#### Network Analysis and Devices, Physics tutorial

Introduction to Network Analysis and Devices:

A network, in the framework of electronics, is a collection of interrelated components. Network analysis is the procedure of finding the voltages across and the currents via, in each and every component in the network. There are numerous different methods for computing these values.

Passive Components:

The component is stated to be passive when the net energy delivered to it from the rest of the circuit is for all time non-negative. There are usually three types of passive components:

a) Resistors:

A resistor is an electrical machine whose main function is to introduce resistance to the flow of electric current. The magnitude of opposition to the flow of current is termed as the resistance of the resistor. The resistance 'R' of a resistor is represented by:

R = ρl/A

Here, 'ρ' is the resistivity of the material; 'l' is the length of the resistor and 'A' is the cross-sectional area perpendicular to the current flow.

b) Capacitors:

It is a passive electrical device which is intentionally designed to store energy in an electric field is termed as a capacitor. The capability of a capacitor to store energy in an electric field is termed as the capacitance. A capacitor is physically built up of two conducting plates separated through a dielectric medium and its capacitance 'C' is represented by:

C = εA/d

Here, 'A' is the area of the plate; 'ε' is the dielectric constant of an insulating material and 'd' is the separation between plates. 'C' is measured in terms of Farads (F).

c) Inductors:

An inductor is the electrical device designed to store energy in the magnetic field. Inductance is basically a measure of the capability of an inductor to store energy in the magnetic field. An inductor can be built up by winding a coil of wire around a toroidal core and its inductance 'L', is measured in Henrys (H), and is represented by:

L = N2Aμ/2πr

Here, 'N' is the number of turns of wires; 'A' is the cross-sectional area of the torus; 'μ' is the permeability of the material and 'r' is the radius of the torus.

Voltage and current sources:

An ideal voltage source is the circuit element which maintains a set voltage across its terminals in spite of of the current flowing in such terminals.

An ideal current source is the circuit element which maintains a set current via its terminals in spite of the voltage across such terminals.

Circuits:

The electrical circuit is an interconnection of electrical components like passive components and power sources linked altogether in a closed path in such a manner that an electric current might flow constantly. In a DC (direct current) circuit, both the current and voltage encompass their values unchanged. In an AC (alternating current) circuit, their values change from time to time. In common, there are two kinds of AC circuits, namely single-phase circuits and three-phase circuits.

1) Single-phase circuits:

A single-phase circuit is the alternating-current by employing only one, sine wave kind, current flow. It comprises of three wires: live, neutral and ground (earth). The major breaker in a single phase system is the single pole breaker, resembling the others in the panel, only having a higher capacity.

2) Three-phase circuit:

A three-phase circuit comprises of three different sine wave current flows, dissimilar in phase by 120 degrees from each other, a circuit where the major breaker switches off three poles. For most of the home owners this is the equivalent of having three separate main breakers which are divided among the circuits of the home. There are five wires which generally comprise a three phase line, though in lots of homes the three phases merely supply the main and sub panels, however continue all through most of the home as single phase lines. In most of the homes there are not numerous devices which run on three phase electricity. Though, illustrations might comprise a three phase central air conditioner, a three phase oven, a three phase swimming pool pump or a large three phase hot water boiler.

Ohm's law:

The Ohm's Law is a mathematical relationship among the electric current, resistance and voltage. The principle is termed after the German scientist Georg Simon Ohm. The relationship defines that: The potential difference (or voltage) across an ideal conductor is proportional to the current via it.

V = IR

Here, 'V' is voltage measured in volts; 'I' is the current measured in amperes and 'R' is the resistance measured in ohms.

Kirchhoff's law:

In the year 1845, a German physicist, Gustav Kirchhoff introduced a pair or set of rules or laws which mainly deal by the conservation of current and energy in the Electrical Circuits. These two rules are generally termed as: Kirchhoff's Circuit Laws mainly dealing with the current flowing around a closed circuit whereas the other law deals with the voltage sources present in the closed circuit, generally termed as Kirchhoff's Voltage Law (or KVL).

1) Kirchhoff's First Law - The Current Law (KCL):

Kirchhoff's Current Law or KCL, defines that the total current or charge entering a junction or node is precisely equivalent to the charge leaving the node as it consists of no other place to go apart from to leave, as no charge is lost in the node. In another words the algebraic sum of all the currents entering and leaving a node should be equivalent to zero, I(exiting) + I(entering) = 0. This theory proposed by Kirchhoff is generally termed as the Conservation of Charge.

