Network Graph Theory MCQ

1. If the number of branches in a network is B, the number of nodes is N, the number of independent loops is L, then the number of independent node equations will be

1. N + L – 1
2. B – 1
3. N – 1
4. B – N

2. An electric circuit with 10 branches and 7 nodes will have ________ loop equations.

1. 3
2. 4
3. 7
4. 10

3. A network has 12 branches and 8 independent loops. The number of nodes in the network is

1. 4
2. 5
3. 6
4. 3

4. An electrical network with 8 independent nodes will have _______ nodal equations.

1. 4
2. 8
3. 7
4. 9

5. What is the number of links for a network of 10 branches and 4 nodes?

1. 7
2. 6
3. 5
4. 4

6. The number of nodes in a graph is 4. The number of tree in the graph is

1. 4
2. 8
3. 16
4. 2

7. A terminal where three or more branches meet is known as

1. terminus/junction
2. loop
3. mesh
4. node

8. Which network topology term got reference directions and marked on the edges of the graph by arrow heads?

1. sub-graph
2. node
3. vertex
4. oriented graph

9. The number of independent equations to solve a network is equal to

1. the number of chords
2. the number of branches
3. a sum of the number of branches and chords
4. a sum of the number of branches, chords and nodes

10. A node in a circuit is defined as a

1. closed path
2. junction of two or more elements
3. group of interconnected
4. open terminal of an element

11. An electric circuit with 12 branches and 9 nodes will have ________ loop equations.

1. 5
2. 4
3. 8
4. 9

12. The laws used in cutsets and tiesets of a network are

1. ohms law
2. kirchoff’s law
3. biot savart’s law
4. lorentz law

13. For N nodes and B branches, the number of independent loops is

1. B – N + 1
2. B – N
3. N – 1
4. None

14. A connected network of N > 2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network

1. must have atleast N branches for one or more closed paths to exist
2. can have an unlimited number of branches
3. can only have atmost N branches
4. can have a minimum number of branches not decided by N

15. A network has 4 nodes and 3 independent loops. What is the number of branches in the network?

1. 5
2. 6
3. 7
4. 8

16. A network has 10 nodes and 17 branches. The number of different node pair voltage would be

1. 45
2. 9
3. 7
4. 10

17. In an electric circuit, the number of independent meshes M is (where B is number of branches and N is number of nodes)

1. 2B – N + 1
2. B – N + 1
3. 2B – N – 1
4. B – N – 1

18. The total number of branches in a network is equal to b. The graph of the network has n number of branches. The minimum number of line currents is

1. b + n
2. b
3. b – n
4. n

19. Consider the following statements for a network graph, if B_f is its fundamental tie set matrix, and B_t and B_l are its sub-matrices corresponding to twigs and links, respectively.

1. B_t is a unit matrix.
2. B_l is a rectangular matrix.
3. Rank of B_f is (b – n – 1).

(where b is the number of branches n is the number of nodes)

Which of the above statements are correct?

1. 1 and 2 only
2. 1 and 3 only
3. 2 and 3 only
4. None of these

20. The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are

1. 2 and 5
2. 5 and 2
3. 3 and 4
4. 4 and 3