Nodal analysis/Answers

Model Answer

KCL @ Node b:

i2 = i1 + i6

Thus by applying Ohms law to above equation we get.

Therefore

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

KCL @ Node c:

i3 = i2 + i4

Thus by applying Ohms law to above equation we get.

Therefore

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

KCL @ Node d:

i5 = i4 + i6

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 V_b;V_candV_d as follows:

1.

2.

3.

Now we can apply Ohm's law to solve for the current through R₃ as follows: