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Concept explainers
(a)
Calculate the number of branches in the circuit.
(a)
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Answer to Problem 1P
The number of branches in the circuit is 12 branches.
Explanation of Solution
Given data:
Refer to Figure P4.1 in the textbook.
The given circuit is modified as shown in Figure 1.
A branch is defined as a single electrical device or elements.
In Figure 1, there are 12 branches in the circuit. They are,
That is, 2 branch with a dependent source, 2 branches with independent sources, and 8 branches with resistors.
Conclusion:
Thus, the number of branches in the circuit is 12 branches.
(b)
Find the number of branches where the current is unknown.
(b)
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Answer to Problem 1P
The number of branches in which the current unknown is 11 branches.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
In Figure 1, the only one known current in the circuit which is the
Conclusion:
Thus, the number of branches in which the current unknown is 11 branches.
(c)
Find the number of essential branches in the circuit.
(c)
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Answer to Problem 1P
The number of essential branches in the circuit is 10 essential branches.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
Essential branch: It is defined as a path that attaches essential nodes without passing through an essential node.
The essential branches in the circuit are,
In the circuit,
Therefore, the circuit has 10 essential branches.
Conclusion:
Thus, the number of essential branches in the circuit is 10 essential branches.
(d)
Find the number of essential branches where the current is unknown in the circuit.
(d)
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Answer to Problem 1P
The number of essential branches where the current unknown is 9 essential branches.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
Refer to Part (c), the circuit has 10 essential branches.
In Figure 1, the current is known only in the essential branch that containing the
Therefore, in 9 essential branches the current is unknown.
Conclusion:
Thus, the number of essential branches where the current unknown is 9 essential branches.
(e)
Find the number of nodes in the circuit.
(e)
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Answer to Problem 1P
The number of nodes in the circuit is 7 nodes.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
Node: It is defined as a connection point between two or more branches.
In Figure 1, the nodes present in the circuit are,
Conclusion:
Thus, the number of nodes in the circuit is 7 nodes.
(f)
Find the number of essential nodes in the circuit.
(f)
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Answer to Problem 1P
The number of essential nodes in the circuit is 5 essential nodes.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
Essential node: It is a node that joins three or more electrical element or devices
In Figure 1, the essential nodes present in the circuit are
Conclusion:
Thus, the number of essential nodes present in the circuit is 5 essential nodes.
(g)
Find the number of meshes present in the circuit.
(g)
![Check Mark](/static/check-mark.png)
Answer to Problem 1P
The number of meshes present in the circuit is 6 meshes.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
Mesh: It is defined as a closed loop path that has no any other smaller loops present inside.
In Figure 1, the closed loops present in the circuit are
Conclusion:
Thus, the number of meshes present in the circuit is 6 meshes.
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