Problems

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Problems

Section 4.2 Linearity Property

4.1 Calculate the current io in the circuit of Fig. 4.69. What value of input voltage is necessary to make io equal to 5 amps?

Figure 4.69

For Prob. 4.1.

• 4.3 (a) In the circuit of Fig. 4.71, calculate vo and io when v^s = 1 V.
  • (b) Find vo and io when v^s = 10 V.
  • (c) What are vo and io when each of the 1-Ω resistors is replaced by a 10-Ω resistor and v^s = 10 V?

For Prob. 4.3.

4.4 Use linearity to determine io in the circuit of Fig. 4.72.

4.5 For the circuit in Fig. 4.73, assume v^o = 1 V, and use linearity to find the actual value of vo.

Figure 4.73

For Prob. 4.5.

4.6 For the linear circuit shown in Fig. 4.74, use linearity to complete the following table.

Figure 4.74

For Prob. 4.6.

4.7 Use linearity and the assumption that Vo = 1 V to find the actual value of Vo in Fig. 4.75.

Section 4.3 Superposition

4.8 Using superposition, find Vo in the circuit of Fig. 4.76. Check with PSpice or MultiSim.

Problems 161

4.9 Given that I = 6 amps when Vs = 160 volts and Is = −10 amps and I = 5 amp when Vs = 200 volts and Is = 0, use superposition and linearity to determine the value of I when Vs = 120 volts and Is = 5 amps.

4.10 Using Fig. 4.78, design a problem to help other students better understand superposition. Note, the letter k is a gain you can specify to make the problem easier to solve but must not be zero.

Figure 4.78 For Prob. 4.10.

4.11 Use the superposition principle to find io and vo in the circuit of Fig. 4.79.

For Prob. 4.11.

4.12 Determine vo in the circuit of Fig. 4.80 using the superposition principle.

4.13 Use superposition to find vo in the circuit of Fig. 4.81.

4.14 Apply the superposition principle to find vo in the circuit of Fig. 4.82.

Figure 4.82

For Prob. 4.14.

4.15 For the circuit in Fig. 4.83, use superposition to find i. Calculate the power delivered to the 3-Ω resistor.

Figure 4.83 For Probs. 4.15 and 4.56.

4.16 Given the circuit in Fig. 4.84, use superposition to obtain io.

For Prob. 4.16.

Figure 4.85 For Prob. 4.17.

4.18 Use superposition to find Vo in the circuit of Fig. 4.86.

Figure 4.86

• For Prob. 4.18.
• 4.19 Use superposition to solve for vx in the circuit of Fig. 4.87.

Figure 4.87

For Prob. 4.19.

Section 4.4 Source Transformation

4.20 Use source transformation to reduce the circuit between terminals a and b shown in Fig. 4.88 to a single voltage source in series with a single resistor.

Figure 4.88 For Prob. 4.20.

4.21 Using Fig. 4.89, design a problem to help other students better understand source transformation.

Figure 4.89 For Prob. 4.21.

4.22 For the circuit in Fig. 4.90, use source transformation to find i.

Figure 4.90

For Prob. 4.22.

4.23 Referring to Fig. 4.91, use source transformation to determine the current and power absorbed by the 8-Ω resistor.

Figure 4.91 For Prob. 4.23.

4.24 Use source transformation to find the voltage Vx in the circuit of Fig. 4.92.

Problems 163

4.25 Obtain vo in the circuit of Fig. 4.93 using source transformation. Check your result using PSpice or MultiSim.

Figure 4.93

For Prob. 4.25.

4.26 Use source transformation to find io in the circuit of Fig. 4.94.

Figure 4.94

For Prob. 4.26.

4.27 Apply source transformation to find vx in the circuit of Fig. 4.95.

4.28 Use source transformation to find Io in Fig. 4.96.

For Prob. 4.28.

4.29 Use source transformation to find vo in the circuit of Fig. 4.97.

Figure 4.97

For Prob. 4.29.

