This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Link Currents: Tie-Set Matrix”.

1. The current in a closed path in a loop is called?
a) loop current
b) branch 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.

2. 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.

3. 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.

4. Consider the graph shown below. If a tree of the graph has branches 4, 5, 6, then one of the links will be?

a) 3
b) 4
c) 5
d) 6

Explanation: The branches of the co-tree are called links. So the links will be 1, 2, 3. For a given tree of a graph addition of each link between any two nodes form a loop called fundamental loop.

5. 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.
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6. Consider the graph shown below. The direction of the loop currents will be? (ACW – Anticlockwise, CW – Clockwise).

a) I1 ACW
b) I2 ACW
c) I3 CW
d) I4 ACW

Explanation: The direction of the loop current will be along the direction of the link current in a basic loop. So I1 – ACW, I2 – CW, I3 – ACW, I4 – CW.

7. 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.

8. If a row of the tie set matrix is as given below, then its corresponding equation will be?

```     1    2   3   4     5   6   7   8
I1 -1  +1   0   0   +1   0   0   0
```

a) -V1+V2+V3=0
b) -I1+I2+I3=0
c) -V1+V2-V3=0
d) -I1+I2-I3=0

Explanation: KVL equations are derived from tie set matrix and these include voltages not currents. So, -V1+V2+V3=0.

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.

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