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.