Calculate the number of branches in the circuit.

Question

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Answer 1

Question

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

(a)

Expert Solution

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.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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)

To determine

Find the number of branches where the current is unknown.

(b)

Expert Solution

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

(c)

To determine

Find the number of essential branches in the circuit.

(c)

Expert Solution

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

(d)

Expert Solution

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

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)

To determine

Find the number of nodes in the circuit.

(e)

Expert Solution

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

(f)

To determine

Find the number of essential nodes in the circuit.

(f)

Expert Solution

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

(g)

To determine

Find the number of meshes present in the circuit.

(g)

Expert Solution

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.

Conclusion:

Thus, the number of meshes present in the circuit is 6 meshes.

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05:21

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Answer 2

Question

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

(a)

Expert Solution

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.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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)

To determine

Find the number of branches where the current is unknown.

(b)

Expert Solution

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

(c)

To determine

Find the number of essential branches in the circuit.

(c)

Expert Solution

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

(d)

Expert Solution

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

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)

To determine

Find the number of nodes in the circuit.

(e)

Expert Solution

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

(f)

To determine

Find the number of essential nodes in the circuit.

(f)

Expert Solution

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

(g)

To determine

Find the number of meshes present in the circuit.

(g)

Expert Solution

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.

Conclusion:

Thus, the number of meshes present in the circuit is 6 meshes.

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05:21

Answer 3

Question

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

(a)

Expert Solution

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.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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)

To determine

Find the number of branches where the current is unknown.

(b)

Expert Solution

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

(c)

To determine

Find the number of essential branches in the circuit.

(c)

Expert Solution

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

(d)

Expert Solution

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

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)

To determine

Find the number of nodes in the circuit.

(e)

Expert Solution

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

(f)

To determine

Find the number of essential nodes in the circuit.

(f)

Expert Solution

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

(g)

To determine

Find the number of meshes present in the circuit.

(g)

Expert Solution

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.

Conclusion:

Thus, the number of meshes present in the circuit is 6 meshes.

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05:21

Answer 4

Question

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

(a)

Expert Solution

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.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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)

To determine

Find the number of branches where the current is unknown.

(b)

Expert Solution

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

(c)

To determine

Find the number of essential branches in the circuit.

(c)

Expert Solution

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

(d)

Expert Solution

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

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)

To determine

Find the number of nodes in the circuit.

(e)

Expert Solution

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

(f)

To determine

Find the number of essential nodes in the circuit.

(f)

Expert Solution

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

(g)

To determine

Find the number of meshes present in the circuit.

(g)

Expert Solution

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.

Conclusion:

Thus, the number of meshes present in the circuit is 6 meshes.

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05:21

Answer 5

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

(a)

Expert Solution

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.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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)

To determine

Find the number of branches where the current is unknown.

(b)

Expert Solution

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

(c)

To determine

Find the number of essential branches in the circuit.

(c)

Expert Solution

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

(d)

Expert Solution

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

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)

To determine

Find the number of nodes in the circuit.

(e)

Expert Solution

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

(f)

To determine

Find the number of essential nodes in the circuit.

(f)

Expert Solution

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

(g)

To determine

Find the number of meshes present in the circuit.

(g)

Expert Solution

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.

Conclusion:

Thus, the number of meshes present in the circuit is 6 meshes.

Answer 6

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

(a)

Expert Solution

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.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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.

Answer 7

Chapter 4, Problem 1P

(a)

To determine

Calculate the number of branches in the circuit.

Answer 8

(a)

Expert Solution

Answer to Problem 1P

The number of branches in the circuit is 12 branches.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given data:

Refer to Figure P4.1 in the textbook.

The given circuit is modified as shown in Figure 1.

Electric Circuits, Global Edition, Chapter 4, Problem 1P

A branch is defined as a single electrical device or elements.

In Figure 1, there are 12 branches in the circuit. They are, 25 mA, 2 V, R1, R2,R3, R4, R5, R6, R7, R8, 18vΔ, and 5iΔ.

