Problems

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Problems

Sections 3.2 and 3.3 Nodal Analysis

3.1 Using Fig. 3.50, design a problem to help other students better understand nodal analysis.

Figure 3.50

For Prob. 3.1 and Prob. 3.39.

3.2 For the circuit in Fig. 3.51, obtain v1 and v2.

Figure 3.51 For Prob. 3.2.

3.3 Find the currents I1 through I4 and the voltage vo in the circuit of Fig. 3.52.

Figure 3.52 For Prob. 3.3.

3.4 Given the circuit in Fig. 3.53, calculate the currents i1 through i4.

For Prob. 3.4.

3.5 Obtain vo in the circuit of Fig. 3.54.

For Prob. 3.5.

3.6 Solve for V1 in the circuit of Fig. 3.55 using nodal analysis.

3.7 Apply nodal analysis to solve for Vx in the circuit of Fig. 3.56.

For Prob. 3.7.

3.8 Using nodal analysis, find vo in the circuit of Fig. 3.57.

Figure 3.57 For Prob. 3.8 and Prob. 3.37.

3.9 Determine Ib in the circuit in Fig. 3.58 using nodal analysis.

Figure 3.58 For Prob. 3.9.

3.10 Find Io in the circuit of Fig. 3.59.

Figure 3.59 For Prob. 3.10.

3.11 Find Vo and the power dissipated in all the resistors in the circuit of Fig. 3.60.

Figure 3.60 For Prob. 3.11.

3.12 Using nodal analysis, determine Vo in the circuit in Fig. 3.61.

Figure 3.61 For Prob. 3.12.

3.13 Calculate v1 and v2 in the circuit of Fig. 3.62 using nodal analysis.

Figure 3.62

For Prob. 3.13.

3.14 Using nodal analysis, find vo in the circuit of Fig. 3.63.

Figure 3.63

For Prob. 3.14.

3.15 Apply nodal analysis to find io and the power dissipated in each resistor in the circuit of Fig. 3.64.

For Prob. 3.15.

3.16 Determine voltages v1 through v3 in the circuit of Fig. 3.65 using nodal analysis.

For Prob. 3.16.

3.17 Using nodal analysis, find current io in the circuit of Fig. 3.66.

Figure 3.66 For Prob. 3.17.

3.18 Determine the node voltages in the circuit in Fig. 3.67 using nodal analysis.

For Prob. 3.18.

3.19 Use nodal analysis to find v1, v2, and v3 in the circuit of Fig. 3.68.

Figure 3.68 For Prob. 3.19.

3.20 For the circuit in Fig. 3.69, find v1, v2, and v3 using nodal analysis.

Figure 3.69

For Prob. 3.20.

3.21 For the circuit in Fig. 3.70, find v1 and v2 using nodal analysis.

Figure 3.70

For Prob. 3.21.

3.22 Determine v1 and v2 in the circuit of Fig. 3.71.

Figure 3.71 For Prob. 3.22.

3.23 Use nodal analysis to find Vo in the circuit of Fig. 3.72.

For Prob. 3.23.

3.24 Use nodal analysis and MATLAB to find Vo in the circuit of Fig. 3.73.

Figure 3.73 For Prob. 3.24.

• 3.25 Use nodal analysis along with MATLAB to determine
  • the node voltages in Fig. 3.74.

3.26 Calculate the node voltages v1, v2, and v3 in the circuit of Fig. 3.75.

3.27 Use nodal analysis to determine voltages v1, v2, and v3 in the circuit of Fig. 3.76. *

Figure 3.76

For Prob. 3.27.

3.28 Use MATLAB to find the voltages at nodes a, b, c, and d in the circuit of Fig. 3.77. *

Figure 3.77

For Prob. 3.28.

3.29 Use MATLAB to solve for the node voltages in the circuit of Fig. 3.78.

Figure 3.78

For Prob. 3.29.

* An asterisk indicates a challenging problem.

3.30 Using nodal analysis, find vo and io in the circuit of Fig. 3.79.

3.31 Find the node voltages for the circuit in Fig. 3.80.

Figure 3.80 For Prob. 3.31.

