INTRODUCTION:
An
Electric circuit is an interconnection of various elements in which there is at
least one closed path in which current can flow. An Electric circuit is used as
a component for any engineering system.
The
performance of any electrical device or machine is always studied by drawing
its electrical equivalent circuit. By simulating an electric circuit, any type
of system can be studied for e.g., mechanical, hydraulic thermal, nuclear,
traffic flow, weather prediction etc.
All control systems are studied by
representing them in the form of electric circuits. The analysis, of any system
can be learnt by mastering the techniques of circuit theory.
The analysis of any system can be
learnt by mastering the techniques of circuit theory.
Elements of an Electric circuit:
Elements of an Electric circuit:
An Electric circuit consists of two types of elements
a) Active elements or sources
b) Passive elements or sinks
Active elements are the elements of a
circuit which possess energy of their own and can impart it to other element of the circuit.
Active elements are of two types
a) Voltage source b) Current source
A
Voltage source has a specified voltage across its terminals, independent of
current flowing through it.
A
current source has a specified current through it independent of the voltage
appearing across it.
Independent
& Dependent sources
If
the voltage of the voltage source is completely independent source of current
and the current of the current source is completely independent of the voltage,
then the sources are called as independent sources.
The
special kind of sources in which the source voltage or current depends on some
other quantity in the circuit which may be either a voltage or a current
anywhere in the circuit are called Dependent sources or Controlled sources.
There are four possible dependent
sources.
a) Voltage dependent Voltage source
b) Current dependent Current source
c) Voltage dependent Current source
d) Current dependent Current source
Ideal & Practical sources
An ideal voltage source is one which
delivers energy to the load at a constant terminal voltage, irrespective of the
current drawn by the load.
An ideal current source is one, which
delivers energy with a constant current to the load, irrespective of the
terminal voltage across the load.
A Practical source always possesses a
very small value of internal resistance r. The internal resistance of a voltage
source is always connected in series with it & for a current source, it is
always connected in parallel with it.
As the value of the internal resistance
of a practical voltage source is very small, its terminal voltage is assumed to
be almost constant within a certain limit of current flowing through the load.
Passive Elements:
The passive elements of an electric
circuit do not possess energy of their own. They receive energy from the
sources. The passive elements are the resistance, the inductance and the
capacitance. When electrical energy is supplied to a circuit element, it will
respond in one and more of the following ways.
If the energy is consumed, then the circuit
element is a pure resistor.
If the energy is
stored in a magnetic field, the element is a pure inductor.
And if the
energy is stored in an electric field, the element is a pure capacitor.
Linear and Non-Linear Elements.
Linear and Non-Linear Elements.
Linear elements show the linear
characteristics of voltage & current. That is its voltage-current
characteristics are at all-times a straight-line through the origin.
For example, the current passing
through a resistor is proportional to the voltage applied through its and the
relation is expressed as V›I or V = IR. A linear element or
network is one which satisfies the principle of superposition, i.e., the
principle of homogeneity and additivity.
Resistors, inductors and capacitors
are the examples of the linear elements and their properties do not change with
a change in the applied voltage and the circuit current.
Non linear element’s V-I
characteristics do not follow the linear pattern i.e. the current passing
through it does not change linearly with the linear change in the voltage
across it. Examples are the semiconductor devices such as diode, transistor .
Bilateral and Unilateral Elements:
An element is said to be bilateral,
when the same relation exists between voltage and current for the current
flowing in both directions.
Ex:
Voltage source, Current source, resistance, inductance & capacitance.
The
circuits containing them are called bilateral circuits.
An element is said to be unilateral,
when the same relation does not exist between voltage and current when current
flowing in both directions. The circuits containing them are called unilateral
circuits.
Ex:
Vacuum diodes, Silicon Diodes, Selenium Rectifiers etc.
Lumped and Distributed Elements
Lumped
elements are those elements which are very small in size & in which simultaneous
actions takes place. Typical lumped elements are capacitors, resistors,
inductors.
Distributed
elements are those which are not electrically separable for analytical
purposes.
For example a transmission
line has distributed parameters along its length and may extend for hundreds of
miles.
The
circuits containing them are called unilateral circuits.
Voltage Current Relationship for passive elements
Voltage Current Relationship for passive elements
Resistance
Resistance is
that property of a circuit element which opposes the flow of electric current
and in doing so converts electrical energy into heat energy.
It is the
proportionality factor in ohm’s law relating voltage and current.
Ohm’s law states
that the voltage drop across a conductor of given length and area of cross
section is directly proportional to the current flowing through it.
v œ i
V=Ri
i=
= GV
where
the reciprocal of resistance is called conductance G. The unit of resistance is
ohm and the unit of conductance is mho or Siemens.
When
current flows through any resistive material, heat is generated by the
collision of electrons with other atomic particles. The power absorbed by the
resistor is converted to heat and is given by the expression
P= vi= i2R where i is the resistor in amps, and v is
the voltage across the resistor in volts.
Inductance
Inductance is
the property of a material by virtue of which it opposes any change of
magnitude and direction of electric current passing through conductor. A wire
of certain length, when twisted into a coil becomes a basic conductor. A change
in the magnitude of the current changes the electromagnetic field.
Increase in
current expands the field & decrease in current reduces it. A change in current produces change in the
electromagnetic field. This induces a voltage across the coil according to Faradays
laws of Electromagnetic Induction.
Induced Voltage
V = L di/dt
V = Voltage
across inductor in volts
I = Current through inductor in amps
Conclusions
1) The
induced voltage across an inductor is zero if the current through it is
constant. That means an inductor acts as short circuit to dc.
2) For
minute change in current within zero time (dt = 0) gives an infinite voltage
across
the
inductor which is physically not at all feasible.
In
an inductor, the current cannot change abruptly. An inductor behaves as open
circuit just
after switching across dc voltage.
3)
The
inductor can store finite amount of energy, even if the voltage across the
inductor is zero.
4) A pure inductor never dissipates energy,
it only stores it. Hence it is also called as a non–dissipative passive element.
However, physical inductor dissipate power due to internal resistance.
Capacitance parameter
·
A
capacitor consists of two metallic surfaces or conducting surfaces separated by
a dielectric medium.
·
It
is a circuit element which is capable of storing electrical energy in its
electric field.
·
Capacitance
is its capacity to store electrical energy.
·
Capacitance
is the proportionality constant relating the charge on the conducting plates to
the potential.
Charge on the capacitor q › V
q = CV
Where `C` is the
capacitance in farads, if q is charge in coulombs and V is the potential difference across the
capacitor in volts.
V-I Relation of circuit elements
Circuit elements
|
Voltage(V)
|
Current(A)
|
Power(W)
|
Resistor
R (Ohms Ω)
|
V=RI
|
I=
|
P
=i2R
|
Inductor
L (Henry H)
|
V=L
|
I
=
|
P
=Li
|
Capacitor
C (Farad F)
|
I=
where
v0 is the initial voltage across capacitor
|
I
=C
|
P
=C
|
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