NORTON'S THEOREM

Any two terminal linear bilateral dc network can be replaced by an equivalent circuit consisting of a current source and a parallel resistor as shown in figure. 

 

The steps leading to the values of IN and RN are listed:

 

1. Remove that portion of the network across which the Norton equivalent circuit is to be found 

2. Mark the terminals of the remaining two terminal network (a,b). 

3. Calculate Rn by first setting all sources to zero (voltage sources are replaced with short circuits and current sources with open circuits) and then finding the resultant resistance between the two marked terminals. (If internal resistance of the voltage and/or current sources is included in the original network it must remain when the sources are set to zero). 

 4: Calculate In by first setting all sources to their original position and then finding the short circuit current between the marked terminals. 

5. Draw the Norton equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit. 

Series-Parallel Circuits.

Two elements are in series if they exclusively share a single node (and thus carry the very same current).
Components that are in parallel, on the other hand, share the same two nodes.

Nodes are connection points between components.

The nodes are labelled "a", "b", and "c". This basic knowledge forms the basis for circuit analysis.
Series components have the same current flowing through them, and parallel components have the same voltage across them. The following example shows the steps involved in using this knowledge to solve electrical circuit network problems.

Step (1):
Simplify the circuit in a step-by-step fashion by combining groups of resistors in series or parallel to an equivalent single resistor, thereby producing an equivalent circuit which can be more easily solved.

For the example shown,two combinations will be required.

Step (2):
Solve the simplified circuit by application of the basic rules for either a series or a parallel circuit.

For the example, applying the basic rules of series circuits and using Ohm's Law, we can solve for the current flow through and voltage drop across each element.

Applying Ohm's Law for the whole circuit,

Recalling the Rule for a simple series circuit from the Series-Resistance section

Then applying Ohm's Law to each element

Step (3):
Using the information from the equivalent circuit, work backwards in a step by step process towards the original circuit. For the example problem this will require two steps.

(3a) Knowing the voltage drop across R₂₃₄ = 30 V, we see the voltage across the two parallel resistors R₂ and R₃₄ is 30 V. Therefore, we can solve for the current flow through each of the resistors.

(3b) Knowing the current flow through R₃₄ = 1.5 amp, we now know the current flow through each of the two resistors (R₃ and R₄) in the series must be 1.5 amp. Therefore, we can solve for the voltage drop across each of the two resistors.

We have now successfully solved for the current flow through and the voltage drop across each element of the series-parallel combination circuit.

Kirchoff’s Voltage Law and Example

Kirchoff’s Voltage Law

Kirchoff’s Voltage Law (KVL) states that the algebraic sum of the voltages across any set of
branches in a closed loop is zero.

Note that a current direction must have been assumed. The assumed current creates a voltage
across each resistor and fixes the position of the “+” and “-” signs so that the passive sign convention
is obeyed. The assumed current direction and polarity of the voltage across each resistor must be in agreement with the passive sign convention for KVL analysis to work.

Consider the following worked Example.

Magnetic Circuit Calculations

The calculations involved in magnetic circuit are analogous to electric circuits with flux being analogous to current, mmf to emf and resistance to reluctance.

Superposition Theorem

The superposition theorem states that: In a multi-source linear circuit,  the current through or voltage across any element in the circuit is the sum of the currents or voltages produced by each source acting independently.

To calculate the contribution of each source, all the other sources must be removed. To remove the source, a voltage source is replaced by a short circuit or its internal resistance if given, and a current source is replaced by an open circuit or its parallel internal resistance if given.

When you sum the contributions from the sources, you should be careful to take their signs into account. It is best to assign a reference direction to each unknown quantity, if it is not already given. 

The total voltage or current is calculated as the algebraic sum of the contributions from the sources. If a contribution from a source has the same direction as the reference direction, it has a positive sign in the sum; if it has the opposite direction, then a negative sign.

In order to use the superposition theorem with circuit currents and voltages, all of the components must be linear; that is, for all resistive components, the current must be proportional to the applied voltage (satisfying Ohm’s law).

Note that the superposition theorem is not applicable to power, since power is not a linear quantity. The total power delivered to a resistive component must be determined using the total current through or the total voltage across the component and cannot be determined by a simple sum of the powers produced by the sources independently.

The example below illustrates this principle.  To enable studying, the solution has been written in the short cut form but if explanations are required, they will be given per request.

Electrical and Electronic Engineering Fields of Study

Power:

Creation, storage, and distribution of electricity

Control:

Design of dynamic systems and controllers for the systems

Electronics/Microelectronics:

Design of integrated circuits, microprocessors, etc

Signal Processing: Analysis of signals

Telecommunications:

Design of transmission systems (voice, data)

Computer:

Design and development of computer systems

Instrumentation:

Design of sensors and data acquisition equipment

Jog your memory with these basic Multiple choice Electrical Engineering Questions.

Choose correct or the best alternative in the following:

Q.1 The “Superposition theorem” is essentially based on the concept of
 (A) duality. (B) linearity.
 (C) reciprocity. (D) non-linearity.

 Ans: B

Q.2 Cells are connected in parallel in order to
(A) increase the voltage available. (B) reduce cost of wiring.
(C) increase the current available. (D) reduce the time required to fully
 charge them after use.
 Ans: C

Q.3 The power factor of a purely resistive circuit is
 (A) zero. (B) unity.
(C) lagging. (D) leading.

 Ans: B

Q.4 The power taken by a 3-phase load is given by the expression
 (A) V 3 L I L cos φ . (B) V 3 L I L cos φ .
(C) V 3 L I L sin φ . (D) V 3 L I L sin φ .

 Ans: B

Q.5 Which of the following generating stations has the minimum running cost?
 (A) hydro-electric station. (B) nuclear power station.
(C) thermal power station. (D) diesel power plant.

 Ans: A

Introduction to Electric and Electronic Engineering forum.

After some years of working in the academic field both as a student, a tutor, a researcher and a lecturer, I found it good to start a blog where we help each other in tackling most of the questions that students are asked in their engineering studies. We focus mainly on the electrical and electronic engineering field.

I hereby invite authors so that we can assist each other with questions and answers. Any interested person can send me an email and we can see how we can go around this. I have a big pool of questions and answers for electrical and electronic engineering levels up to undergrad. For Masters guys, we like you to be authors as well.

The response that I get from this will tell me if its a good venture. Share with others.

In the photo we were introducing RFID technology in Zimbabwe, showing off our RFID projects in Harare. The first project uses RFID technology for toll gates, the second one uses the technology in supermarkets for scanning good purchased and the most recent one uses the technology in libraries.

More to come

Snow came rather too early in Cape Town.

Cape Town is well known for its harsh winter season and for those who love travelling, winter is rather a reserved choice to visit Cape Town. The snow is normally seen late in September and this signifies the end of the winter season. However, 2014 seems to have its own ways, just like the soccer world cup which is full of surprises. The picture above shows snow at the top of one of the mountains in Stellenbosch, south Africa.

As one leaves the Du Toit train station torwards the Stellenbosch University, the snow was clearly visible and pedestrians had tough times with the cold.

Everyone was taken by surprise because this is a rare occurrence. However, for some it was a blessing in disguise because they may not have seen the snow on this mountain especially in June.

This scenario comes as a warning to travelers. When you are in Cape Town, you have to watch the weather forecast on daily basis because it can change unexpectedly. For those with smart phones it is even more advisable to check the hourly changes.

I remember that the weather once caught me by surprise one day and from there on I knew why people keep jackets in their offices even when it is hot. It comes quickly like scores in Spain's first 2014 world cup game.

Cheers. see you here.