4.30 Use source transformation on the circuit shown in Fig 4.98 to find ix.

4.31 Determine vx in the circuit of Fig. 4.99 using source transformation.

Figure 4.99 For Prob. 4.31.

4.32 Use source transformation to find ix in the circuit of Fig. 4.100.

Sections 4.5 and 4.6 Thevenin’s and Norton’s Theorems

• 4.33 Determine the Thevenin equivalent circuit, shown in Fig. 4.101, as seen by the 7-ohm resistor.
  • Then calculate the current flowing through the 7-ohm resistor.

For Prob. 4.33.

4.34 Using Fig. 4.102, design a problem that will help other students better understand Thevenin equivalent circuits.

Figure 4.104

For Prob. 4.37.

4.38 Apply Thevenin’s theorem to find Vo in the circuit of Fig. 4.105.

Figure 4.105 For Prob. 4.38.

4.39 Obtain the Thevenin equivalent at terminals a-b of the circuit shown in Fig. 4.106.

Figure 4.106

For Prob. 4.39.

4.40 Find the Thevenin equivalent at terminals a-b of the circuit in Fig. 4.107.

For Prob. 4.40.

Figure 4.102

For Probs. 4.34 and 4.49.

• 4.35 Use Thevenin’s theorem to find vo in Prob. 4.12.
• 4.36 Solve for the current i in the circuit of Fig. 4.103 using Thevenin’s theorem. (Hint: Find the Thevenin equivalent seen by the 12-Ω resistor.)

4.41 Find the Thevenin and Norton equivalents at terminals a-b of the circuit shown in Fig. 4.108.

For Prob. 4.41.

4.42 For the circuit in Fig. 4.109, find the Thevenin equivalent between terminals a and b. *

Figure 4.109

For Prob. 4.42.

4.43 Find the Thevenin equivalent looking into terminals a-b of the circuit in Fig. 4.110 and solve for ix.

Figure 4.110

For Prob. 4.43.

4.44 For the circuit in Fig. 4.111, obtain the Thevenin equivalent as seen from terminals:

Figure 4.111

For Prob. 4.44.

* An asterisk indicates a challenging problem.

4.45 Find the Thevenin equivalent of the circuit in Fig. 4.112 as seen by looking into terminals a and b.

Figure 4.112

For Prob. 4.45.

4.46 Using Fig. 4.113, design a problem to help other students better understand Norton equivalent circuits.

Figure 4.113 For Prob. 4.46.

4.47 Obtain the Thevenin and Norton equivalent circuits of the circuit in Fig. 4.114 with respect to terminals a and b.

Figure 4.114

For Prob. 4.47.

4.48 Determine the Norton equivalent at terminals a-b for the circuit in Fig. 4.115.

Figure 4.115 For Prob. 4.48.

4.49 Find the Norton equivalent looking into terminals a-b of the circuit in Fig. 4.102. Let V = 40 V, I = 3 A, R¹ = 10 Ω, R² = 40 Ω, and R³ = 20 Ω.

4.50 Obtain the Norton equivalent of the circuit in Fig. 4.116 to the left of terminals a-b. Use the result to find current i.

Figure 4.116

For Prob. 4.50.

4.51 Given the circuit in Fig. 4.117, obtain the Norton equivalent as viewed from terminals:

Figure 4.117

For Prob. 4.51.

4.52 For the transistor model in Fig. 4.118, obtain the Thevenin equivalent at terminals a-b.

4.53 Find the Norton equivalent at terminals a-b of the circuit in Fig. 4.119.

4.54 Find the Thevenin equivalent between terminals a-b of the circuit in Fig. 4.120.

For Prob. 4.54.

4.55 Obtain the Norton equivalent at terminals a-b of the circuit in Fig. 4.121. *

For Prob. 4.55.

4.56 Use Norton’s theorem to find Vo in the circuit of Fig. 4.122.

Figure 4.122 For Prob. 4.56.

