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If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will be
- a)n + l - 1
- b)b - 1
- c)b - n + 1
- d)n - 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the number of branch in a network is b, the number of nodes is n an...
The number of independent node equation are n - 1.
Most Upvoted Answer
If the number of branch in a network is b, the number of nodes is n an...
Explanation:
In a network, the number of independent node equations can be calculated using Kirchhoff's current law (KCL). According to KCL, the sum of currents entering and leaving a node should be zero. This can be written as an equation for each node in the network. However, not all of these equations are independent. Some of them can be derived from others.
Formula:
The formula to calculate the number of independent node equations is:
n - 1 - l
where n is the number of nodes in the network and l is the number of dependent loops.
Reasoning:
The reasoning behind this formula is that there are n nodes in the network, but one of them can be taken as a reference node (usually the ground). This node does not need an equation because its voltage is defined as zero. Therefore, there are only n-1 nodes that need equations.
However, some of these equations may be dependent on each other. This happens when two or more nodes are connected by a loop (a closed path in the network). In this case, the sum of currents around the loop is zero, which can be used to derive an equation for one of the nodes in the loop from the others. Therefore, the number of independent node equations is reduced by the number of dependent loops, which is l.
Conclusion:
Therefore, the correct answer is option D, which is n-1, because it represents the number of nodes minus the reference node, minus the number of dependent loops.
In a network, the number of independent node equations can be calculated using Kirchhoff's current law (KCL). According to KCL, the sum of currents entering and leaving a node should be zero. This can be written as an equation for each node in the network. However, not all of these equations are independent. Some of them can be derived from others.
Formula:
The formula to calculate the number of independent node equations is:
n - 1 - l
where n is the number of nodes in the network and l is the number of dependent loops.
Reasoning:
The reasoning behind this formula is that there are n nodes in the network, but one of them can be taken as a reference node (usually the ground). This node does not need an equation because its voltage is defined as zero. Therefore, there are only n-1 nodes that need equations.
However, some of these equations may be dependent on each other. This happens when two or more nodes are connected by a loop (a closed path in the network). In this case, the sum of currents around the loop is zero, which can be used to derive an equation for one of the nodes in the loop from the others. Therefore, the number of independent node equations is reduced by the number of dependent loops, which is l.
Conclusion:
Therefore, the correct answer is option D, which is n-1, because it represents the number of nodes minus the reference node, minus the number of dependent loops.
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If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer?.
If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will bea)n + l - 1b)b - 1c)b - n + 1d)n - 1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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