Power system analysis MCQ Part 10 is focused on the Element Node Incidence matrix graph theory. Initially, some fundamental concepts of the theory are discussed afterwards multiple-choice questions are posted.

## Theory of Incidence matrix graph

- e is the number of elements. Here we have 6 elements (1,2,3,4,5,6)
- n is the number of nodes. Here we have 4 nodes (0,1,2,3)
- The dimension of the element-node incidence matrix is
*e*n* - If q is supposed a node, and p is an element then the incidence is indicated by the following:
- α_pq =1; if p is directed away from q
- α_pq =-1; if p is directed towards q
- α_pq =-1; if p is not incident to q

Observe the graph below and then answer questions below.

## Which alphabet will be replaced by E

If E represents the number of elements in element incidence node matrix then which alphabet in the table will be replaced by E:

- A
- B

Correct answer: 1. A

## Which alphabet will be replaced by N

If N represents the number of nodes in element incidence node matrix then which alphabet in the table will be replaced by N:

- A
- B

Correct answer: 2. B

## What is the dimension of Element Node Incidence matrix

If E is number of elements and N is number of nodes then dimension of Element node incidence matrix is:

- E*N
- E/N
- E+N
- E-N

Correct answer: 1. E*N

## J will be replaced by which number

J will be replaced by which number:

- 0
- 1
- -1

Correct answer: 2. 1

Since 4 is directed away from 3, J will be replaced by 1

## K will be replaced by which number

K will be replaced by which number:

- 0
- 1
- -1

Correct answer: 2. 1

## X will be replaced by which number

K will be replaced by which number:

- 0
- 1
- -1

Correct answer: 3. -1

## Y will be replaced by which number

Y will be replaced by which number:

- 0
- 1
- -1

Correct answer: 2. 1

## Z will be replaced by which number

Z will be replaced by which number:

- 0
- 1
- -1

Correct answer: 3. -1