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Which of the following properties of the circuits of a graph are correct?
  1. The minimum number of branches possible in a circuit will be equal to the number of elements in a circuit.
  2. There are exactly two paths between any pair of vertices in a circuit.
  3. There are at least two branches in a circuit.
Select the correct answer using the code given below.
  • a)
    1 and 2 only
  • b)
    1 and 3 only
  • c)
    2 and 3 only
  • d)
    1, 2 and 3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following properties of the circuits of a graph are corre...
  • The number of nodes present in a graph will be equal to the number of principal nodes present in an electric circuit.
  • The number of branches present in a graph will be less than or equal to the number of branches present in an electric circuit.
  • In a graph there is one and only one path between every pair of vertices.
  • Branches are the connections between nodes. A branch is an element(resistor, capacitor, source).
  • The number of branches in a circuit is equal to the number of elements.
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Community Answer
Which of the following properties of the circuits of a graph are corre...
Explanation:
In order to determine which properties of the circuits of a graph are correct, let's analyze each option:

Option 1: The minimum number of branches possible in a circuit will be equal to the number of elements in a circuit.
This statement is incorrect. The number of branches in a circuit is always greater than the number of elements. Each element in a circuit contributes at least one branch.

Option 2: There are exactly two paths between any pair of vertices in a circuit.
This statement is incorrect. A circuit is a closed loop, so there is only one path between any pair of vertices. A path refers to a sequence of edges, and in a circuit, there is only one path that connects two vertices.

Option 3: There are at least two branches in a circuit.
This statement is correct. In a circuit, there must be at least two branches to form a closed loop. A branch is a connection between two vertices, and in a circuit, there must be at least two connections to form a closed loop.

Therefore, the correct answer is Option B: 1 and 3 only.
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Which of the following properties of the circuits of a graph are correct? The minimum number of branches possible in a circuit will be equal to the number of elements in a circuit. There are exactly two paths between any pair of vertices in a circuit. There are at least two branches in a circuit.Select the correct answer using the code given below.a)1 and 2 onlyb)1 and 3 onlyc)2 and 3 onlyd)1, 2 and 3Correct answer is option 'B'. Can you explain this answer?
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