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ARRDEKTA INSTITUTE OF
TECHNOLOGY


GUIDED BY.
Prof.Y.B.Vaghela.
Asst.prof in electrical
Department

PREPARED BY.

GandhiChandani
(130930107002)
Joshi Ishani
(130930107004)
Patel Devangi
(130930107007)
Rathwa Vaishali
(130930109030)
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

Overview of Circuit Theory
Electrical circuit elements are idealized
models of physical devices that are defined
by relationships between their terminal
voltages and currents. Circuit elements can
have two or more terminals.
 An electrical circuit is a connection of
circuit elements into one or more closed
loops.

Overview of Circuit Theory
Basic quantities are voltage, current, and
power.
 The sign convention is important in
computing power supplied by or absorbed
by a circuit element.
 Circuit elements can be active or passive;
active elements are sources.

Overview of Circuit Theory
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Current is moving positive electrical charge.
Measured in Amperes (A) = 1 Coulomb/s
Current is represented by I or i.
In general, current can be an arbitrary function
of time.
Constant current is called direct current (DC).
 Current that can be represented as a sinusoidal
function of time (or in some contexts a sum of
sinusoids) is called alternating current (AC).

Overview of Circuit Theory
Voltage is electromotive force provided by
a source or a potential difference between
two points in a circuit.
 Measured in Volts (V): 1 J of energy is
needed to move 1 C of charge through a 1
V potential difference.
 Voltage is represented by V or v.

Overview of Circuit Theory
The lower case symbols v and i are usually
used to denote voltages and currents that
are functions of time.
 The upper case symbols V and I are usually
used to denote voltages and currents that
are DC or AC steady-state voltages and
currents.
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Overview of Circuit Theory
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Current has an assumed direction of flow; currents in
the direction of assumed current flow have positive
values; currents in the opposite direction have negative
values.
Voltage has an assumed polarity; volt drops in with the
assumed polarity have positive values; volt drops of the
opposite polarity have negative values.
In circuit analysis the assumed polarity of voltages are
often defined by the direction of assumed current flow.
Overview of Circuit Theory
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Power is the rate at which energy is being
absorbed or supplied.
Power is computed as the product of voltage
and current:
pt   vt it  or P  VI

Sign convention: positive power means that
energy is being absorbed; negative power means
that power is being supplied.
Overview of Circuit Theory
i(t)
Rest of
circuit
+
v(t)
• If p(t) > 0, then the circuit
element is absorbing power
from the rest of the circuit.
• If p(t) < 0, then the circuit
element is supplying power
to the rest of the circuit.
Circuit element under
consideration
Overview of Circuit Theory
If power is positive into a circuit element,
it means that the circuit element is
absorbing power.
 If power is negative into a circuit element,
it means that the circuit element is
supplying power. Only active elements
(sources) can supply power to the rest of a
circuit.
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Active and Passive Elements
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Active elements can generate energy.
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Passive elements cannot generate energy.
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Examples of active elements are independent and
dependent sources.
Examples of passive elements are resistors,
capacitors, and inductors.
In a particular circuit, there can be active
elements that absorb power – for example, a
battery being charged.
Independent and Dependent
Sources
An independent source (voltage or
current) may be DC (constant) or timevarying; its value does not depend on other
voltages or currents in the circuit.
 A dependent source has a value that
depends on another voltage or current in the
circuit.

Independent Sources
vs t 
is t 
Voltage Source
Current Source
Dependent Sources
+
v=f(vx)
+
v=f(ix)
-
-
Voltage
Controlled
Voltage Source
(VCVS)
Current
Controlled
Voltage Source
(CCVS)
Dependent Sources
I=f(Vx)
Voltage
Controlled
Current Source
(VCCS)
I=f(Ix)
Current
Controlled
Current Source
(CCCS)
Passive Lumped Circuit Elements

Resistors
R
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Capacitors
C
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Inductors
L
Topology of Circuits
A lumped circuit is composed of lumped
elements (sources, resistors, capacitors,
inductors) and conductors (wires).
 All the elements are assumed to be
lumped, i.e., the entire circuit is of
negligible dimensions.
 All conductors are perfect.

