. such as the
circuit in a flashlight containing two batteries, a light
bulb and a switch.
Electrical Circuits
 The “conductors” that interconnect these components are
usually wires or metal pathways integrated on a printed
circuit hoard.
Electrical Circuits
 Most electrical circuits. however, are much more
complex than a flashlight. A standard television
contains, among other things: power supplies,
amplifiers speakers, and a cathode ray tube.
 The microprocessor in a computer may contain the
equivalent of millions of transistors interconnected
in a single chip that is smaller than a fingernail
Motherboard and CPU
Pentium 4
Electrical Circuits Examples
Electrical Circuits
 The gravitational force is an attractive force that
tends to move objects toward one another, the most
common example being the earth’s gravitational
force that attracts objects toward the center of the
earth. Gravitational forces govern the motions of
planets. stars, galaxies. and other celestial objects in
the universe, and yet it is the weakest of all the
natural forces. A type of force that is much stronger
than gravity is electrical in nature.
Electric Charge
 An electrical force is established
between two charged particles.
The force between the particles is
attractive if the charges are
unlike (i.e.. if one charge is
positive and the other is
negative). The force is repulsive if
the charges are alike, that is. if
both charges are either positive
or negative. This force is referred
to as an electrostatic force
because the charges are static or
stationary. The branch of
electrical studies that deals with
static charges is called
electrostatics.
q  1.602 10
19
C
Electron Mass
e
Q
n
m
M
1.60E-19
1
6.24E+18
9.11E-31
5.68626E-12
C
C
Number of Electrons in 1C
kg
kg
Mass of 1C of electrons
Coulomb's Law
 Like charges repel, unlike charges attract. The electric force acting
on a point charge q1 as a result of the presence of a second point
charge q2 is given by Coulomb's Law:
 0 is the permitivit y of space
Coulomb's Law
Electric Current
 En electric circuit theory
current is generally
considered to he the
movement of positive charges
This convention is based on
the work of Benjamin
Franklin (1706—1790), who
conjectured that electricity
flowed from positive to
negative. Today. we know that
electric current in wires and
other conductors is due to the
drift of free electrons
(negatively charged particles)
in the atoms of the conductor.
Different Types of Current
 Direct Current (DC)
 Alternating Current (AC)
 Others
 Electric current is
measured by means of an
instrument called an
ammeter. There are
basically two types of
ammeters:


analog and
digital.
Example
Rectangles
Dt
1
t
0.00
0.5
i
5
5
0.25
t
i
0.00
5
0.50 1.8394
t
i
0.00
5
0.25 3.0327
0.50 1.8394
0.75 1.1157
3.4197
2.7469
0.125
t
0
0.125
0.25
0.375
0.5
0.625
0.75
0.875
i
5
3.894004
3.032653
2.361833
1.839397
1.432524
1.115651
0.86887
2.443116
Exact
0
2.5
1 0.338338
2.161662
Trapeze
Dt
1
t
0.5
i
t
0.25
i
0.00
5
1.00 0.676676
0.00
5
0.50 1.839397
1.00 0.676676
2.838338
2.338868
t
i
0.00
0.25
0.50
0.75
1.00
5
3.032653
1.839397
1.115651
0.676676
2.20651
0.125
t
0
0.125
0.25
0.375
0.5
0.625
0.75
0.875
1
i
5
3.894004
3.032653
2.361833
1.839397
1.432524
1.115651
0.86887
0.676676
2.172909
Exact
0
2.5
1 0.338338
2.161662
Exponential Function
Electric Potential Energy and Voltage
 Potential energy can be defined as the capacity for doing work which
arises from position or configuration.
 Voltage is electric potential energy per unit charge, measured in joules
per coulomb ( = volts). It is often referred to as "electric potential",
which then must be distinguished from electric potential energy by
noting that the "potential" is a "per-unit-charge" quantity.
Voltage Difference
 The word difference denotes that voltage is always
taken between two points. To speak of voltage “at a
point is meaningless, unless a second point
(reference point) is implied. A voltage exists across
the positive and negative terminals of a battery.
Voltage
Notation
 Time varying quantities - lower case
e.g. v(t), i(t)
 sometimes assume time: v(t) = v
 Time invariant quantities upper case
e.g. V, R,
 Remember to include units of measure
e.g. 15 V, 7A
Electric Power
Dw
Dq
Dw Dq Dw
v
;i
; v i 


; hence,
Dq
Dt
Dq Dt Dt
p  v  i ( J / s)
P  VI ( J / s)
The passive sign convention
 When we observe that positive current enters the positive
terminal of a component, we say that the component obeys
the passive sign convention (PSC). Therefore, when the
passive sign convention is being obeyed, it indicates that a
component is dissipating energy (or power) as charge is
being displaced from a higher potential to a lower potential.
Resistance
 Electrical resistance may be defined as an impedance
to current flow through a circuit element.
 All circuit elements, including even the conductors
(wires) that connect them impede the flow of current
to some extent.
The resistance element
i  v/R
I V / R
Resistors Combinations
 Resistance is measured by
means of an instrument called
an ohmmeter. Like ammeters
and voltmeters that measure
current and voltage, there are
basically two types of
ohmmeters: analog and
digital.


