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ELECTRICAL CIRCUIT ANALYSIS TECHNIQUES


In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit. From these nodal voltages the currents in the various branches of the circuit are easily determined.In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit. From these nodal voltages the currents in the various branches of the circuit are easily determined.

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The Mesh Current Method is quite similar to the Branch Current method in that it uses simultaneous equations, Kirchhoff’s Voltage Law, and Ohm’s Law to determine unknown currents in a network. It differs from the Branch Current method in that it does not use Kirchhoff’s Current Law, and it is usually able to solve a circuit with less unknown variables and less simultaneous equations, which is especially nice if you’re forced to solve without a calculator.
Let’s see how this method works on the same example problem:

In this section we use the format approach for solving circuit problems using mesh analysis. This technique generates a set of equations, which can be solved using determinant algebra and the application of Cramers rule. We will assign the SAME DIRECTION for each current flow in each branch of a particular circuit. We can then write the loop equation by inspection. Let the sum of the impedances in the loop be positive and the mutual or transfer impedance, be negative. The mutual or transfer impedance is that impedance which is
common to two loops. KVL states that the sum of the e.f.m`s in a closed loop  must be equal to the sum of the potential differences. If the e.m.f is in the same direction as the current direction, it is given a positive e.m.f. If it is in the opposite direction to the current direction, it is assigned a negative sign.

Click the link to know more about thevenin's equivalent circuit.

Click the link to know more about norton's equivalent circuit.

The material covered in this class will be as follows: 
⇒ Source Transformation 
⇒ Use of Source Transformation in Circuit Analysis 
At the end of this class you should be able to: 
⇒  Understand the meaning of source transformation 
⇒  Apply source transformation 
⇒  Recognize when source transformation is not applicable 
⇒  Use source transformation to simplify and analyze circuits 

Superposition theorem is one of those strokes of genius that takes a complex subject and simplifies it in a way that makes perfect sense. A theorem like Millman's certainly works well, but it is not quite obvious why it works so well. Superposition, on the other hand, is obvious.
The strategy used in the Superposition Theorem is to eliminate all but one source of power within a network at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately. Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all “superimposed” on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active. Let's look at our example circuit again and apply Superposition Theorem to it:

Many introductory circuits texts state or imply that superposition of dependent sources cannot be used in linear circuit analysis. Although the use of superposition of only independent sources leads to the correct solution, it does not make use of the full power of superposition. The use of superposition of dependent sources often leads to a simpler solution than other techniques of circuit analysis. A formal proof is presented that superposition of dependent sources is valid provided the controlling variable is not set to zero when the source is deactivated. Several examples are given which illustrate the technique.

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