2) Kirchhoff's Second Law - The Voltage Law (KVL):

Kirchhoff's Voltage Law or KVL defines that in any closed loop network, the net voltage around the loop is equivalent to the sum of all the voltage drops in the similar loop, which is as well equivalent to zero. In another words the algebraic sum of all voltages in the loop should be equivalent to zero. This theory proposed by Kirchhoff is termed as the Conservation of Energy.

Node and Mesh analysis:

Node analysis:

This is a process of analyzing the linear electric networks, which is, a process of finding out the currents in the branches of such a network and the voltages between the terminals of the passive elements and active elements (that is, sources of energy) in the network.

In examining a circuit by using Kirchhoff's circuit laws, one can either do nodal analysis by using Kirchhoff's current law (or KCL) or mesh analysis by using Kirchhoff's voltage law (or KVL). Nodal analysis represents an equation at each and every electrical node, requiring that the branch currents incident at a node should sum to zero. The branch currents are written in terms of the circuit node voltages. As an effect, each and every branch constitutive relation should provide current as a function of voltage; an admittance representation. For illustration, for a resistor, Ibranch = Vbranch * G, here G (=1/R) is the admittance (or conductance) of the resistor.

Mesh analysis:

A mesh analysis is the set of mathematical equations which help in finding out the paths of electrical currents. The analysis procedure employs Ohm's law and Kirchhoff's voltage law to inspect how dissimilar points on a circuit board form the communication bonds. It comprises isolating a circuit board's loops, recognizing opposite voltage charges and replacing values into equations to resolve the unknown direction of the currents. The mesh analysis is one of many processes employed to examine electrical currents and is as well termed as the loop current method.

The most complex portion of the mesh analysis method is making the equations which reveal whether the supposed current direction is right or wrong. Kirchhoff's voltage law takes the first circuit's resistor's voltage value and then adds it to the amount of the unknown value of the first current and the second current, which is then multiplied by two. This outcome is as well added to the unknown value of the first current multiplied by four. The value of first side of the equation is set to equivalent zero and is resolved mathematically.

Network theorems:

1) Linearity:

In general usage, linearity signifies to a mathematical function or relationship which can be graphically exhibited as a straight line, as in two quantities which are directly proportional to one other, such as current or voltage in a simple DC circuit, or the mass and weight of the object.

2) Superposition Theorem:

The principle of superposition theorem define that 'the voltage across (or current via) an element in a linear circuit is the arithmetical sum of the voltages across (or currents via) that element due to each and every independent source acting alone.

To determine the contribution of each and every individual source, all of the other sources first should be turned off (that is, set to zero) by:

• Substituting all other independent voltage sources by a short circuit (thus removing difference of potential that is, V = 0; internal impedance of the ideal voltage source is zero (that is, short circuit)).
• Substituting all other independent current sources by an open circuit (thus removing current that is, I = 0; internal impedance of the ideal current source is infinite (that is, open circuit)).

3) Thevenin's Theorem:

Thevenin's theorem defines that 'any linear circuit having some voltages and resistances can be substituted by merely a single voltage in series by a Single Resistor'. In another words, it is possible to simplify any linear circuit, no matter how complicated, to an equivalent circuit by merely a single voltage source in series by a resistance joined to a load.

In terms of DC resistive circuits, the Thevenin's theorem holds that:

Any linear electrical network having voltage and current sources and only resistances can be substituted at terminals A-B through an equivalent voltage source Vth in series connection by an equivalent resistance Rth.

This equivalent voltage Vth is the voltage acquired at terminals A-B of the network having terminals A-B open circuited.

This equivalent resistance Rth is the resistance acquired at terminals A-B of the network by all its independent current sources open circuited and each and every independent voltage sources short circuited.

4) Norton's theorem:

Norton's Theorem defines that 'any linear circuit having some energy sources and resistances can be substituted through a single constant current generator in parallel having a Single Resistor'.

Any linear electrical network having voltage and current sources and only resistances can be substituted at terminals A-B through an equivalent current source INO in parallel connection having an equivalent resistance RNO.

This equivalent current INO is the current acquired at terminals A-B of the network having terminals A-B short circuited.

This equivalent resistance RNO is the resistance acquired at terminals A-B of the network by all its voltage sources short circuited and each and every current source open circuited.

Maximum power transfer theorem:

The maximum power transfer theorem defines the given:

A load will obtain maximum power from a network if its total resistive value is precisely equivalent to the Thevenin's resistance of the network exerted to the load. That is,

RL = RTh

For loads joined directly to a dc voltage supply, maximum power will be delivered to the load if the load resistance is equivalent to the internal resistance of the source; that is, if:

RL = Rint

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