Electric Circuit Analysis/Nodal Analysis/Answers

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Exercise 7: Answers


EE-102-L07-Fig4-Final.jpg

Model Answer

KCL @ Node b:


Thus by applying Ohms law to above equation we get.

  

Therefore

   ...............   (1)


KCL @ Node c:


Thus by applying Ohms law to above equation we get.

  

Therefore

   ...............   (2)


KCL @ Node d:


Thus by applying Ohms law to above equation we get.

  

Therefore

   ...............   (3)

etc thus equations 1; 2 & 3 will be re-written as follows:


Now we can create a matrix with the above equations as follows:


The following matrix is the above with values substituted:


Now that we have arranged equations 1; 2 & 3 into a matrix we need to get Determinants of the General matrix, and Determinants of alterations of the general matrix as follows:

Solving determinants of:

  • Matrix A : General matrix A from KCL equations
  • Matrix A1 : Genral Matrix A with Column 1 substituted by .
  • Matrix A2 : Genral Matrix A with Column 2 substituted by .
  • Matrix A3 : Genral Matrix A with Column 3 substituted by .

As follows:






Now we can use the solved determinants to arrive at solutions for Node voltages as follows:


1.

2.

3.

Now we can apply Ohm's law to solve for the current through as follows: