# Network Theory Questions and Answers – Cut-Set and Tree Branch Voltages

This set of Network Theory Interview Questions and Answers focuses on “Cut-Set and Tree Branch Voltages”.

1. What is the direction of the cut-set?
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: A cut-set is a minimal set of branches of a connected graph such that the removal of these branches causes the graph to be cut into exactly two parts. The direction of the cut-set is same as the direction of the branch current.

2. Consider the graph shown below. The direction of the cut-set of node ‘a’ is?

a) right
b) left
c) upwards
d) downwards

Explanation: The direction of the cut set at node ‘a’ will be the direction of the branch current at node ‘a’. So the direction of the current will be upwards.

3. Consider the graph shown below. The direction of the cut-set at node ‘b’ will be?

a) upwards
b) right
c) downwards
d) left

Explanation: The direction of the current will be towards right. The direction of the cut set at node ‘b’ will be the direction of the branch current at node ‘b’. So the direction of the current will be towards right.

4. In the graph shown below, the direction of the cut-set at node ‘c’ is?

a) downwards
b) upwards
c) left
d) right

Explanation: The direction of the cut set at node ‘c’ will be the direction of the branch current at node ‘c’. So the direction of the current will be upwards.

5. In the graph shown below, the direction of the cut-set at node ‘d’ will be?

a) left
b) downwards
c) right
d) upwards

Explanation: The direction of the cut set at node ‘d’ will be the direction of the branch current at node ‘d’. So the direction of the current will be upwards.

6. The row formed at node ‘a’ in the cut set matrix in the figure shown below is?

a) +1 +1 +1 +1 0 0 0 0
b) +1 0 0 0 +1 0 0 +1
c) -1 0 0 0 -1 0 0 -1
d) -1 -1 0 0 -1 -1 0 0

Explanation: The direction of the cut set at node ‘a’ is towards node ‘a’. So the current direction of I1 is same as cut set direction. So it is +1. Similarly for all other currents.

7. The row formed at node ‘c’ in the cut set matrix in the following figure?

a) -1 -1 0 0 +1 -1 0 0
b) 0 0 +1 0 0 -1 -1 0
c) +1 0 0 0 +1 0 0 +1
d) -1 0 0 0 -1 0 0 -1

Explanation: The direction of the cut set at node ‘c’ is away from node ‘c’. So the current direction of I3 is same as cut set direction. So it is +1. Similarly for all other currents.

8. The number of cut 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 cut set matrix. So there will be NN-2 cut set matrices.

9. For every tree there will be _____ number of cut set matrices.
a) 1
b) 2
c) 3
d) 4

Explanation: For every tree, there will a unique cut set matrix. So, number of cut-set matrices for every tree = 1.

10. If a row of the cut set matrix formed by the branch currents of the graph is shown below. Then which of the following is true?

``` I1   I2   I3   I4    I5   I6   I7  I8
-1   -1   0   0   +1  -1   0   0
```

a) -V1-V2+V5-V6=0
b) -I1-I2+I5-I6=0
c) -V1+V2+V5-V6=0
d) -I1+I2+I5-I6=0

Explanation: KCL equations are derived from cut set matrix and these include currents not voltages. So, -I1-I2+I5-I6=0.

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