An analog ohmmeter provides
a resistance reading by means
of a needle or pointer that
moves across a calibrated
scale.
Digital ohmmeters provide a
resistance reading by
displaying numbers in a
window.
Example
 Find the total resistance
for the resistor circuit
shown in the Figure
 Suppose that we are
designing a powersupply circuit. Our
circuit design calls for a
resistor that carries a
direct current of 800 mA
and has a voltage drop of
24 V.


What is the resistance of
the resistor?
What power rating must
the resistor have?
Common circuit elements and their schematic
symbols
Independent Current and Voltage Sources
Independent Current and Voltage Sources
 An independent voltage source is a two terminal
circuit element, such as a battery or generator, that
maintains a specified voltage between its terminals.
The voltage is independent of the current through
the element.


Because the voltage is independent of current, the internal
resistance of the independent voltage source is zero. Actual
voltage sources such as batteries do not have a zero internal
resistance, but the internal resistance can be neglected it the
resistance of the external circuit is large.
Thus, the independent voltage source is an idealization that
simplifies circuit analysis.
Independent Current and Voltage Sources
 An independent current source is a two-terminal
circuit element through which a specified current
flows. The current is independent of the voltage
across the element.
 Hence, like the independent voltage source, the
independent current source is an idealization.
Example
 The DC circuit shown in
the Figure consists of a
10-V independent
voltage source connected
to two resistors in series.
Find:
1. The current.
2. The voltage across each
resistor, and
3. The power dissipated by
each resistor.
Example
 The DC circuit shown in
the Figure consists of a
200-mA independent
current source connected
to two resistors in
parallel. Find:
1. the voltage across the
resistors and
2. the current in each
resistor.
Nodes and Branches
 A node is defined as a
point of connection of
two or more circuit
elements. The actual
node may or may not be
a physical point where
the conductors from two
or more circuit elements
come together.
 Branch, an open path in
a circuit including one or
more circuit elements
and no essential nodes
Short and Open Circuits
 Short Circuit.
 Basic Circuit element whose voltage is always 0. (Resistance
=0)
 Symbol
 Open Circuit
 Basic Circuit element whose current is always 0. (Resistance =
infinity)
 Symbol
Kirchhoff’s Laws
 Kirchhoff’s current law (KCL):
 The algebraic sum of all the currents at any node in a circuit
equals zero.

Plumber’s Law
 Kirchhoff’s voltage law
 The algebraic sum of all the voltages around any closed path in
a circuit equals zero

Roller Coaster Law
Example
 For the DC circuit shown
in the Figure, find the
voltage across each
resistor and the current
in each resistor.
Example
0
24
24
1
50
0
1
0
200
0
24
24
1
50
0
0
24
24
1
50
0
1
0
200
0
24
24
1
50
0
-1
10
10
1
50
0
1
0
200
-1
10
10
1
50
0
-1
10
10
1
50
0
1
0
200
-1
10
10
1
50
0
=
0
0
0
=
0
=
1200
0
4800
=
6000
-6000
=
-10000
0
0
=
-10000
=
500
0
2000
=
2500
-12500
-1
10
10
0
24
24
1
0
200
-1
10
10
0
24
24
-1
10
10
0
24
24
1
0
200
-1
10
10
0
24
24
-1
10
10
1
50
0
1
0
200
-1
10
10
1
50
0
-1
10
10
1
50
0
1
0
200
-1
10
10
1
50
0
=
-4800
0
240
=
-4560
=
240
0
0
=
240
-4800
=
-10000
0
0
=
-10000
=
500
0
2000
=
2500
-12500
-1
10
10
1
50
0
0
24
24
-1
10
10
1
50
0
-1
10
10
1
50
0
0
24
24
-1
10
10
1
50
0
-1
10
10
1
50
0
1
0
200
-1
10
10
1
50
0
-1
10
10
1
50
0
1
0
200
-1
10
10
1
50
0
=
-1200
240
0
=
-960
=
0
0
240
=
240
-1200
=
-10000
0
0
=
-10000
=
500
0
2000
=
2500
-12500
Determinants in Excel
-1
10
10
1
50
0
0
24
24
=
-1200
Homework
A standard power value for a household
incandescent light bulb is 60W. What is the current
through the filament of such a light bulb if the
voltage is 110 V?
1.

Is the entire 60W of electrical power converted into visible
light?
2. Using an order-of-magnitude analysis. estimate the
amount of electrical energy (J) used per person in
the United States each year. What is the
corresponding power (W)?
Homework
3. Find the total resistance
for the resistor circuit
shown in the Figure.
4. For the DC circuit
shown in the Figure,
find the voltage across
each resistor and the
current in each resistor.
Homework
For the DC circuit shown
in the Figure, find the
voltage across each
resistor and the current in
each resistor. Find the
power dissipations in the
2 Ω, 5 Ω and 22 Ω
resistors.
6. For the DC circuit shown
in the Figure, find the
voltage across each
resistor and the current in
each resistor.
5.