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A network has 10 nodes and 17 branches. The number of different node pair voltage would be
- a)10
- b)45
- c)7
- d)9
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A network has 10 nodes and 17 branches. The number of different node p...
Number of different node-pair voltage = Number of KCL equations = n - 1 =10 - 1 = 9
Most Upvoted Answer
A network has 10 nodes and 17 branches. The number of different node p...
Explanation:
In a network with n nodes, the number of branch currents and node voltages can be determined using Kirchhoff's laws.
Using Kirchhoff's Current Law (KCL), we can write:
Total current entering a node = Total current leaving the node
Therefore, we have n-1 independent equations (one equation for each node except a reference node) for the branch currents.
Using Kirchhoff's Voltage Law (KVL), we can write:
Sum of voltage drops around a closed loop = 0
Therefore, we have b independent equations (one equation for each branch) for the node voltages.
From the above two equations, we can write:
n-1 = b - k
where k is the number of independent loops in the network.
In a simple network with no loops, k = 0 and we have:
n-1 = b
Therefore, the number of independent node pair voltages is given by:
n(n-1)/2 - b
Substituting n = 10 and b = 17, we get:
10(10-1)/2 - 17 = 9
Therefore, the correct answer is option D (9).
In a network with n nodes, the number of branch currents and node voltages can be determined using Kirchhoff's laws.
Using Kirchhoff's Current Law (KCL), we can write:
Total current entering a node = Total current leaving the node
Therefore, we have n-1 independent equations (one equation for each node except a reference node) for the branch currents.
Using Kirchhoff's Voltage Law (KVL), we can write:
Sum of voltage drops around a closed loop = 0
Therefore, we have b independent equations (one equation for each branch) for the node voltages.
From the above two equations, we can write:
n-1 = b - k
where k is the number of independent loops in the network.
In a simple network with no loops, k = 0 and we have:
n-1 = b
Therefore, the number of independent node pair voltages is given by:
n(n-1)/2 - b
Substituting n = 10 and b = 17, we get:
10(10-1)/2 - 17 = 9
Therefore, the correct answer is option D (9).
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Community Answer
A network has 10 nodes and 17 branches. The number of different node p...
The Number of Node pair voltage = n(n-1)/2
The Number of Node pair voltage = 10(10-1)/2
= 45
The Number of Node pair voltage = 10(10-1)/2
= 45
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A network has 10 nodes and 17 branches. The number of different node pair voltage would bea)10 b)45c)7 d)9Correct answer is option 'D'. Can you explain this answer?
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