3.32 Obtain the node voltages v1, v2, and v3 in the circuit of Fig. 3.81.

Figure 3.81 For Prob. 3.32.

Sections 3.4 and 3.5 Mesh Analysis

3.33 Which of the circuits in Fig. 3.82 is planar? For the planar circuit, redraw the circuits with no crossing branches.

3.34 Determine which of the circuits in Fig. 3.83 is planar and redraw it with no crossing branches.

Figure 3.83

For Prob. 3.34.

• 3.35 Rework Prob. 3.5 using mesh analysis.
• 3.36 Use mesh analysis to obtain ia, ib, and ic in the circuit in Fig. 3.84.

Figure 3.84 For Prob. 3.36.

3.37 Solve Prob. 3.8 using mesh analysis.

3.38 Apply mesh analysis to the circuit in Fig. 3.85 and obtain Io.

Figure 3.85 For Prob. 3.38.

3.39 Using Fig. 3.50 from Prob. 3.1, design a problem to help other students better understand mesh analysis.

3.40 For the bridge network in Fig. 3.86, find io using mesh analysis.

3.41 Apply mesh analysis to find i in Fig. 3.87.

Figure 3.87 For Prob. 3.41.

Figure 3.88

For Prob. 3.42.

3.43 Use mesh analysis to find vab and io in the circuit of Fig. 3.89.

Figure 3.89 For Prob. 3.43.

3.44 Use mesh analysis to obtain io in the circuit of Fig. 3.90.

Figure 3.90 For Prob. 3.44.

3.45 Find current i in the circuit of Fig. 3.91.

For Prob. 3.45.

3.46 Calculate the mesh currents i1 and i2 in Fig. 3.92.

For Prob. 3.46.

3.47 Rework Prob. 3.19 using mesh analysis.

3.48 Determine the current through the 10-kΩ resistor in the circuit of Fig. 3.93 using mesh analysis.

3.49 Find vo and io in the circuit of Fig. 3.94.

Figure 3.94 For Prob. 3.49.

3.50 Use mesh analysis to find the current io in the circuit of Fig. 3.95.

For Prob. 3.50.

3.51 Apply mesh analysis to find vo in the circuit of Fig. 3.96.

Figure 3.96 For Prob. 3.51.

3.52 Use mesh analysis to find i1, i2, and i3 in the circuit of Fig. 3.97.

3.53 Find the mesh currents in the circuit of Fig. 3.98 using MATLAB.

Figure 3.98 For Prob. 3.53.

3.54 Find the mesh currents i1, i2, and i3 in the circuit in Fig. 3.99.

Figure 3.99

For Prob. 3.54.

Figure 3.100 For Prob. 3.55.

3.56 Determine v1 and v2 in the circuit of Fig. 3.101.

Figure 3.101

For Prob. 3.56.

3.57 In the circuit of Fig. 3.102, find the values of R, V1, and V2 given that io = 15 mA.

3.58 Find i1, i2, and i3 in the circuit of Fig. 3.103.

Figure 3.103

For Prob. 3.58.

3.59 Rework Prob. 3.30 using mesh analysis.

3.60 Calculate the power dissipated in each resistor in the circuit of Fig. 3.104.

Figure 3.104

For Prob. 3.60.

3.61 Calculate the current gain io∕is in the circuit of Fig. 3.105.

Figure 3.105

For Prob. 3.61.

3.62 Find the mesh currents i1, i2, and i3 in the network of Fig. 3.106.

For Prob. 3.62.

3.63 Find vx and ix in the circuit shown in Fig. 3.107.

3.66 Write a set of mesh equations for the circuit in Fig. 3.110. Use MATLAB to determine the mesh currents.

Figure 3.110 For Prob. 3.66.

Section 3.6 Nodal and Mesh Analyses by Inspection

3.67 Obtain the node-voltage equations for the circuit in Fig. 3.111 by inspection. Then solve for Vo.

Figure 3.111

For Prob. 3.67.

