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Message: <blockquote data-quote="Little DJ" data-source="post: 10853456" data-attributes="member: 320663">Branch-Current Analysis - Network Analysing Methods : Part 02In previous post  Kirchhoff’s circuit law and Kirchhoff’s voltage law have used to solve equations for circuits having a single voltage source. In this section, these powerful tools will be used to analyse circuits having more than one source.Branch-current analysis allows to directly calculate the current in each branch of a circuit. The steps for branch analysis are as follows.1. Arbitrarily assign current directions to each branch in the network. If a particular branch has a current source, then this step is not necessary since you already know the magnitude and direction of the current in this branch.2. Using the assigned currents, label the polarities of the voltage drops across all resistors in the circuit.3. Apply Kirchhoff’s voltage law around each of the closed loops. Write just enough equations to include all branches in the loop equations. If a branch has only a current source and no series resistance, it is not necessary to include it in the KVL equations.4. Apply Kirchhoff’s current law at enough nodes to ensure that all branch currents have been included. In the event that a branch has only a current source, it will need to be included in this step.5. Solve the resulting simultaneous linear equations.Example:<img src="http://3.bp.blogspot.com/-yi4WP5mQAhM/TkwOiEiUMjI/AAAAAAAAAFs/E1YdakdYkJc/s320/yyy.JPG" alt="" class="fr-fic fr-dii fr-draggable " style="" />Step 1: Assign currents as shown in above figure.Step 2: Indicate the polarities of the voltage drops on all resistors in the circuit, using the assumed current directions.Step 3: Write the Kirchhoff voltage law equations.Loop abcda:  6 V -  2xI1 +  2xI2  - 4 V = 0 V ---------------------(1)Notice that the circuit still has one branch which has not been included in the KVL equations, namely the branch cefd. This branch would be included if a loop equation for cefdc or for abcefda were written. There is no reason for choosing one loop over another, since the overall result will remain unchanged even though the intermediate steps will not give the same results.Loop cefdc: 4 V -  2xI2 - 4xI3 + 2 V = 0 V --------------------(2)Now that all branches have been included in the loop equations, there is no need to write any more. Although more loops exist, writing more loop equations would needlessly complicate the calculations.Step 4: Write the Kirchhoff current law equation(s).By applying KCL at node c, all branch currents in the network are included.Node c:  I3 = I1 + I2 -------------------------------(3)Solving above (1), (2) and (3), required current values can be obtained and using them voltage of each resistor can be calculated.                                                    I1 = 1.2 A                                                    I2 = 0.2 A                                                    I3 = 1.4 A</blockquote>

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