Thevenin's Theorem

Thevenin's Theorem

-States that"Any linear circuit containing several voltages and resistance can be replaced by just a single voltage in series with a single resistor".In other words, it is possible to simplify and Linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source in series with a resistance connected to a load

Example:

as far as the load resistor RL is connected, any network consisting of resistive circuit elements and energy source can be replaced by one single Equivalent resistence Rs and equivalent voltage Vs, where Rs is the source resistance value looking back into the circuit and Vs is the open circuit at the terminals.

For example:

 Consider the circuit from the previous section

First, we have to remove the center 40Ω resistor and short out all the emf's connected to the circuit, or open circuit any current sources. the value of Rs is found by calculating the total resistance at the terminal A and B with the emf's removed, and the value of the voltage required Vs is the total voltage across terminals A and B with an open circuit and no load resistor Rs connected.then we get the following circuit.

We now need to reconnect the two voltages back into the circuit, and as Vs=Vab the current flowing around the loop is calculated as:

so the voltage drop across the 20Ω resistor can be calculated as:

Vab=20 - (20Ω x 0.33A)= 13.33V 

then the thevenins Equivalent circuit is shown below with the 40Ω resistor connected.

and from this current flowing in the circuit is given as:

I=(13.33V/6.67 + 40)=0.286A

SUPERPOSITION

WHAT IS SUPERPOSITION?

-is a another algorithm circuit analysis method, with a prescribed procedure, like the node voltage or loop current method

-it applies on;y in circuits with 2 or more independent sources.

The superposition procedure

1. make a partial circuit by choosing one source to keep and turning of all the other independent sources.

2. Solve this "partial circuit" for the quantities of interest. Use whatever techniques are applicable to the partial circuit.

3. Go back to the original and create another circuit by choosing another source to keep (different than the first one) and turning off all the other sources in the circuit.

4. Solve the second partial circuit for the quantities of interest.

5. Repeat the process until each independent source has been used in partial circuit

6. Sum up all the partial results to get total results for the quantities of interest 

If there are n independent sources in a circuit, then when using superposition, you would expect to solve n partial circuit and find n partial results for the whatever you are looking for 

Example of the superposition method

Consider the circuit below. It has one voltage source and one current source, and we are asked to find the voltage VR2.

1. Choose one source. It doesn't matter which, so start with the voltage source. Turn off the current source (make it open circuit) to create the first partial circuit.

2. Solve the partial circuit

3. Now turn off the voltage source (by using it out) and keeping the current source.

4. Solve the partial circuit

5. Sum the partial solution to get total solution:

     

MESH ANALYSIS

What is mesh analysis?

Branch
-This is a circuit elements that connected two nodes

Loop
-This a closed path in a circuit. A set of these loops are used to create constraint equations.


Mesh
-A loop passing though at least on branch
Basic rule: The sum of voltage around any loop must be Zero.(from KVL) 

Manual Mesh/Loop Analysis algorithm:

* Choose a conventional current flow

* Identify and Number Loops or meshes

* Apply KVL to identified mesh and formulate circuit equation

* Create Matrix system from KVL equation obtained

* Solve matrix for unknown Mesh Currents by using Cramer's rule

* Uses solved Mesh Currents to solve for the desired circuit entity

Example:

Consider this figure with the following Parameter:

V1 = 15 V

V2 = 7 V

R1 = 2

R2 = 20

R3 = 10

R4 = 5

R5 = 2

R6 = 2

Find current through R3 using mesh analysis method
solution:

-We can see that there are three closed paths (loop) where we can apply KVL in, Mesh 1,2 and 3 as shown in the figure
- We can now apply KVL around the Mesh remembering Passive Convention When defining Currents and Voltages 

WYE TO DELTA

WHAT IS DELTA-WYE?

DELTA -WYE - is a type of three phase electric power transformer design that employs delta-connected windings on its primary and wye/star connected windings on its secondary.

example:

to solve DELTA-WYE

to solve WYE-DELTA

NODAL ANALYSIS

What is NODAL ANALYSIS?

