Electrical Engineering
EE-103
Department of Aerospace Engineering,
School of Mechanical & Manufacturing Engineering (SMME),
NUST, H-12, Islamabad
E-Mail: mnmumtaz.qadri@smme.nust.edu.pk
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Lecture 2
CIRCUIT ELEMENTS AND SIMPLE CIRCUIT LAWS -I
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Voltage and Current Sources
• An electric source is a device capable of converting non-electric energy to electric energy and
vice versa
• Example:
• Discharging battery converts chemical energy to electrical energy
• Dynamo is a machine that converts mechanical energy to electrical energy
• Motor is a machine which converts electrical to mechanical energy
• Electric sources either deliver or absorb electric power while maintaining either voltage or
current
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Voltage and Current Sources
• An Ideal Voltage Source: A circuit element that maintains a prescribed voltage across its
terminals regardless of the current flowing in those terminals.
• An Ideal Current Source: A circuit element that maintains a prescribe current through its
terminals regardless of the voltage across those terminals
• REMEMBER!!! … These circuit elements do not exist as practical devices – they are
idealized models of actual voltage and current sources.
• The common practical examples of voltage sources are cells, batteries, generators, and other
devices that can generate a voltage.
• The common practical example(s) of current sources is a permanently excited AC generator
etc.
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Voltage and Current Sources
• Ideal voltage and current sources can be further described as either independent sources or
dependent sources.
• An independent source establishes a voltage or current in a circuit without relying on voltages
or currents elsewhere in the circuit. The value of the voltage or current supplied is specified by
the value of the independent source alone.
• A dependent source in contrast, establishes a voltage or current whose value depends on the
value of a voltage or current elsewhere in the circuit. Its value cannot be specified unless you
know the value of the voltage or current on which it depends.
• These include BJTs modelled as Current-Controlled Current sources, field effect transistors may be modelled as
Voltage controlled current source. Different amplifier circuits are modelled as Voltage controlled voltage source etc.
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Voltage and Current Sources
Circuit symbols for (a) an ideal independent
voltage source and (b) an ideal independent
current source.
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Voltage and Current Sources
Circuit symbols for ideal dependent voltage sources and current sources
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Voltage and Current Sources
• Note that the ideal independent and dependent voltage and current sources generate either
constant voltages or currents.
• Constant sources are often called dc sources
• Also, ideal sources are examples of active circuit elements, which are models of devices
capable of generating electric energy
• Passive circuit elements model physical devices that cannot generate electric energy such as
Resistors, Inductors and Capacitors
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Testing Interconnections of Ideal Sources
Permitted: Each source supplies
voltage across the same pair of
terminals, marked a and b. This
requires that each source supply the
same voltage with the same
polarity, which they do.
NOT Permitted: Each source supplies
voltage across the same pair of
terminals, marked a and b. This
requires that each source supply the
same voltage with the same polarity,
which THEY DO NOT.
Permitted: Each source supplies
current through the same pair of
terminals, marked a and b. This
requires that each source supply the
same current in the same direction,
which they do.
NOT Permitted: Each source supplies
current through the same pair of
terminals, marked a and b. This
requires that each source supply the
same current in the same direction,
which THEY DO NOT.
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Testing Interconnections of Ideal Sources
Permitted: The voltage source supplies voltage across the
pair of terminals marked a and b. The current source supplies
current through the same pair of terminals. Because an ideal
voltage source supplies the same voltage regardless of the
current, and an ideal current source supplies the same
current regardless of the voltage, this connection is
permitted.
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Testing Interconnections of Ideal Independent and
Dependent Sources
NOT Permitted: Both the independent
source and the dependent source supply
voltage across the same pair of terminals, a
and b. This requires that each source
supply the same voltage with the same
polarity. The independent source supplies 5
V, but the dependent source supplies 15 V.
Permitted: The independent voltage
source supplies voltage across the pair of
terminals marked a and b. The dependent
current source supplies current through
the same pair of terminals. Because an
ideal voltage source supplies the same
voltage regardless of current, and an ideal
current source supplies the same current
regardless of voltage.
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Permitted: The independent current
source supplies current across the pair of
terminals marked a and b. The dependent
voltage source supplies voltage through the
same pair of terminals. Because an ideal
current source supplies the same current
regardless of voltage, and an ideal voltage
source supplies the same voltage
regardless of current.
NOT Permitted: Both the independent
source and the dependent source supply
current through the same pair of terminals,
labelled a and b. This requires that each
source supply the same current in the same
direction. The independent source supplies
2 A, but the dependent source supplies 6 A
in the opposite direction.
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Ohm’s Law
• Resistance is the capacity of materials to impede flow of current or, more
specifically, the flow of electric charge.
