Nodal Analysis With Voltage Source

Nodal Analysis With Voltage Source

There are three things which we should consider before doing the nodal analysis;

First: We should identify and point out how many nodes are present in the circuit given.

Second: If a supernode is present, consider in mind that a supernode has no voltage identified as its own.

Third: Put a reference node. 

Remember that voltage source affects the nodal analysis and we should analyze the possibilities and the pros and cons. There are cases to be followed especially in doing the analysis of the nodes.

CASE 1.

        If the voltage source is connected between the reference node and non-reference node, the non-reference node is equal to the voltage source.

CASE 2.

        If the voltage source is connected into two non-reference node. The non-reference node is called a SUPERNODE.

* KCL and KVL are to be applied to determine the voltages on that par

There are three nodes present in this circuit. Nodes V1, V2, & V3.

Defined from our last blog, a supernode means closed surface connected with a voltage source and two nodes.

Therefore, the node formed V2 & V3 is called a SUPERNODE.

NODAL ANALYSIS WITH CURRENT SOURCES

GOOD DAY! :)


First of all, we want to introduce to you this new topic in our blog.


WHAT IS A NODAL ANALYSIS?

A nodal analysis is a method of determining or identifying the voltage or the potential difference between the nodes in an electric circuit in terms of the branch currents. In this case, choosing a node voltage is easier than choosing other elements as current variables.


WHAT IS A NODE?

A node is a point where elements or branches are connected.


WHAT ARE THE STEPS IN DETERMINING NODE VOLTAGES?

STEP 1. Choose a node as the reference node. A reference node is a node with 0 potential.

STEP 2. Assign voltages V1, V2... Vn-1 to the remaining n-1 nodes. The voltages are referenced with respect to the reference node.

STEP 3. Apply KCL to each of the n-1 non-reference nodes. Use Ohm's law to express the branch currents in terms of node voltages.

STEP 4. Solve to determine the unknown node voltages. Use substitution method or Cramers rule.

Wye - Delta Transformation

G'day, mates :)

This is the continuation of our previous blog last week. So, if you start wondering what are these triangles and y's doing in the circuit here's why:

The transformation is used to establish equivalence for networks with three terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedance. For equivalence, the impedance between any pair of terminals must be the same for both networks. 

Now, I will start answering the questions from your curious, little minds. HOW TO TRANSFORM A CIRCUIT FROM Wye to Delta, and vice-versa Delta to Wye? 

Detailed equations and formulas are to be precisely used  to get the value on y's and on deltas. So, to all the clumsy and happy-go-lucky mates out there, this is a big perimeter-securing on your part.

DELTA to Y:

Formula in getting the Y-values are the following:

R1 = RbRc / (Ra+Rb+Rc)

R2 = RaRc / (Ra+Rb+Rc)

R3 = RaRb / (Ra+Rb+Rc)

There's a technique in doing this without using any formula, if you're asked to get the y-value the resistors which are on its adjacent sides are to be multiplied then divide it to the sum of all the resistors in the circuit. TAKE NOTE: "ADJACENT".

Y to DELTA:

Ra = (R1R2+R2R3+R3R1) / R1

Rb = (R1R2+R2R3+R3R1) / R3

Rc = (R1R2+R2R3+R3R1) / R2

Some say that Y to DELTA is very complex because some circuits in WYE-DELTA TRANSFORMATION are placed in neither parallel nor series connections.

If you have doubts about our blog please try to solve this diagram and mail us at dominiclargo@gmail.com. THANK YOU. GOODBYE.

      

Wye and Delta and Combination Circuits

Wye & Delta Connection and Combination Circuits. What is the first thing that comes to your mind when you hear these? Well, let me tell you mine - Connections! Yes, connections were our topic for the week and as promised, we will share with you our learnings here in our blog.


Combination Circuits - A connection of a circuit that can either be a series or a parallel connection that are combined.

Wye and Delta Connection - A connection that is neither a parallel nor a series connection.


Now, we will focus first on combination circuits then the latter.

Combination circuit (notice the presence of series and parallel connections)

Process:

1. Find Req of both series and parallel connections
2. Find total resistance
3. Find current voltage

We ought to find the total resistance so the process would be combining the series and parallel connections or also known as the "resistance equivalent". The R2 and R3 are connected in a series connection, thus, we are able to add the two resistors to find the resistance equivalent.

(Refer to the previous article for the formulas)

Req = 8Ω + 4Ω = 12Ω

We have one series connection and two parallel connections which are 6Ω and two 12Ω, respectively. Next process is to obtain the resistance equivalent of the two parallel resistors.

1/Req = 1/12Ω + 1/12 Ω = 6Ω

Now we have two series connected resistors and these two can be summed up to arrive to the Req of the whole circuit.

Req = 6Ω + 6Ω = 12Ω

Last thing we do is to find the current flowing through the circuit by using Ohm's Law (you can also apply KVL and KCL, whichever you find easy).

i = V/R

i = 12V / 12Ω

i = 1 ampere

As long as you understand the illustration and know the formula, it will be as easy as eating - no sweat plus, you enjoyed!

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The Wye connection joins together one end of each of the coils and applies the individual phases to the open ends. These two connections produce very different results when power is applied.

An advantage of the Delta connection is it has a higher reliability. If one of the three primary windings fails, the secondary will still produce a full voltage on all three phases.

(to be continued...)