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#### Concept explainers

(a)

Calculate the number of branches in the circuit.

(a)

## 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)

## 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)

## 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)

## 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)

## 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, *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)

Find the number of essential nodes in the circuit.

(f)

## 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 *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)

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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# Chapter 4 Solutions

Electric Circuits (10th Edition)

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