Download voltage sources in parallel

EE201 Fundamentals of Electric
Circuits
by
Dr. Ibraheem Nasiruddin
WHEEL-2
1
Connect / Attend
Connect: Group Activity
Ask the students to form groups randomly in the class to hold their neighbors hand and only two
students have their one hand unoccupied in the group?
Identify one of the unoccupied hand as input and provide eatables and ask them to pass on or
consume it ?
Collect the eatable from last unoccupied hand as output.
Attend:
• Listen individual Responses after observation by them
conclude connect and attend activity and compile thoughts
 Ask them to list down their observation based on the discussion
 List down various properties to identify electrical elements
2
Image
BASIC PARAMETERS AND SIMPLE
RESISTIVE CIRCUITS
Mind Map
Series-Parallel Network
Series Circuits and KVL
Parallel Circuits and KCL
Simple Resistive Circuits
TA
NETWORK
Energy
Basic Concepts
Power
Current
Voltage
Ohm's Law
Resistance
5
The Electric Current
• The free electron is the charge carrier in a
copper wire or any other solid conductor of
electricity.
• With no external forces applied, the net flow
of charge in a conductor in any one direction
is zero.
Basic Electric Circuit
• To create the simplest of electric circuits.
The battery, at the expense of
chemical energy, places a net positive charge at one terminal
and a net negative charge on the other.
• The instant the final connection is made, the free electrons
(of negative charge) will drift toward the positive terminal,
while the positive ions left behind in the copper wire will
simply oscillate in a mean fixed position.
• The negative terminal is a “supply” of electrons to be drawn
from, while the electrons of the copper wire drift toward the
positive terminal.
• The flow of charge (electrons) through the bulb will heat up
the filament of the bulb through friction to the point that it
will glow red hot and emit the desired light.
• A coulomb (C) of charge was defined as the total
charge associated with 6.242x1018 electrons.
The charge associated with one electron can
then be determined from
Potential Difference
• In the battery, the internal chemical action will establish
(through an expenditure of energy) an accumulation of negative
charges (electrons) on one terminal (the negative terminal) and
positive charges (positive ions) on the other (the positive
terminal).
• A “positioning” of the charges has been established that will
result in a potential difference between the terminals. If a
conductor is connected between the terminals of the battery,
the electrons at the negative terminal have sufficient potential
energy to overcome collisions with other particles in the
conductor and the repulsion from similar charges to reach the
positive terminal to which they are attracted.
• A potential difference of 1 volt (V) exists between two points if
1 joule (J) of energy is exchanged in moving 1 coulomb (C) of
charge between the two points.
Conductors and Insulators
The Resistor
SI Prefixes
SUPERCONDUCTORS
• Superconductors are conductors of electric charge that, for all practical
purposes, have zero resistance.
TYPES OF RESISTORS
• Fixed Resistors
• Variable Resistors
Home Assignment-3
Solve Examples from each section
Submit solution of selected question
20
QUIZ-3
21
Series Resistor Circuits
Two elements are in series if
1. They have only one terminal in common
(i.e., one lead of one is connected to only
one lead of the other).
2. The common point between the two
elements is not connected to another
current-carrying element.
The current is the same through series
elements.
EXAMPLE Determine RT, I, and V2 for the circuit
VOLTAGE SOURCES IN SERIES
KIRCHHOFF’S VOLTAGE LAW
• Kirchhoff’s voltage law (KVL) states that the algebraic
sum of the potential rises and drops around a closed
loop (or path) is zero.
VOLTAGE DIVIDER RULE
• the voltage across the resistive
elements will divide as the
magnitude of the resistance levels.
INTERNAL RESISTANCE
OF VOLTAGE SOURCES
Home Assignment-4
Solve Examples from each section
Submit solution of selected question
35
QUIZ-4
36
Parallel Resistors Circuits
• Two elements, branches, or
networks are in parallel if
they have two points in common as shown
TOTAL CONDUCTANCE AND RESISTANCE
PARALLEL CIRCUITS
KIRCHHOFF’S CURRENT LAW
CURRENT DIVIDER RULE
The current divider rule (CDR) will determine how the
current entering a set of parallel branches will split
between the elements.
For two parallel elements of equal value, the current will
divide equally.
For two parallel elements with different values, the
smaller the resistance, the greater the share of input
current with a ratio equal to the inverse of their resistor
values.
Example
Two Examples
Determine the resistance R1 to effect the division of current.
Solve for R1
VOLTAGE SOURCES IN PARALLEL
Voltage sources are placed in parallel as shown in the Figure
only if they have the same voltage rating. The primary reason for
placing two or more batteries in parallel of the same terminal
voltage would be to increase the current rating (and, therefore,
the power rating) of the source. The current rating of the
combination is determined by Is= I1 + I2 at the same terminal
voltage. The resulting power rating is twice that available with
one supply.
OPEN AND SHORT CIRCUITS
An open circuit can have a potential difference
(voltage) across its terminals, but the current is
always zero amperes.
A short circuit can carry a current of a level
determined by the external circuit, but the
potential difference (voltage) across its terminals
is always zero volts.
SERIES-PARALLEL NETWORKS
series-parallel networks are networks that contain both
series and
parallel circuit configurations.
Examine each region of the network independently before
tying them together in series-parallel combinations. This will
usually simplify the network and possibly reveal a direct
approach toward obtaining one or more desired unknowns. It
also eliminates many of the errors that might result due to the
lack of a systematic approach.
Redraw the network as often as possible with the reduced
branches and undisturbed unknown quantities to maintain
clarity and provide the reduced networks for the trip back to
unknown quantities from the source.
Reduce and Return Approach
For many single-source, seriesparallel networks, the analysis
is one that works back to the
source, determines the source
current, and then finds its way
to the desired unknown. In the
shown Fig., for instance, the
voltage V4 is desired.
Block Diagram
Approach
There will be some concern about identifying series and parallel elements and branches and choosing the
best procedure to follow toward a solution.
In the above Fig., blocks B and C are in parallel (points b and c in common), and the voltage source E is in
series with block A (point a in common). The parallel combination of B and C is also in series with A and
the voltage source E due to the common points b and c, respectively.
The following notation will be used for series and parallel combinations of elements. For series resistors R1
and R2, a comma will be inserted between their subscript notations, as shown here:
For parallel resistors R1 and R2, the parallel symbol will be inserted between their subscript notations, as
follows:
Example
Example
Example
Example
Note that the unknown voltages do not have to be across elements but
can exist between any two points in a network.
In addition, the importance of redrawing the network in a more
familiar form is clearly revealed by the analysis to follow.
Find the voltages V1, V3, and Vab for the shown network and Calculate the
source current Is.
Using the voltage divider rule to determine V1 and V3.
The open-circuit voltage Vab is determined by applying Kirchhoff’s
voltage law around the indicated loop of the shown Fig. in the clockwise
direction starting at terminal a.
Example
Determine the voltages V1 and V2 and the current I.
It would indeed be difficult to analyze the network in its original form with the
symbolic notation for the sources and the reference or ground connection in the
upper left-hand corner of the diagram.
However, when the network is redrawn as shown, the unknowns and the
relationship between branches become significantly clearer.
It is now obvious that V2 = - E1 = - 6 V
Applying Kirchhoff’s voltage law to the loop indicated, we obtain: -E1 + V1 - E2 =
0
LADDER NETWORKS
The reason for the terminology is quite obvious
for the repetitive structure. Basically two
approaches are used to solve networks of this
type.
• Method 1: Calculate the total resistance and
resulting source current, and then work back
through the ladder until the desired current
or voltage is obtained.
Method 1
Method 2
CURRENT SOURCES
The current source is often referred to as the dual
of the voltage source.
• A battery supplies a fixed voltage, and the source
current can vary; but the current source supplies
a fixed current to the branch in which it is located,
while its terminal voltage may vary as determined
by the network to which it is applied.
• Note from the above that duality simply implies
an interchange of current and voltage to
distinguish the characteristics of one source from
the other.
Examples
CURRENT SOURCES IN
PARALLEL
If two or more current
sources are in parallel,
they may all be replaced
by one current source having the magnitude
and direction of the resultant current.
Home Assignment-5
Solve Examples from each section
Submit solution of selected question
71
QUIZ-5
72