INTRODUCTION TO ELECTRICAL CIRCUITS -1
•Concept of Network and circuit
•Types of Elements
•Types of Sources
•Source Transformation
•R-L-C Parameters
•Voltage -Current relationships for Passive Elements
An Electric circuit is an inter-connection of various element's 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 ex., mechanical, hydraulic thermal, traffic flow, weather prediction etc.All control systems are studied by representing of them in the form of electric circuits. The analysis, of any system can be learnt by mastering the techniques of circuit theory.
Elements of an Electric circuit:
An Electric circuit consists of following types of elements.
Active elements:
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.
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 or dissipated, then the circuit element is a pure resistor.
If the energy is stored in the form of a magnetic field, the element is a pure inductor.
And if the energy is stored in the form of an electric field, the element is a pure capacitor.
Linear and Non-Linear Elements:
Linear elements show the linear characteristics of the 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 VI or V = IR. A linear element or network is one which satisfies the principle of superposition, i.e., the principle of homogeneity and additive.
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:
Lumped elements are those elements which are very small in size & in which their simultaneous actions takes place. Typical lumped elements are capacitors, resistors, inductors.
Distributed elements are those which are not electrically separable for analytical purposes.For ex: a transmission line has distributed parameters along its length and may extend for hundreds of Kms.
Types of Sources:
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 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 possibility dependent sources:
a.Voltage dependent Voltage source
b.Current dependent Current source
c.Voltage dependent Current source
d.Current dependent Current source
The constants of proportionalities are written as B, g, a, r in which B & a has no units,
r has units of ohm & g units of mho .
Independent sources actually exist as physical entities such as battery, a dc generator & an alternator. But dependent sources are used to represent electrical properties of electronic devices such as diode,Transistors etc.,
Ideal & Practical sources:
1.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 at any time.
2.An ideal current source is one, which delivers energy with a constant current to the load, irrespective of the terminal voltage across the load at any time.
3.A Practical voltage 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.
4.A practical current source is also assumed to deliver a constant current, irrespective of the terminal voltage across the load connected to it.
The equivalent single ideal voltage sum is given by V= V1 + V2
Any n number of ideal voltage sources connected in series can be represented by a single ideal voltage sum taking in to account the polarities connected together in to consideration.
When two ideal voltage sources are of e.m.f's V1 & V2 are connected in parallel,what voltage appears across its terminals is ambiguous.Hence such connections should not be made.However if V1 = V2= V, then the equivalent voltage sum is represented by V.In this case also, such a connection is unnecessary as only one voltage source serves the purpose.
When ideal current sources are connected in series, what current flows through the line is ambiguous. Hence such a connection is not permissible.However, it I1 = I2 = I, then the current in the line is I.But, such a connection is not necessary as only one current source serves the purpose.
Two ideal current sources in parallel can be replaced by a single equivalent ideal current source.
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