4.11 Summary

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4.11 Summary

• 1. A linear netw ork consists of linear elements, linear dependent sources, and linear independent sources.
• 2. Network theorems are used to reduce a complex circuit to a simpler one, thereby making circuit analysis much simpler.
• 3. The superposition principle states that for a circuit ha ving multiple independent sources, the voltage across (or current through) an element is equal to the algebraic sum of all the individual voltages (or currents) due to each independent source acting one at a time.
• 4. Source transformation is a procedure for transforming a v oltage source in series with a resistor to a current source in parallel with a resistor, or vice versa.
• 5. Thevenin’s and Norton’s theorems allow us to isolate a portion of a network while the remaining portion of the netw ork is replaced by an equivalent network. The Thevenin equivalent consists of a v oltage source VTh in series with a resistor RTh, while the Norton equivalent consists of a current source IN in parallel with a resistor RN. The two theorems are related by source transformation.

$$R_N = R_{\text{Th}}, \qquad I_N = \frac{V_{\text{Th}}}{R_{\text{Th}}}$$

• 6. For a gi ven Thevenin equivalent circuit, maximum po wer transfer occurs when RL = RTh; that is, when the load resistance is equal to the Thevenin resistance.
• 7. The maximum po wer transfer theorem states that the maximum power is delivered by a source to the load RL when RL is equal to RTh, the Thevenin resistance at the terminals of the load.
• 8. PSpice can be used to v erify the circuit theorems co vered in this chapter.
• 9. Source modeling and resistance measurement using the Wheatstone bridge provide applications for Thevenin’s theorem.

Review Questions

4.1 The current through a branch in a linear network is 2 A when the input source voltage is 10 V. If the voltage is reduced to 1 V and the polarity is reversed, the current through the branch is:

(a) − 2 A (b) − 0.2 A (c) 0.2 A (d) 2 A (e) 20 A

4.2 For superposition, it is not required that only one independent source be considered at a time; any number of independent sources may be considered simultaneously.

(a) True (b) False

4.3 The superposition principle applies to power calculation.

(a) True (b) False

• 4.4 Refer to Fig. 4.67. The Thevenin resistance at terminals a and b is:
  • (a) 25 Ω (b) 20 Ω

Figure 4.67

For Review Questions 4.4 to 4.6.

4.5 The Thevenin voltage across terminals a and b of the circuit in Fig. 4.67 is:

(a) 50 V	(b) 40 V
(c) 20 V	(d) 10 V

4.6 The Norton current at terminals a and b of the circuit in Fig. 4.67 is:

(a) 10 A	(b) 2.5 A
(c) 2 A	(d) 0 A

4.7 The Norton resistance RN is exactly equal to the Thevenin resistance RTh.

(a) True (b) False

4.8 Which pair of circuits in Fig. 4.68 are equivalent?

(a) a and b	(b) b and d
(c) a and c	(d) c and d

Figure 4.68

For Review Question 4.8.

4.9 A load is connected to a network. At the terminals to which the load is connected, RTh = 10 Ω and VTh = 40 V. The maximum possible power supplied to the load is:

(a) 160 W	(b) 80 W
(c) 40 W	(d) 1 W

4.10 The source is supplying the maximum power to the load when the load resistance equals the source resistance.

(a) True (b) False

Answers: 4.1b, 4.2a, 4.3b, 4.4d, 4.5b, 4.6a, 4.7a, 4.8c, 4.9c, 4.10a.