4.57 Obtain the Thevenin and Norton equivalent circuits at terminals a-b for the circuit in Fig. 4.123.

Figure 4.123 For Probs. 4.57 and 4.79.

4.58 The network in Fig. 4.124 models a bipolar transistor common-emitter amplifier connected to a load. Find the Thevenin resistance seen by the load.

Figure 4.124

For Prob. 4.58.

4.59 Determine the Thevenin and Norton equivalents at terminals a-b of the circuit in Fig. 4.125.

Figure 4.125

For Probs. 4.59 and 4.80.

4.60 For the circuit in Fig. 4.126, find the Thevenin and Norton equivalent circuits at terminals a-b. *

Figure 4.126

For Probs. 4.60 and 4.81.

4.61 Obtain the Thevenin and Norton equivalent circuits at terminals a-b of the circuit in Fig. 4.127. *

For Prob. 4.61.

4.62 Find the Thevenin equivalent of the circuit in Fig. 4.128. *

Figure 4.128 For Prob. 4.62.

4.63 Find the Norton equivalent for the circuit in Fig. 4.129.

Figure 4.129

For Prob. 4.63.

4.64 Obtain the Thevenin equivalent seen at terminals a-b of the circuit in Fig. 4.130.

Figure 4.130

For Prob. 4.64.

For Prob. 4.65.

4.65 For the circuit shown in Fig. 4.131, determine the relationship between Vo and Io.

Section 4.8 Maximum Power Transfer

4.66 Find the maximum power that can be delivered to the resistor R in the circuit of Fig. 4.132.

Figure 4.132

For Prob. 4.66.

• 4.67 The variable resistor R in Fig. 4.133 is adjusted until it absorbs the maximum power from the circuit.
  • (a) Calculate the value of R for maximum power. (b) Determine the maximum power absorbed by R.

Figure 4.133

For Prob. 4.67.

4.68 Consider the 30-Ω resistor in Fig. 4.134. First compute the Thevenin equivalent circuit as seen by the 30-Ω resistor. Compute the value of R that results in Thevenin equivalent resistance equal to the 30-Ω resistance and then calculate power delivered to the 30-Ω resistor. Now let R = 0 Ω, 110 Ω, and ∞, calculate the power delivered to the 30-Ω resistor in each case. What can you say about the value of R that will result in the maximum power that can be delivered to the 30-Ω resistor? *

Figure 4.134

For Prob. 4.68.

4.69 Find the maximum power transferred to resistor R in the circuit of Fig. 4.135.

Figure 4.135 For Prob. 4.69.

4.70 Determine the maximum power delivered to the variable resistor R shown in the circuit of Fig. 4.136.

Figure 4.136

4.71 For the circuit in Fig. 4.137, what resistor connected across terminals a-b will absorb maximum power from the circuit? What is that power?

Figure 4.137 For Prob. 4.71.

• 4.72 (a) For the circuit in Fig. 4.138, obtain the Thevenin equivalent at terminals a-b.
  • (b) Calculate the current in RL = 13 Ω.
  • (c) Find RL for maximum power deliverable to RL.
  • (d) Determine that maximum power.

Figure 4.138 For Prob. 4.72.

4.73 Determine the maximum power that can be delivered to the variable resistor R in the circuit of Fig. 4.139.

Figure 4.139

• For Prob. 4.73.
  • 4.74 For the bridge circuit shown in Fig. 4.140, find the load RL for maximum power transfer and the maximum power absorbed by the load.

Figure 4.140 For Prob. 4.74.

• 4.75 For the circuit in Fig. 4.141, determine the value of R such that the maximum power delivered to the load is 12 mW. *

For Prob. 4.75.

Section 4.9 Verifying Circuit Theorems with PSpice

• 4.76 Solve Prob. 4.34 using PSpice or MultiSim. Let V = 40 V, I = 3 A, R¹ = 10 Ω, R2 = 40 Ω, and R3 = 20 Ω.

