Exercise 8: Answers
KVL arround abca loop:
KVL arround acda loop:
KVL arround bcdb loop:
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 .
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 .