Nodal Analysis

  - provides a general procedure for analyzing circuits using voltage as the circuits variable.choosing node voltages instead of element voltage as circuits variable is convenient and reduces the number of equations one must solve simultaneously. To simply matters, we shall assume in this section that circuits do not contain voltage source.

Example: use nodal analysis to find the voltage at each node of the circuit.

NOTE: that pair of nodes at the bottom is actually 1 extend node and the number of node is 3


I will number the nodes as shown below haha

- then i will choose node 2 as the reference node and assign it a voltage of zero

-then write down KCL for each node. use V1 the voltage node 1, V3 at node 3, and remember that V2=0. the result is the following system of equations:

The first equation results from KCL applied ate node 1 the second equation results from KCL applied at node 3. collecting terms this becomes:

this form for the system of equation could have been gotten immediately by using the inspection method.

solving the system of equation using elimination methods gives following voltage:

V1=68.2 and V2=27.3 volts

awesome!!!!

Week poor ^_^ lols

What are series and parallel circuits?????

Series circuits

  - all components are connected end to end, forming a single path for electrons to flow

 sample of series connections:

Formula for the series circuits:


*If the sum of the potential drops is equal to the 
potential rise of the source

     V_T= V_R1 + V_R2 + V_R3 ….

*If the current is the same everywhere in the series 

 circuits

          I_Total = I₁ = I₂ = I₃ = 

*If the total resistance of the circuits is equal to the

 sum of the individual resistances.

         R_Total = R₁ + R₂ + R₃ …

Parallel circuits

 - a parallel circuits has two or more paths for current flow

  example:

  

 Consider this figure with a two resistor R₁

And R₂ connected in parallel: 

And consider an equivalent figure with

One resistor R_T

then

  By KCL, I_T = I₁ + I₂           and by ohm’s law,

   Or I_T = V/R₁ + V/R₂            I_T = V/R_T

    But for equivalent circuits, V is the same

                    For the different Figures

         So, the equivalent total resistance for

         Resistor in parallel is given by the formula:

                1/R_T = 1/R₁ + 1/R₂ + …1/R_n

                               parallel

     
Also note from the 1^st figure that:

  I = V/R  but  V_T = I_TR_T

  Thus I₂ = I_TR_T/R₂

                Where 1/R_T = 1/R₁ + 1/R₂

This is called the Current Divider Rule

  And is usually written:

I _X= I_T(R_T/R_x)

Week Three ^_^

How to determine the number of nodes, branches and loops in a circuit?


 *Node - a point or junction where two or more circuit's elements (resistor,capacitor,inductor etc) meet is called node

 *Branch - that part or section of circuit which locate between two junctions is called branch in a branch, one or more elements can be connected and they have two terminals.


 *Loop - a closed path in circuit where more than two meshes can be occurred is called loop.

Finding node in a circuits

Finding branches in a circuits

Finding loops in a circuits

====================================

    Kirchhoff's Law 

Kirchhoff's Current Law (KCL)
 - This is Kirchhoff's First law
 - The sum of all currents that enter an electrical circuit junction is 0. when the currents enter junction is positive sign and the current that leave the junction have negative sign:

                  ∑ I_IN = ∑ I_OUT


example:

           

I₁ + I₂ + I₃ = I₄ + I₅

Kirchhoff's Voltage Law (KVL)

 - This is Kirchhoff's second law

 - States that the sum of the voltage in a closed 

   loop is always equal to zero

                     ∑ V = 0

example:

                  V₁ + V₂ + V₃ + V₄ = 0

Learning's :

                    Wow!!, its awesome,

        where should i start?, By the way i learned so many things this past few weeks in our circuits 1, but this week it took me to long to understand our new topic the "kirchhoff's law" and definitely i learned how to find the nodes, branches and loops in a circuit.