Electric Circuit Analysis/Mesh Analysis/Answers

Exercise 8: Answers

Model Answer

KVL arround abca loop:


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

KVL arround acda loop:



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

KVL arround bcdb loop:



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

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 KVL 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 Mesh Currents as follows:




Now we can solve for the current through as follows:

The negative sign means that is flowing in the direction of .