• The circuit element modelling this behaviour is the resistor
• A resistor is an ideal basic circuit element, which is described
mathematically usings its voltage and current.
• The relationship between voltage and current for a resistor is known as
Ohm’s law
• v = iR
• Where, v is the voltage in volts, i is the current in amperes and R is the
resistance in ohms.
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Ohm’s Law
• Resistance is measured in the SI units, Ohms (Ω)
• The reciprocal of the resistance is referred to as conductance, and is
symbolized by the letter G and is measured in siemens (S).
• G = 1/R
• We can also calculate the power at the terminals of a resistor in terms of
current
• 𝑝 = 𝑣𝑖 = 𝑖𝑅 𝑖 = 𝑖 2 𝑅
• Similarly, 𝑝 = −𝑣𝑖 = − −𝑖𝑅 𝑖 = 𝑖 2 𝑅
• This demonstrates that regardless of voltage polarity and current direction,
the power at the terminals of a resistor is positive.
• Hence, resistors absorb power from the circuit.
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Ohm’s Law
• Power of resistor in terms of voltage and resistance can also be used;
• 𝑝 = 𝑣𝑖 = 𝑣
𝑣
𝑅
𝑣2
=
𝑅
• Sometimes a resistor’s value will be expressed as a conductance rather than
a resistance
• Power equations using conductance are as follows;
•
𝑖2
𝑝 = and 𝑣 2 𝐺
𝐺
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Resistance - Resistivity
• Technically speaking, any material will provide resistance to
current flow.
• Resistance is determined by (1) the inherent resistivity of a
material, (2) the device geometry.
• Resistivity (ρ) refers to the electrical resistance of a conductor of
a particular unit cross section area and unit length
• Units are Ω.m
• 𝑅= 𝜌
𝑙
𝐴
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Network Topology
• An interconnected set of electrical components
is called a network.
• Each component of a network is called an
element. Elements are connected by wires.
• When two or more elements are connected Simple
Node
together then the common point is called as the
node.
• When two elements are connected together then
the common point is called as the simple node
• When more than two elements are connected
together then the common point is called as the
principle node
Principle
Node
branch
R1
+
--
R2
R3
Principle
Node
• A branch is a single path, i.e., one element
with one node at each end.
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Network Topology
• To define a path;
• Suppose we start at a node and pass through a
simple basic circuit element to the node at the
other end.
• We then continue from that node through a
different element to the next node, and
continue this movement until we have gone
through as many elements as we wish
Path-2
R1
Path-1
+
--
R3
R2
• If no node was encountered more than once,
then the set of nodes and elements that we
have passed through is defined as a path
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Network Topology
• If the node at which we started is the same as the node on which we ended, then the path is, by
definition, a closed path or loop.
Loop-1
R1
Loop-3
Loop-2
R2
+
--
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R3
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Network Topology
• (a) A circuit containing three nodes and five branches. (b) Node 1 is redrawn to look like two
nodes; it is still one node.
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Kirchhoff’s Laws
• A circuit is solved when we determine the voltage across and the current in very element.
• While Ohm’s law is an important tool, it is still insufficient to provide a complete solution.
• Hence, two additional algebraic relationships, known as Kirchhoff’s laws, are needed to solve
most of the circuits.
• Connecting the circuit elements constrains the relationships among the terminal voltages and
currents.
• These constraints are called Kirchhoff’s laws. Additionally, the two laws that state these
constraints in mathematical form are known as Kirchhoff’s Current Law and Kirchhoff’s
Voltage Law
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Kirchhoff’s Laws
• Kirchhoff’s Current Law (KCL)
• The algebraic sum of all the currents at any node in a
circuit equals zero
i1
node
i2
• To use KCL at a node, assign an algebraic sign
corresponding to the current’s reference direction for
every current at the node.
• +ve sign for current leaving the node and vice versa OR
• +ve sign for current entering the node and vice versa
i1 flows into the node
i2 flows out of the node
i3 flows out of the node
i 1 = i2 + i3
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i3
Kirchhoff’s Laws
• Kirchhoff’s Voltage Law (KVL)
• The algebraic sum of all the voltages around any closed path (loop) in a circuit equals zero.
+ v2
+
v1
–
+
_
–
+
v3
–
+
v4
–
For the inner arrow:
–v1 + v2 + v3 = 0
For the outer arrow:
–v4 – v2 + v1 = 0
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Example 1
• If ix = 1.5A and the 9V source supplies a current of 7.6 A,
what is the value of RA?
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Example 2
• Determine the current labelled I3 in the circuit
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Example 3
In the circuit shown, it is determined that v1 = 3 V and v3 = 1.5 V.
Calculate vR and v2.
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Example 4
Determine the value of vx as labelled in the circuit.
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End
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