BLOG 5 - ELECTRICAL CIRCUIT 1

Nodal analysis

Kirchhoff's current law is the basis of 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, I_branch = V_branch * G, where G (=1/R) is the admittance (conductance) of the resistor.

Nodal analysis is possible when all the circuit elements' branch constitutive relations have an admittance representation. Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer. Because of the compact system of equations, many circuit simulation programs (e.g. SPICE) use nodal analysis as a basis. When elements do not have admittance representations, a more general extension of nodal analysis, modified nodal analysis, can be used.

While simple examples of nodal analysis focus on linear elements, more complex nonlinear networks can also be solved with nodal analysis by using Newton's method to turn the nonlinear problem into a sequence of linear problems.

Steps to determine node voltages:

1. Select a node as the reference node. Assign voltage v1, v2,...., vn-1 to remaining n - 1 nodes. The voltages are referenced with respect to the reference node.

2. 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.

3. Solve the resulting simultaneous equations to obtain the unknown node voltages.   

• Current flows from a HIGHER POTENTIAL to a LOWER POTENTIAL in a resistor.

i = vhigher - vlower / R

Nodal analysis with voltage sources

Nodal analysis is the method to determine voltage or current using nodes of the circuit. In nodal analysis we choose node voltage instead of element voltages and hence the equations reduces in this process. We have to consider voltage source is not in this circuit. We have to solve a circuit with n nodes without voltage sources. To solve a circuit using nodal analysis method you must have good knowledge about node branch loop in a circuit. If you have no clear idea read the article then come back here. There are three steps to solve a circuit using nodal analysis

1. Select a node as a reference node. Give names v₁, v_2,…. v_n-1 to remaining n-1 nodes. All the voltages are the referenced voltages respecting to the reference node.

1. Apply KCL and KVL to each non reference node. To express the branch currents in terms of node voltages us ohm’s law.

1. Solve the equations to get unknown node voltages.

First step is to select a reference node. It is also called datum node. The reference node commonly called the ground. It has zero potential.

In circuit the reference node is denoted by any of the three symbols in figure 1. Figure 1 (c) is called a chassis ground because it is used in the case chassis act, enclosure as a reference point in the circuit. Figure 1 (a) and (b) are used when the potential of the earth taken as reference. I use symbol (b).

In two cases nodal analysis can be done with voltage sources.

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,

                                   v₁ = 20V

What is 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.

In figure 2 node 2 and node 3 form a supernode. Applying KCL at super node which are node 2 and 3 we get,

                                        i₁ + i₄  = i₂ + i₃

To apply KVL redrawing the figure 2 circuit to figure 3 and going around the loop in the clockwise direction gives,

                       – v₂ + 10 + v₃ = 0

                        Or  v₂ – v₃ = 10      ————————— (ii)

From equation (i),(ii) we will obtain node voltages using any solution method.

                              

BLOG 4 - ELECTRICAL CIRCUIT 1

THIS BLOG CONTAIN ABOUT SERIES AND PARALLEL RESISTOR

Resistors in Series

   Resistors are said to be connected in Series, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.

Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:

 

In the following example the resistors R₁, R₂ and R₃ are all connected together in series between points A and B with a common current, I flowing through them.

Series Resistor Circuit

 

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, R_T of the circuit must be equal to the sum of all the individual resistors added together. That is

and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, R_EQ is therefore given as:

 R_EQ = R₁ + R₂ + R₃ = 1kΩ + 2kΩ + 6kΩ = 9kΩ

Equivalent resistance  

Equivalent resistance of any number of resistors connected in series is the sum of the individual resistance.

Resistors in Parallel

Resistors are said to be connected together in “Parallel” when both of their terminals are respectively connected to each terminal of the other resistor or resistors. Unlike the previous series resistor circuit, in a parallel resistor network the circuit current can take more than one path as their are multiple nodes. Then parallel circuits are current dividers.

Since there are multiple paths for the supply current to flow through, the current is not the same at all points in a parallel circuit. However, the voltage drop across all of the resistors in a parallel resistive network is the same. Then, Resistors in Parallel have a Common Voltage across them and this is true for all parallel connected elements.

So we can define a parallel resistive circuit as one where the Resistors are connected to the same two points (or nodes) and is identified by the fact that it has more than one current path connected to a common voltage source. Then in our parallel resistor example below the voltage across resistor R₁equals the voltage across resistor R₂ which equals the voltage across R₃ and which equals the supply voltage. Therefore, for a parallel resistor network this is given as:

 

In the following resistors in parallel circuit the resistors R₁, R₂ and R₃ are all connected together in parallel between the two points A and B as shown.