Topology of Circuits
A schematic diagram is an electrical
representation of a circuit.
 The location of a circuit element in a
schematic may have no relationship to its
physical location.
 We can rearrange the schematic and have
the same circuit as long as the connections
between elements remain the same.
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Topology of Circuits
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Example: Schematic of a circuit:
“Ground”: a
reference point
where the voltage
(or potential) is
assumed to be zero.
Topology of Circuits
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Only circuit elements that are in closed loops
(i.e., where a current path exists) contribute to
the functionality of a circuit.
This circuit
element can be
removed without
affecting
functionality. This
circuit behaves
identically to the
previous one.
Topology of Circuits
A node is an equipotential point in a circuit. It
is a topological concept – in other words, even if
the circuit elements change values, the node
remains an equipotential point.
 To find a node, start at a point in the circuit.
From this point, everywhere you can travel by
moving only along perfect conductors is part of a
single node.
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Topology of Circuits
A loop is any closed path through a circuit in
which no node is encountered more than once.
 To find a loop, start at a node in the circuit.
From this node, travel along a path back to the
same node ensuring that you do not encounter any
node more than once.
 A mesh is a loop that has no other loops inside
of it.
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Topology of Circuits
If we know the voltage at every node of a
circuit relative to a reference node (ground),
then we know everything about the circuit –
i.e., we can determine any other voltage or
current in the circuit.
 The same is true if we know every mesh
current.
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Resistors
A resistor is a circuit element that
dissipates electrical energy (usually as heat).
 Real-world devices that are modeled by
resistors: incandescent light bulb, heating
elements (stoves, heaters, etc.), long wires
 Parasitic resistances: many resistors on
circuit diagrams model unwanted
resistances in transistors, motors, etc.
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Resistors
i(t)
The
Rest of
the
Circuit
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+
R
v(t)
vt   Ri t 
-
Resistance is measured in Ohms (W)
The relationship between terminal voltage and current
is governed by Ohm’s law
Ohm’s law tells us that the volt drop in the direction of
assumed current flow is Ri
KCL and KVL
Kirchhoff’s Current Law (KCL) and Kirchhoff’s
Voltage Law (KVL) are the fundamental laws of
circuit analysis.
 KCL is the basis of nodal analysis – in which
the unknowns are the voltages at each of the
nodes of the circuit.
 KVL is the basis of mesh analysis – in which
the unknowns are the currents flowing in each of
the meshes of the circuit.
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KCL and KVL
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KCL
 The sum of all currents
entering a node is zero,
or
 The sum of currents
entering node is equal
to sum of currents
leaving node.
i1(t)
i5(t)
i2(t)
i4(t)
i3(t)
n
 i (t )  0
j 1
j
KCL and KVL

KVL
 The sum of voltages
around any loop in a
circuit is zero.
-
v1(t)
+
+ v2(t) -
n
v
j 1
+
v3(t)
-
j
(t )  0
KCL and KVL
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In KVL:
A voltage encountered + to - is positive.
 A voltage encountered - to + is negative.
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Arrows are sometimes used to represent voltage
differences; they point from low to high voltage.
+
v(t)
-
≡
v(t)
Resistors in Series
A single loop circuit is one which has only
a single loop.
 The same current flows through each
element of the circuit - the elements are in
series.
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Resistors in Series
Two elements are in series if the current that
flows through one must also flow through
the other.
Series
R1
R2
Resistors in Series
If we wish to replace the two series
resistors with a single equivalent resistor
whose voltage-current relationship is the
same, the equivalent resistor has a value
given by

Req  R1  R2
Resistors in Series
For N resistors in series, the equivalent
resistor has a value given by

R1
R2
R3
Req  R1  R2  R3    RN
Req
Resistors in Parallel

When the terminals of two or more circuit
elements are connected to the same two
nodes, the circuit elements are said to be in
parallel.
Resistors in Parallel
If we wish to replace the two parallel
resistors with a single equivalent resistor
whose voltage-current relationship is the
same, the equivalent resistor has a value
given by
R1 R2
Req 
R1  R2

Resistors in Parallel
For N resistors in parallel, the equivalent
resistor has a value given by

R1
R2
R3
1
Req 
1
1
1
1

 
R1 R2 R3
RN
Req
Energy Storage Elements
Capacitors store energy in an electric field.
 Inductors store energy in a magnetic field.
 Capacitors and inductors are passive
elements:

 Can
store energy supplied by circuit
 Can return stored energy to circuit
 Cannot supply more energy to circuit than is
stored.
Energy Storage Elements
Voltages and currents in a circuit without
energy storage elements are solutions to
algebraic equations.
 Voltages and currents in a circuit with
energy storage elements are solutions to
linear, constant coefficient differential
equations.
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Capacitors
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Capacitance occurs when two conductors are separated
by a dielectric (insulator).
Charge on the two conductors creates an electric field
that stores energy.
The voltage difference between the two conductors is
proportional to the charge.
qt   C vt 
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The proportionality constant C is called capacitance.
Capacitance is measured in Farads (F).
Capacitors
The voltage across a capacitor cannot
change instantaneously.
 The energy stored in the capacitors is given
by
1 2
wC (t )  Cv (t )
2
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Inductors
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Inductance occurs when current flows through a (real)
conductor.
The current flowing through the conductor sets up a
magnetic field that is proportional to the current.
The voltage difference across the conductor is
proportional to the rate of change of the magnetic flux.
The proportionality constant is called the inductance,
denoted L.
Inductance is measured in Henrys (H).