1. If A represents incidence matrix, I represents branch current vectors, then?
a) AI = 1
b) AI = 0
c) AI = 2
d) AI= 3
Explanation: If A represents incidence matrix, I represents branch current vectors, then the relation is AI= 0 that is its characteristic equation must be equated to zero
2. If a graph consists of 5 nodes, then the number of twigs in the tree is?
a) 1
b) 2
c) 3
d) 4
Explanation: Number of twigs = n-1. As given number of nodes are 5 then n = 5. On substituting in the equation, number of twigs = 5 -1 = 4.
3. If there are 4 branches, 3 nodes then number of links in a co-tree are?
a) 2
b) 4
c) 6
d) 8
Explanation: Number of links = b-n+1. Given number of branches = 4 and number of nodes = 3. On substituting in the equation, number of links in a co-tree = 4 – 3 + 1 = 2.
4. The current in a closed path in a loop is called?
a) loop current
b) branch current
c) link current
d) twig current
Explanation: In a loop there exists a closed path and a circulating current which is called link current. The current in any branch can be found by using link currents.
5. Tie-set is also called?
a) f loop
b) g loop
c) d loop
d) e loop
Explanation: The fundamental loop formed by one link has a unique path in the tree joining the two nodes of the link. This loop is also called f-loop.
6. Consider the graph shown below. If a tree of the graph has branches 4, 5, 6, then one of the twigs will be?
a) 1
b) 2
c) 3
d) 4
Explanation: Branches of the tree are called twigs. So 4, 5, 6 are the twigs of the tree. The current in any branch of a graph can be found by using link currents.
7. The loop current direction of the basic loop formed from the tree of the graph is?
a) same as the direction of the branch current
b) opposite to the direction of the link current
c) same as the direction of the link current
d) opposite to the direction of the branch current
Explanation: The loop current direction of the basic loop formed from the tree of the graph is same as the direction of the link current.
8. For Tie-set matrix, if the direction of current is same as loop current, then we place ______ in the matrix.
a) +1
b) -1
c) 0
d) +1 or -1
Explanation: For Tie-set matrix, if the direction of current is same as loop current, then we place +1 in the matrix.
9. The matrix formed by link branches of a tie set matrix is?
a) Row matrix
b) Column matrix
c) Diagonal matrix
d) Identity matrix
Explanation: As the direction of the basic loops of the tree are taken along the direction of the link currents, then the matrix formed by the link currents will be an identity matrix.
10. The number of tie set matrices formed from a graph is?
a) NN-1
b) NN
c) NN-2
d) NN+1
Explanation: For every tree, there will be a unique tie set matrix. So there will be NN-2 tie set matrices.