Mesh or Loop Analysis For Electric Circuits

This is also called Loop Analysis.This method uses simultaneous equations, Kirchhoff's Voltage Law, and Ohm's Law to determine unknown currents in a network.

Mesh Analysis only works for planar circuits :circuits that can be drawn on a plane (like on a paper) with out any elements or wires cossing each other. In some cases a circuit that looks nonplanar can be made in to a planar circuit by moving some of the connecting wires.

The first step in the mesh Current method is to identify "loops" with in the circuit encompassing all components. Represent all the loops with different loop currents in one direction.The choice of each loop current's direction is entirely arbitrary.

The next step is to label all voltage drop polarities across resistors according to the assumed directions of the mesh currents.

Next write the KVL equations for each mesh and solve all the equations for mesh (loop)currents.

Example :



KVL equation for Loop1 : -28 + 2(I1+I2) + 4*I1 =0.
KVL equation for Loop2 : -2(I1+I2) + 7 - 1I2=0.Solving these 2 equations we get I1=5A I2=-1A.
The solution of -1 amp for I2 means that our initially assumed direction of current was incorrect. In actuality, I2 is flowing in a counter-clockwise direction at a value of (positive) 1 amp.

For additional information click on the below links :
http://www.allaboutcircuits.com/vol_1/chpt_10/3.html
http://utwired.engr.utexas.edu/rgd1/lesson07.cfm
www.eas.asu.edu/~holbert/ece201/ECE201Lect-10.ppt
http://www.ibiblio.org/kuphaldt/socratic/output/dcmesh.pdf ----- Practice Problems
http://www.analyzethat.net/78_loop_circuit_analysis.php --- Loop circuit analysis examples

Kirchhoff 's Voltage Law or Kirchhoff 's loop rule

This law is also called Kirchhoff 's loop rule. It is a consequence of the principle of conservation of energy. It states that " The algebraic sum of the potential differences around a circuit must be zero".

Considering that electric potential is defined as line integral of electric field, Kirchhoff's voltage law can be expressed equivalently with equation

For more information on this topic see the below links :

www.allaboutcircuits.com/vol_1/chpt_6/2.html

www.eas.asu.edu/~holbert/ece201/kvl.html

www.wisc-online.com/objects/index.asp?objID=DCE3002 --- online example

www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.KVL.html

www.wisc-online.com/objects/index.asp?objID=DCE5303 ---- Practice Problems

Kirchhoff 's Curent Law (KCL)

This law is also called Kirchhoff's junction rule or Kirchhoff's point rule. This law states that " At any point in an electrical circuit where charge density is not changing in time, the sum of currents flowing towards that point is equal to the sum of currents flowing away from that point.

A charge density changing in time would mean the accumulation of a net positive or negative charge, which typically cannot happen to any significant degree because of the strength of electrostatic forces: the charge buildup would cause repulsive forces to disperse the charges.

For more information on this visit the following links :

www.allaboutcircuits.com/vol_1/chpt_6/4.html

www.wisc-online.com/objects/index.asp?objID=DCE3102 ---- Online Example

www.eas.asu.edu/~holbert/ece201/kcl.html

www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.KCL.html

www.wisc-online.com/objects/index.asp?objID=ACE1302

www.wisc-online.com/objects/index.asp?objID=DCE5203 ----- Practice Problems

Dependent Voltage (Current) Sources

Dependent Voltage Sources :
Some voltage (current) sources have their voltage (current) values proportional to some other voltage or current in the circuit. They are called dependent voltage (current) sources or controlled voltage (current) sources.Thus there are 4 types of dependent sources.

1. Voltage dependent voltage source

2. Current dependent voltage source

3. Voltage dependent current source

4. Current dependent current source.
Variables in brackets are the controlling variables whose values affect the value of the source.

Independent Voltage and Current Sources

Independent Voltage Source :
An independent voltage source maintains a voltage (fixed or varying with time) which is not affected by any other quantity.

Independent Current Source :
An independent current source maintains a current (fixed or time-varying) which is unaffected by any other quantity.

DC Voltage Source

DC Voltage Source :

A voltage source is any device or system that produces an electromotive force between its terminals OR derives a secondary voltage from a primary source of the electromotive force.

An ideal voltage source is a theoretical circuit component that supplies a fixed potential difference across its terminals that is completely independent of the current it supplies.

DC Current Source

DC Current Source :
A current source is an electrical or electronic device that delivers or absorbs electric current. Current sources can be theoretical or practical. A current source is the dual of a voltage source.

An ideal current source is a conceptual source used in network theory and analysis that delivers or absorbs electrical energy such that the electrical current is independent of the voltage across its terminals.

Ohm's Law

Ohm's Law :

Ohm's law states that, At constant temperature, in an electrical circuit, the current passing through a conductor, from one terminal point on the conductor to another terminal point on the conductor, is directly proportional to the potetial difference (i.e. voltage drop or vltage) across the two terminal points and inversely proportional to the resistance of the conductor between the two terminal points.

In mathematical terms this is written as :
I=V/R,

where I is the current, V is the potential difference, and R is a constant called the resistance. The potential difference is also known as the voltage drop, and is sometimes denoted by E or U instead of V.

For more information on this vsit the following sites :

http://utwired.engr.utexas.edu/rgd1/lesson01.cfm

http://en.wikipedia.org/wiki/Ohm's_law

http://www.csgnetwork.com/ohmslaw.html --- Ohm's law calculations

Linear,Nonlinear,Active and Passive elements

Linear elements :
In an electric circuit, a linear element is an electrical element with a linear relationship between current and voltage. Resistors are the most common example of a linear element; other examples include capacitors, inductors, and transformers.

Nonlinear Elements :
A nonlinear element is one which does not have a linear input/output relation. In a diode, for example, the current is a non-linear function of the voltage.Most semiconductor devices have non-linear characteristics.

Active Elements :
The elements which generates or produces electrical energy are called active elements. Some of the examples are batteries, generators,transistors,operational amplifiers,vacuum tubes etc.

Passive Elements :
All elements which consume rather than produce energy are called passive elements, like resistors,inductors and capacitors.

Current,Voltage and Potential difference

Current :
The rate of flow of electrons through a circuit is defined as current . In general current is denoted with "I or i".The unit of current is coulombs/sec which is called as "amperes(A)".

Voltage or Potential:
Voltage is measure of the work required to move charge from one point to another in electric field. Its unit is Joules/Coloumb called as Volt (V). V=w/q.

Potential difference :
(i) the difference in electrical potential between two points in a circuit expressed in volts(V).
(ii) the difference in electrical charge between two points in a circuit expressed in volts(V).

Branch,Node,Graph,Electrical engineering

Branch :
A direct path joining two nodes of a network or graph is called branch.

Node :
A terminal of any branch of a network or an interconnection common to two or more branches of a network.

Graph :
A graph is that one which shows the geometrical interconnection of the elements of a network.

Electrical engineering :The branch of engineering that deals with the technology of electricity, especially the design and application of circuitry and equipment for power generation and distribution, machine control, and communications.

Electrical Circuit,Electrical Network,Bilateral Circuit,loop,mesh

Electrical Circuit :
An electrical circuit is a closed conducting path through which electric current either flows or is intended to flow.

Electrical Network :
An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches. It may not be a closed path.Thats why an electrical circuit is a network but not vice versa.

Bilateral Circuit :
A circuit whose properties remains same in either directions is called bilateral circuit.

Loop :
A closed electric circuit is called a loop. It may or may not contain any closed path in it.

Mesh :
A mesh is a set of branches that forms a closed path in a network and which contains no closed path in it. A mesh can be called as a loop but not vice versa.

Alternating Current

Alternating Current :

Electric current that reverses direction periodically, usually many times per second. Electrical energy is ordinarily generated by a public or a private utility organization and provided to a customer, whether industrial or domestic, as alternating current.
One complete period, with current flow first in one direction and then in the other, is called a cycle.Household utility current in most countries is AC with a frequency of 60 hertz (60 complete cycles per second), although in some countries it is 50 Hz.
A waveform is a representation of how alternating current (AC) varies with time. The most familiar AC waveform is the sine wave, which derives its name from the fact that the current or voltage varies with the sine of the elapsed time. Other common AC waveforms are the square wave, the ramp, the sawtooth wave, and the triangular wave. Their general shapes are shown .

For more details on this topic visit the below site :

http://www.kpsec.freeuk.com/acdc.htm

What is Direct Current ?

Direct Current :

Electric current which flows in one direction only through a circuit or equipment. The associated direct voltages, in contrast to alternating voltages, are of unchanging polarity. Direct current corresponds to a drift or displacement of electric charge in one unvarying direction around the closed loop or loops of an electric circuit. Direct currents and voltages may be of constant magnitude or may vary with time.

For more detailson this topic see the following site :
http://www.kpsec.freeuk.com/acdc.htm

Electric Power

Electric Power :
(electricity) The rate at which electric energy is converted to other forms of energy, equal to the product of the current and the voltage drop.

power, electric, energy dissipated in an electrical or electronic circuit or device per unit of time. The electrical energy supplied by a current to an appliance enables it to do work or provide some other form of energy such as light or heat. Electric power is usually measured in Watts,kilowatts (1,000 watts), and megawatts (1,000,000 watts). The amount of electrical energy used by an appliance is found by multiplying its consumed power by the length of time of operation. The units of electrical energy are usually watt-seconds (joules), watt-hours, or kilowatt-hours. For commercial purposes the kilowatt-hour is the unit of choice.

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