Chapter 3, Problem 1E

Referring to the circuit depicted in Fig. 3.45, count the number of (a) nodes;

(b) elements; (c) branches.

FIGURE 3.45

To determine

Find the number of nodes in the circuit.

Answer to Problem 1E

Number of nodes in the circuit is $5$.

Explanation of Solution

The circuit diagram is redrawn as shown in Figure 1.

Refer to the redrawn Figure 1.

A point where two or more branches have common connection is known as node.

In Figure 1 two branches are connected at point $a$, three branches are connected at point $b$, two branches are connected at point $c$, two branches are connected at point $d$ and three branches are connected at point $e$. From this it concludes that the number of nodes in the given circuit is $5$.

Conclusion:

Thus, the number of nodes in the circuit is $5$.

To determine

Find the number of elements in the circuit.

Answer to Problem 1E

Number of elements in the circuit is $6$.

Explanation of Solution

Refer to the redrawn Figure 1.

Each component (either passive or active device) present in the electrical circuit is an element.

There are $2$ current source and $4$ resistors available in the circuit. So, the total number of elements is $6$.

Conclusion:

Thus, the number of elements in the circuit is $6$.

To determine

Find the number of branches in the circuit.

Answer to Problem 1E

Number of branches in the circuit is $6$.

Explanation of Solution

Refer to the redrawn Figure 1.

Each electrical element or device present in the circuit is known as branch.

There are $2$ current source and $4$ resistors present in the circuit. Therefore, total number of branches is $6$.

Conclusion:

Thus, the number of branches in the circuit is $6$.