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(a)
Find the number of branches present in the circuit.
(a)
Answer to Problem 1P
The number of branches present in the circuit is 11 branches.
Explanation of Solution
Given data:
Refer to Figure given in the textbook.
The voltage source is
The current source is
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 11 branches in the circuit. They are,
That is, 1 branch with a dependent source, 2 branches with independent sources, and 8 branches with resistors.
Conclusion:
Thus, the number of branches present in the circuit is 11 branches.
(b)
Find the number of branches where the current is unknown.
(b)
Answer to Problem 1P
The number of branches in which the current is unknown is 10 branches.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
In Figure 1, the only one known current in the circuit is the
Conclusion:
Thus, the number of branches in which the current is unknown is 10 branches.
(c)
Find the number of essential branches in the circuit.
(c)
Answer to Problem 1P
The number of essential branches in the circuit is 9 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 9 essential branches.
Conclusion:
Thus, the number of essential branches in the circuit is 9 essential branches.
(d)
Find the number of essential branches where the current is unknown in the circuit.
(d)
Answer to Problem 1P
The number of essential branches where the current is unknown is 8 essential branches.
Explanation of Solution
Given data:
Refer to Figure 1 in Part (a).
From Part (c), the circuit has 9 essential branches.
In Figure 1, the current is known only in the essential branch that containing the
Conclusion:
Thus, the number of essential branches where the current is unknown is 8 essential branches.
(e)
Find the number of nodes present in the circuit.
(e)
Answer to Problem 1P
The number of nodes present in the circuit is 6 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 present in the circuit is 6 nodes.
(f)
Find the number of essential nodes present in the circuit.
(f)
Answer to Problem 1P
The number of essential nodes present in the circuit is 4 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 4 essential nodes.
(g)
Find the number of meshes present in the circuit.
(g)
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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