• 4.77 Use PSpice or MultiSim to solve Prob. 4.44.

• 4.78 Use PSpice or MultiSim to solve Prob. 4.52.

• 4.79 Obtain the Thevenin equivalent of the circuit in Fig. 4.123 using PSpice or MultiSim.

• 4.80 Use PSpice or MultiSim to find the Thevenin equivalent circuit at terminals a-b of the circuit in Fig. 4.125.

• 4.81 For the circuit in Fig. 4.126, use PSpice or MultiSim to find the Thevenin equivalent at terminals a-b.

Section 4.10 Applications

• 4.82 An automobile battery has an open circuit voltage of 14.7 V which drops to 12 V when connected to two 65-W headlights. What is the resistance of the headlights and the value of the internal resistance of the battery?
• 4.83 The following results were obtained from measurements taken between the two terminals of a resistive network.

Terminal Voltage	72 V	0 V
Terminal Current	0 A	9 A

Find the Thevenin equivalent of the network.

• 4.84 When connected to a 4- Ω resistor, a battery has a terminal voltage of 10.8 V but produces 12 V on an open circuit. Determine the Thevenin equivalent circuit for the battery.
• 4.85 The Thevenin equivalent at terminals a-b of the linear network shown in Fig. 4.142 is to be determined by measurement. When a 10-kΩ resistor is connected to terminals a-b, the voltage Vab is measured as 20 V. When a 30-kΩ resistor is connected to the terminals, Vab is measured as 40 V. Determine: (a) the Thevenin equivalent at terminals a-b, (b) Vab when a 20-kΩ resistor is connected to terminals a-b.

Figure 4.142

For Prob. 4.85.

4.86 A black box with a circuit in it is connected to a variable resistor. An ideal ammeter (with zero resistance) and an ideal voltmeter (with infinite resistance) are used to measure current and voltage as shown in Fig. 4.143. The results are shown in the table on the next page.

• (a) Find i when R = 12 Ω.
• (b) Determine the maximum power from the box.

R(Ω)	V(V)	i(A)
2	6	3
8	16	2
14	21	1.5

4.87 A transducer is modeled with a current source Is and a parallel resistance Rs. The current at the terminals of the source is measured to be 9.975 mA when an ammeter with an internal resistance of 20 Ω is used.

• (a) If adding a 2-kΩ resistor across the source terminals causes the ammeter reading to fall to 9.876 mA, calculate Is and Rs.
• (b) What will the ammeter reading be if the resistance between the source terminals is changed to 4 kΩ?
• 4.88 Consider the circuit in Fig. 4.144. An ammeter with internal resistance Ri is inserted between A and B to measure Io. Determine the reading of the ammeter if: (a) Ri = 500 Ω, (b) Ri = 0 Ω. (Hint: Find the Thevenin equivalent circuit at terminals a-b.)

Figure 4.144

For Prob. 4.88.

4.89 Consider the circuit in Fig. 4.145. (a) Replace the resistor RL by a zero resistance ammeter and determine the ammeter reading. (b) To verify the reciprocity theorem, interchange the ammeter and the 12-V source and determine the ammeter reading again.

Figure 4.145 For Prob. 4.89.

4.90 The Wheatstone bridge circuit shown in Fig. 4.146 is used to measure the resistance of a strain gauge. The adjustable resistor has a linear taper with a maximum value of 100 Ω. If the resistance of the strain gauge is found to be 42.6 Ω, what fraction of the full slider travel is the slider when the bridge is balanced?

For Prob. 4.90.

• can measure Rx in the range of 0–25 Ω.
• (b) Repeat for the range of 0–250 Ω.

Figure 4.147

For Prob. 4.91.

4.92 Consider the bridge circuit of Fig. 4.148. Is the bridge balanced? If the 10-kΩ resistor is replaced by an 18-kΩ resistor, what resistor connected between terminals a-b absorbs the maximum power? What is this power? *

For Prob. 4.92.

*