Chapter 3, Problem 1P

(a)

To determine

Mention the resistors connected in series for the given circuits in Figure P3.1.

Explanation of Solution

Given data:

Refer to the given circuit shown in Figure P3.1.

Calculation:

Figure P3.1(a):

Refer to Figure P3.1(a) in the textbook, the resistors connected in series are $6\Omega$ and $12\Omega$, $9\Omega$ and $7\Omega$.

Figure P3.1(b):

Refer to Figure P3.1(b) in the textbook, the resistors connected in series are $3\text{k}\Omega$, $5\text{k}\Omega$, and $7\text{k}\Omega$.

Figure P3.1(c):

The Figure P3.1(c) in the textbook is shown in Figure 1.

In Figure 1, the resistors connected in series (Loop 1) are the $300\Omega$, $400\Omega$, and $500\Omega$ resistors.

Figure P3.1(d):

Refer to Figure P3.1(d) in the textbook, the resistors connected in series are $50\Omega$ and $90\Omega$, $80\Omega$ and $70\Omega$.

Conclusion:

Thus, the resistors connected in series for the given circuits are mentioned.

(b)

To determine

Find the equivalent resistors by simplifying the circuits of the series-connected resistors in Figure P3.1.

Explanation of Solution

Given data:

Refer to the given circuit shown in Figure P3.1.

Calculation:

Figure P3.1(a):

Refer to Figure P3.1(a) in the textbook, $6\Omega$ and $12\Omega$ resistors are connected in series. Therefore, the equivalent resistance for the series connection is

$6\Omega +12\Omega =18\Omega$

Similarly, $9\Omega$ and $7\Omega$ resistors are connected in series. Therefore, the equivalent resistance for the series connection is

$9\Omega +7\Omega =16\Omega$

The modified circuit is shown in Figure 2.

Figure P3.1(b):

Refer to Figure P3.1(b) in the textbook, the resistors $3\text{k}\Omega$, $5\text{k}\Omega$, and $7\text{k}\Omega$ are connected in series. Therefore, the equivalent resistance for series connection is,

$3\text{k}\Omega +5\text{k}\Omega +7\text{k}\Omega =15\text{k}\Omega$

The modified circuit is shown in Figure 3.

Figure P3.1(c):

Refer to Figure P3.1(c) in the textbook, the resistors $300\Omega$, $400\Omega$, and $500\Omega$ are connected in series. Therefore, the equivalent resistance for series connection is,

$300\Omega +400\Omega +500\Omega =1200\Omega$

The modified circuit is shown in Figure 4.

Figure P3.1(d):

Refer to Figure P3.1(d) in the textbook, the resistors $50\Omega$ and $90\Omega$ are connected in series. Therefore, the equivalent resistance for the series connection is,

$50\Omega +90\Omega =140\Omega$

Similarly, the resistors $80\Omega$ and $70\Omega$ are connected in series. Therefore, the equivalent resistance for the series connection is,

$80\Omega +70\Omega =150\Omega$

The modified circuit is shown in Figure 5.

Conclusion:

Thus, the simplified circuit is drawn for the series-connected resistors with equivalent resistors.