Chapter 7, Problem 1P

Which elements (individual elements, not combinations of elements) of the networks in Fig. 7.64. are in series? Which are in parallel? As a check on your assumptions, be sure that the elements in series have the same current and that the elements in parallel have the same voltage. Restrict your decisions to single elements not combinations of elements.

Fig 7.64

To determine

(a)

The elements of the network that are in series and in parallel.

Answer to Problem 1P

$R_{1,}{R}_2\text{ and }E$ elements are in series and $R_{3,}{R}_4\text{ and }{R}_5$ elements are in parallel.

Explanation of Solution

Given:

A network is given as below.

  

Concept Used:

Elements in the series have the same current.

Elements in the parallels have the same voltage.

Calculation:

A network is given as below.

  

Since same current is flowing through $R_{1,}{R}_2\text{ and }E$.

So, $R_{1,}{R}_2\text{ and }E$ are in series.

Also, since same voltage is flowing through $R_{3,}{R}_4\text{ and }{R}_5$.

So, $R_{3,}{R}_4\text{ and }{R}_5$ are in parallel.

Conclusion:

Hence, $R_{1,}{R}_2\text{ and }E$ elements are in series and $R_{3,}{R}_4\text{ and }{R}_5$ elements are in parallel.

To determine

(b)

The elements of the network that are in series and in parallel.

Answer to Problem 1P

$R_1\text{and }E$ Elements are in series and $R_{3,}{R}_4\text{ and }{R}_2$ elements are in parallel.

Explanation of Solution

Given:

A network is given as below.

  

Concept Used:

Elements in the series have the same current.

Elements in the parallels have the same voltage.

Calculation:

A network is given as below.

  

Since same current is flowing through $R_1\text{and }E$.

So, $R_1\text{and }E$ are in series.

And since same voltage is flowing through $R_{3,}{R}_4\text{ and }{R}_2$.

So, $R_{3,}{R}_4\text{ and }{R}_2$ are in parallel.

Conclusion:

Hence, $R_1\text{and }E$ elements are in series and $R_{3,}{R}_4\text{ and }{R}_2$ elements are in parallel.

To determine

(c)

The elements of the network that are in series and in parallel.

Answer to Problem 1P

$R_1\text{ and }E$ Elements are in series and $R_4\text{ and }{R}_2$ elements are in parallel.

Explanation of Solution

Given:

A network is given as below.

  

Concept Used:

Elements in the series have the same current.

Elements in the parallels have the same voltage.

Calculation:

A network is given as below.

  

Since same current is flowing through $R_1\text{ and }E$.

So, $R_1\text{ and }E$ are in series.

Since same voltage is across $R_4\text{ and }{R}_2$.

So, $R_4\text{ and }{R}_2$ are in parallel.

Conclusion:

Hence, $R_1\text{ and }E$ elements are in series and $R_4\text{ and }{R}_2$ elements are in parallel.