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.

Answer 13

(b)

To determine

Find the number of branches where the current is unknown.

(b)

Expert Solution

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

Answer 14

(b)

To determine

Find the number of branches where the current is unknown.

Answer 15

(b)

Expert Solution

Answer to Problem 1P

The number of branches in which the current unknown is 11 branches.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

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 25 mA current source. And the current is unknown in all other branches. Therefore, the current unknown in 11 branches.

Conclusion:

Thus, the number of branches in which the current unknown is 11 branches.

Answer 20

(c)

To determine

Find the number of essential branches in the circuit.

(c)

Expert Solution

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

Answer 21

(c)

To determine

Find the number of essential branches in the circuit.

Answer 22

(c)

Expert Solution

Answer to Problem 1P

The number of essential branches in the circuit is 10 essential branches.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

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, 25 mA, R1, R2,R3, R6, R7, 18vΔ, 5iΔ, (R8−2 V), and (R1−R2).

In the circuit, (R8−2 V) and (R1−R2) are essential branches with two elements and the rest of the eight branches are essential branches that contains single element.

Therefore, the circuit has 10 essential branches.

Conclusion:

Thus, the number of essential branches in the circuit is 10 essential branches.

Answer 27

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

(d)

Expert Solution

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

Therefore, in 9 essential branches the current is unknown.

Conclusion:

Thus, the number of essential branches where the current unknown is 9 essential branches.

Answer 28

(d)

To determine

Find the number of essential branches where the current is unknown in the circuit.

Answer 29

(d)

Expert Solution

Answer to Problem 1P

The number of essential branches where the current unknown is 9 essential branches.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

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 25 mA current source. And the current is unknown in all the other 9 essential branches.

Therefore, in 9 essential branches the current is unknown.

Conclusion:

Thus, the number of essential branches where the current unknown is 9 essential branches.

Answer 34

(e)

To determine

Find the number of nodes in the circuit.

(e)

Expert Solution

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

Answer 35

(e)

To determine

Find the number of nodes in the circuit.

Answer 36

(e)

Expert Solution

Answer to Problem 1P

The number of nodes in the circuit is 7 nodes.

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

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, a, b, c, d, e, f, and g. That is, in Figure 1 three are identified by dotted rectangular boxes, two are identified by dotted triangles, and two are identified by dotted diamonds. Therefore, 7 nodes are present in the circuit.

Conclusion:

Thus, the number of nodes in the circuit is 7 nodes.

Answer 41

(f)

To determine

Find the number of essential nodes in the circuit.

(f)

Expert Solution

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

Answer 42

(f)

To determine

Find the number of essential nodes in the circuit.

Answer 43

(f)

Expert Solution

Answer to Problem 1P

The number of essential nodes in the circuit is 5 essential nodes.

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

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 a, c, d, e, and g. That is, in Figure 1 three are identified with dotted rectangular boxes and two are identified with the dotted triangles. Hence, there are 5 essential nodes in the circuit.

Conclusion:

Thus, the number of essential nodes present in the circuit is 5 essential nodes.

Answer 48

(g)

To determine

Find the number of meshes present in the circuit.

(g)

Expert Solution

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.

Conclusion:

Thus, the number of meshes present in the circuit is 6 meshes.

Answer 49

(g)

To determine

Find the number of meshes present in the circuit.

Answer 50

(g)

Expert Solution

Answer to Problem 1P

The number of meshes present in the circuit is 6 meshes.

Answer 51

(g)

Expert Solution

Answer 52

(g)

Expert Solution

Answer 53

Expert Solution

Answer 54

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 (25 mA−R6), (R6−R3−18vΔ), (18vΔ−R4−R7), (2 V−R5−R7−R8), (R1−R2−R3−R4−R5), and (5iΔ−R1−R2). Therefore, there are 6 meshes present in the circuit.