Week 5: Nodal Analysis

Nodal Analysis

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

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

Nodal Analysis without Voltage Sources

Steps to determine nodal voltages:

To apply the node voltage method to a circuit with n nodes (with m voltage sources), perform the following steps:

Select a reference node (usually ground) and name the remaining n-1 nodes.  Also label currents through each current source. 

-Assign a name to the current through each voltage source.  We will use the convention that the current flows from the positive node to the negative node of the source.

-Apply Kirchoff's current law (KCL) to each node.  We will take currents out of the node to be positive.

-Write an equation for the voltage each voltage source.

-Solve the system of n-1 unknowns.

Example:

Sample Problem

Nodal Analysis with Voltage Sources

In order to solve problems involving Nodal Analysis with Voltage Sources, We need to consider the following cases:

Case 1: If the voltage source (dependent or independent) is connected between two non-reference nodes, the two non-reference nodes form a generalized node or supernode, we apply both KCL and KVL to determine the node voltages.

Case 2: if a voltage source is connected between the reference node and a non-reference node, we simply set the voltage at the non-reference node equal to the voltage of the voltage source in figure 2 for example,

As you can see in Case 1, It said something about a "Supernode". You might be wondering "What is a supernode?", A supernode is:

-formed by enclosing a (dependent or independent) voltage source connected between two non-reference nodes and any elements connected in parallel with it.

Reflection:

In our Cpe Class this week, We reached a new chapter and as a first topic of this chapter, We discussed Nodal Analysis. In my own words, Nodal Analysis is basically a method of determining the voltages between nodes or more commonly known as "Nodal Voltages".  Nodal Analysis most of the time uses Kirchoff's Current Law (KCL) and as long as you follow the steps in solving it properly, then you will be able to solve the problem. For me, I think that Nodal Analysis is one of the most difficult topics I have encountered in this class because it requires extensive knowledge of our previous topics but I believe that if you study hard, Then nothing is hard to learn and you will be able to understand the lesson properly.

Video:

Nodal Analysis:

Nodal Analysis practice problems:

Supernode Problem:

Thank you for visiting my Blog!! The sixth post will be arriving next week. See ya!! 

“There must be a positive and negative in everything in the universe in order to complete a circuit or circle, without which there would be no activity, no motion”

-John McDonald

Week 4: Series-Parallel Circuit

 Series-Parallel Circuit

Series Circuits

What are Series Circuits?

Series Circuit- A series circuit has more than one resistor (anything that uses electricity to do work) and gets its name from only having one path for the charges to move along. Charges must move in "series" first going to one resistor then the next. If one of the items in the circuit is broken then no charge will move through the circuit because there is only one path. There is no alternative route. Old style electric holiday lights were often wired in series. If one bulb burned out, the whole string of lights went off.

What are Parallel Circuits?

Parallel Circuit- A parallel circuit is one that has two or more paths for the electricity to flow, the loads are parallel to each other. If the loads in this circuit were light bulbs and one blew out, there is still current flowing to the others because they are still in a direct path from the negative to positive terminals of the battery.

Difference between the two?

The parallel circuit has very different characteristics than a series circuit. For one, the total resistance of a Parallel Circuit is NOT equal to the sum of the resistors (like in a series circuit). The total resistance in a parallel circuit is always less than any of the branch resistances. Adding more parallel resistances to the paths causes the total resistance in the circuit to decrease. As you add more and more branches to the circuit the total current will increase because Ohm's Law states that the lower the resistance, the higher the current.

Voltage and Current Division

Voltage and Current division allow us to simplify the task of analyzing a circuit.

Voltage Division allows us to calculate what fraction of the total voltage across a series string of resistors is dropped across any one resistor.

Hence:

Current Division allows us to calculate what fraction of the total current into a parallel string of resistors flows through any one of the resistors.

Hence:

Reflection:

In the 4th week of our CpE 311 subject, I learned the two types of Electrical Circuits. These two are Parallel Circuits and Series Circuits. In a Series Circuit, All components are connected end-to-end and there is only one path for the current to flow. In a Parallel Circuit, All components are connected across each other forming exactly two sets of common points. Also in a Series Circuit, The current is equal for there is only one path while in a Parallel Circuit, The voltages are equal because the components are connected across each other. In our laboratory class, I have also learned to measure the voltages and current of a circuit by connecting the circuit in a Power Supply and using a Digital Multimeter to measure both values.

Video:

Series and Parallel Circuits

Voltage and Current Division

Thank you for visiting my Blog!! The fifth post will be arriving next week. See ya!!

“Electricity is actually made up of extremely tiny particles called electrons that you cannot see with the naked eye unless you have been drinking.”

-Dave Barry

Week 3: Nodes, Branches, Loops, & Kirchoff's Laws

Nodes, Branches, & Loops

What are Nodes, Branches, & Loops?

Branch- A branch represents a single element such as voltage source or a current source or a resistor.

Node- A node is the point of connection between two or more branches.

Loop- A loop is any closed path in a circuit.

Kirchoff's Current Law (KCL)

This fundamental law results from the conservation of charge. It applies to a junction or node in a circuit -- a point in the circuit where charge has several possible paths to travel.

In Figure 1, we see that IA is the only current flowing into the node. However, there are three paths for current to leave the node, and these current are represented by IB, IC, and ID.

Once charge has entered into the node, it has no place to go except to leave (this is known as conservation of charge). The total charge flowing into a node must be the same as the the total charge flowing out of the node. So:

IB + IC + ID = IA

Bringing everything to the left side of the above equation, we get

(IB + IC + ID) - IA = 0

Kirchoff's Voltage Law (KVL)

Kirchhoff's Voltage Law (or Kirchhoff's Loop Rule) is a result of the electrostatic field being conservative. It states that the total voltage around a closed loop must be zero. If this were not the case, then when we travel around a closed loop, the voltages would be indefinite. So:

In Figure 1 the total voltage around loop 1 should sum to zero, as does the total voltage in loop 2. Furthermore, the loop which consists of the outer part of the circuit (the path ABCD) should also sum to zero.

Resistor Color Code

We are able to use solve resistance by using the Resistor Color Code

Reflection:

In the 3rd week of our CpE 311 subject, I learned to identify the Nodes, Loops, & Branches of an Electric Circuit. I have also learned that according to Kirchoff's Current Law, A current that enters a circuit is equivalent to a current that leaves a circuit and lastly, I have also learned how to measure the resistance of a resistor using the Resistor Color Code that was discussed in our Laboratory Class.

Videos:

Nodes, Branches, & Loops:

 

Kirchoff's Current Law (KCL):

Kirchoff's Voltage Law (KVL):

I apologize for the delay of my submission. This is because of the non-stop electrical brownouts that keeps on happening in our area -_-" . Also, starting from this post, I will also be adding quotes in my blog. I believe these quotes will help me understand and be truly inspired at the beauty of our CpE 311 subject. Hope you enjoy them as much as I do :D Thank you for visiting my Blog once again and God bless to All XD.

A lot of words in English confuse the idea of life and electricity, like the word "Livewire".

-Laurie Anderson