3.68 Using Fig. 3.112, design a problem, to solve for Vo, to help other students better understand nodal analysis. Try your best to come up with values to make the calculations easier.

Figure 3.108 For Prob. 3.64.

3.65 Use MATLAB to solve for the mesh currents in the circuit of Fig. 3.109. 6 V

Figure 3.109 For Prob. 3.65.

3.69 For the circuit shown in Fig. 3.113, write the nodevoltage equations by inspection.

For Prob. 3.69.

3.70 Write the node-voltage equations by inspection and then determine values of V1 and V2 in the circuit of Fig. 3.114.

For Prob. 3.70.

3.71 Write the mesh-current equations for the circuit in Fig. 3.115. Next, determine the values of i1, i2, and i3.

For Prob. 3.71.

3.72 By inspection, write the mesh-current equations for the circuit in Fig. 3.116.

Figure 3.116

For Prob. 3.72.

3.73 Write the mesh-current equations for the circuit in Fig. 3.117.

Figure 3.117

For Prob. 3.73.

3.74 By inspection, obtain the mesh-current equations for the circuit in Fig. 3.118.

Figure 3.118 For Prob. 3.74.

Section 3.8 Circuit Analysis with PSpice or MultiSim

• 3.75 Use PSpice or MultiSim to solve Prob. 3.58.
• 3.76 Use PSpice or MultiSim to solve Prob. 3.27.

3.77 Solve for V1 and V2 in the circuit of Fig. 3.119 using PSpice or MultiSim.

Figure 3.119

For Prob. 3.77.

• 3.78 Solve Prob. 3.20 using PSpice or MultiSim.
• 3.79 Rework Prob. 3.28 using PSpice or MultiSim.
• 3.80 Find the nodal voltages v1 through v4 in the circuit of Fig. 3.120 using PSpice or MultiSim.

Figure 3.120

For Prob. 3.80.

• 3.81 Use PSpice or MultiSim to solve the problem in Example 3.4.
• 3.82 If the Schematics Netlist for a network is as follows, draw the network.

R_R1	1	2	2K
R_R2	2	0	4K
R_R3	3	0	8K
R R4	3	4	6K
R_R5	1	3	3K
V_VS	4	0	DC	100
I IS.	0	1	DC	4
$F_F1$	1	3	VF F1	$\mathsf{Z}$
$VF_F1$	5	0	0V
E E1	3	2	$\mathbf{1}$	3

3.83 The following program is the Schematics Netlist of a particular circuit. Draw the circuit and determine the voltage at node 2.

$\frac{1}{2}$
R R1	1	2	20
R R2	$\mathsf{Z}$	Ø	50
R R3	2	3	70
R R4	3.	0	30
v vs	1	a	20V
I IS	2	a	DC.

Section 3.9 Applications

3.84 Calculate vo and Io in the circuit of Fig. 3.121.

• 3.85 An audio amplifier with a resistance of 9 Ω supplies power to a speaker. What should be the resistance of the speaker for maximum power to be delivered?
• 3.86 For the simplified transistor circuit of Fig. 3.122, calculate the voltage vo.

Figure 3.122 For Prob. 3.86.

3.87 For the circuit in Fig. 3.123, find the gain vo∕vs.

3.88 Determine the gain vo∕vs of the transistor amplifier circuit in Fig. 3.124. *

Figure 3.124

• For Prob. 3.88.
  • 3.89 For the transistor circuit shown in Fig. 3.125, find IB and VCE. Let β = 100, and VBE = 0.7 V.

Figure 3.125

For Prob. 3.89.

3.90 Calculate vs for the transistor in Fig. 3.126 given that v^o = 6 V, β = 90, VBE = 0.7 V.

Figure 3.126 For Prob. 3.90.

*3.93 Rework Example 3.11 with hand calculation.

3.91 For the transistor circuit of Fig. 3.127, find IB, VCE, and vo. Take β = 150, VBE = 0.7 V.

3.92 Using Fig. 3.128, design a problem to help other students better understand transistors. Make sure you use reasonable numbers!

Figure 3.128 For Prob. 3.92.