Parallel Resistor Circuit

 

In the previous series resistor network we saw that the total resistance, R_T of the circuit was equal to the sum of all the individual resistors added together. For resistors in parallel the equivalent circuit resistance R_T is calculated differently.

Here, the reciprocal ( 1/R ) value of the individual resistances are all added together instead of the resistances themselves with the inverse of the algebraic sum giving the equivalent resistance as shown.

Parallel Resistor Equation

 

Then the inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistances. The equivalent resistance is always less than the smallest resistor in the parallel network so the total resistance, R_T will always decrease as additional parallel resistors are added.

Parallel resistance gives us a value known as Conductance, symbol G with the units of conductance being the Siemens, symbol S. Conductance is the reciprocal or the inverse of resistance, ( G = 1/R ). To convert conductance back into a resistance value we need to take the reciprocal of the conductance giving us then the total resistance, R_T of the resistors in parallel.

We now know that resistors that are connected between the same two points are said to be in parallel. But a parallel resistive circuit can take many forms other than the obvious one given above and here are a few examples of how resistors can be connected together in parallel.

Equivalent Conductance

Equivalent conductance of resistors connected in parallel is the sum of their individual conductance.

Equivalent Resistance

Equivalent resistance of two resistor is equal to the product of their resistance divided by their sum.

LABORATORY

Objective:

• To measure the voltage and current in a resistor.

Materials:

• DC Power Supply 

• Digital Multimeter

• Resistor

• Breadboard 

Overview and learning 

   Last Monday we had our quiz it was about ohms law, kirchhoff’s current law (KCL) and kirchhoff’s voltage law (KVL). On the next day we had our laboratory experiment and some of our classmates discussed about bread boarding on how to use. My group mates also discussed about we had our experiment and use material such dc power supply, digital multi meter, connection wires, resistor and bread boarding. We measure voltage and current in order to know if it flows to the bread board. I also learned how to put a resistor and connecting wire in the bread board correctly. Last Wednesday our professor discussed about the series and parallel resistor and last Friday we had our seatwork and it was about parallel and series resistor.   

BLOG 3 - ELECTRICAL CIRCUIT 1

THIS BLOG CONTAIN ABOUT NODE, BRANCHES, LOOP, KCL and KVL.

BRANCHES - represent a single element such a voltage source or a resistor.

NODE - is the point of conduction between two or more branches.

LOOP - is any closed path in a circuit.

Gustav Kirchhoff
Gustav Kirchhoff
Born	Gustav Robert Kirchhoff 12 March 1824 Königsberg, Kingdom of Prussia (present-day Russia)
Died	17 October 1887 (aged 63) Berlin, Prussia, German Empire (present-day Germany)
Residence	Prussia/German Empire
Nationality	Prussian
Fields	Physics Chemistry
Institutions	University of Berlin University of Breslau University of Heidelberg
Alma mater	University of Königsberg
Doctoral advisor	Franz Ernst Neumann
Doctoral students	Max Noether Ernst Schröder
Known for	Kirchhoff's circuit laws Kirchhoff's law of thermal radiation Kirchhoff's laws of spectroscopy Kirchhoff's law of thermochemistry
Notable awards	Rumford medal (1862) Davy Medal (1877)

KIRCHHOFF’S LAW or (KCL) – state that the algebraic sum of current entering a node (or a closed boundary) is zero.

Mathematically, KCL implies that         

 

Where N is the number of branches connected to the node and in is the nth current entering (or leaving) the node.

KIRCHHOFF’S VOLTAGE LAW or (KVL) – states that the algebraic sum of all voltages around a closed path (or loop) is zero.

                                                         

Expressed mathematically, KVL states that

 

Where M is the number of voltages in the loop (or the number branches in the loop)  andVm is the mth voltage.

OVERVIEW:

       On Monday June 30, 2014 our professor Mr. Jay S Villan is not around in our class but they have a substitute professor to take in charge the class of Mr. Jay S. Villan. The take in charge professor give a seat work on our class. On Tuesday we have a laboratory class and our professor give a work to discuss the deferent color of resistor. We get the result of our group calculation using the only the solving and we get the result of the resistor using the digital multimeter. We compared the result using solving and the result of multimeter. The title of experiment in this laboratory experiment is resistor color code and measurement of resistance. On Wednesday this is the start of our discussion and the topic that discussed of our professor is all about node, branches, and loop and the kirchhoff’s law. On Friday our professor give another seat work and this seat work is so hard to solve and get the answer.