-
The matrix A given below is the node incidence matrix of a network. The columns correspond to branches of the network while the rows correspond to nodes.
Let V = [v1 v2... v6]T denote the vector of branch voltages while I = [i1 i2... i6] T that of branch currents. The vector E = [e1 e2 e3 e4]T denotes the vector of node voltages relative to a common ground.
Which of the following statements is true?
-
- The equations v1 – v2 + v3 = 0, v3 + v4 – v5 = 0 are KVL equations for the network for some loops
- The equations v1 – v3 – v6 = 0, v4 + v5 – v6 = 0 are KVL equations for the network for some loops
- E = AV
- AV = 0 are KVL equations for the network
Correct Option: C
| v1 | v2 | v3 | v4 | v5 | v6 | |
| e1 | 1 | 1 | 1 | 0 | 0 | 0 |
| e2 | 0 | -1 | 0 | -1 | 1 | 0 |
| e3 | -1 | 0 | 0 | 0 | -1 | -1 |
| e4 | 0 | 0 | -1 | 1 | 0 | 1 |
E = [e1 e2 e3 e4]T = AV
