Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Chapter 10, Problem 9P

Use nodal analysis to find vo in the circuit of Fig. 10.58.

Chapter 10, Problem 9P, Use nodal analysis to find vo in the circuit of Fig. 10.58. Figure 10.58

Figure 10.58

Expert Solution & Answer
Check Mark
To determine

Find the voltage vo in the circuit of Figure 10.58 using nodal analysis and MATLAB.

Answer to Problem 9P

The value of voltage vo(t) in the given circuit is 6.154cos(1000t+70.26°)V.

Explanation of Solution

Given data:

Refer Figure 10.58 in the textbook for nodal analysis.

Formula used:

Write the expression to calculate impedance of the inductor.

ZL=jωL (1)

Here,

ω is the angular frequency, and

L is the value of inductor.

Write the expression to calculate impedance of the capacitor.

ZC=1jωC (2)

Here,

C is the value of capacitor.

Write the general representation of sinusoidal function.

V=Vmsin(ωt+ϕ) (3)

Here,

ϕ is the phase angle, and

Vm is the magnitude of source voltage.

Write the general expression to phasor transform of sinusoidal function from time domain to frequency domain.

Vs=P{Vmsin(ωt+ϕ)}=Vmeiϕ

Here,

Vmsin(ωt+ϕ) is the time domain representation of source voltage, and

Vmeiϕ is the frequency domain representation of source voltage.

Write the polar form representation of frequency domain.

Vs=Vmϕ (4)

Calculation:

Comparing given source voltage (10cos1000tV) with equation (3), the magnitude, angular frequency, and phase angle of source voltage are 10V, 1000rads and 0° respectively.

Substitute 10V for Vm and 0° for ϕ in equation (4).

Vs=100°V

Substitute 1000rads for ω and 10mH for L in equation (1) to find ZL.

ZL=j(1000rads)(10mH){1H=1Ωs1mH=1×103H}=j(1000rads)(10×103H)=j10Ω

Substitute 1000rads for ω and 50μF for C in equation (2) to find ZC.

ZC=1j(1000rads)(50μF){1F=1sΩ50μF=50×106F}=1j(1000rads)(50×106sΩ)=j20Ω

The frequency domain representation of given figure with the representation of node voltage is shown in Figure 1.

Fundamentals of Electric Circuits, Chapter 10, Problem 9P

Apply Kirchhoff’s current law at node V1 in Figure 1.

V1(100°)20+V1020+V1V2j20=0V120(100°)20+V120+V1j20+V2j20=0(120+120+1j20)V1+V2j20=(100°)20

Simplify the equation as follows.

(0.05+0.05+j0.05)V1j0.05V2=0.50°(0.1+j0.05)V1j0.05V2=0.50°

(2+j)V1jV2=10 (5)

Apply Kirchhoff’s current law at node V2 in Figure 1.

V2V1j20+V2030+j10+4io=0 (6)

From Figure 1, write the expression for current io.

io=V120Ω (7)

Substitute equation (7) in (6).

V2V1j20+V2030+j10+4(V120)=0V2j20+V1j20+V230+j10+V15=0(15+1j20)V1+(130+j10+1j20)V2=0(0.2j0.05)V1+(0.03j0.01+j0.05)V2=0

Simplify the equation as follows.

(0.2j0.05)V1+(0.03+j0.04)V2=0

(4j1)V1+(0.6+j0.8)V2=0 (8)

MATLAB Code:

Solve the two linear equations (5) and (8) using MATLAB to find the node voltage.

syms v1 v2

eq1 = (2 + 1*1i)*v1 +(-1*1i)*v2 == 10;

eq2 = (4 +(-1*1i))*v1 +(0.6 + 0.8*1i)*v2 == 0;

sol = solve([eq1, eq2], [v1, v2]);

val1 = sol.v1;

val2 = sol.v2;

v1real=real(val1);

v1imag=imag(val1);

v2real=real(val2);

v2imag=imag(val2);

v1=sprintf('%.3f + %.3fi V', v1real, v1imag);

v2=sprintf('%.3f + %.3fi V', v2real, v2imag)

The command window output:

v2 = '0.149 + 6.485i V'

From Figure 1, write the expression for vo.

vo=(3030+j10)V2

Substitute 0.149+j6.485V for V2.

vo=(3030+j10)(0.149+j6.485V)=2.0796+j5.792=6.15470.26°V

Represent the voltage in time domain.

vo(t)=6.154cos(1000t+70.26°)V

Conclusion:

Therefore, the value of voltage vo(t) in the given circuit is 6.154cos(1000t+70.26°)V.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Employ phasor-based analysis to obtain an expression for i(t) in the circuit of Fig. 10.57.   Image attached.
Determine the Norton equivalent of the circuit in Fig. 10.30 as seen from terminals a-b. Use the equivalent to find Io.
Employ phasor analysis techniques to obtain expressions for the two mesh currents i1 and i2 as shown in Fig. 10.61. Circuit attached in image.

Chapter 10 Solutions

Fundamentals of Electric Circuits

Ch. 10.8 - Obtain Vx and Ix in the circuit depicted in Fig....Ch. 10.9 - Determine the equivalent capacitance of the op amp...Ch. 10.9 - In the Wien-bridge oscillator circuit in Fig....Ch. 10 - The voltage Vo across the capacitor in Fig. 10.43...Ch. 10 - The value of the current Io in the circuit of Fig....Ch. 10 - Using nodal analysis, the value of Vo in the...Ch. 10 - In the circuit of Fig. 10.46, current i(t) is: (a)...Ch. 10 - Refer to the circuit in Fig. 10.47 and observe...Ch. 10 - For the circuit in Fig. 10.48, the Thevenin...Ch. 10 - In the circuit of Fig. 10.48, the Thevenin voltage...Ch. 10 - Refer to the circuit in Fig. 10.49. The Norton...Ch. 10 - Figure 10.49 For Review Questions 10.8 and 10.9....Ch. 10 - PSpice can handle a circuit with two independent...Ch. 10 - Determine i in the circuit of Fig. 10.50. Figure...Ch. 10 - Using Fig. 10.51, design a problem to help other...Ch. 10 - Determine vo in the circuit of Fig. 10.52. Figure...Ch. 10 - Compute vo(t) in the circuit of Fig. 10.53. Figure...Ch. 10 - Find io in the circuit of Fig. 10.54.Ch. 10 - Determine Vx in Fig. 10.55. Figure 10.55 For Prob....Ch. 10 - Use nodal analysis to find V in the circuit of...Ch. 10 - Use nodal analysis to find current io in the...Ch. 10 - Use nodal analysis to find vo in the circuit of...Ch. 10 - Use nodal analysis to find vo in the circuit of...Ch. 10 - Using nodal analysis, find io(t) in the circuit in...Ch. 10 - Using Fig. 10.61, design a problem to help other...Ch. 10 - Determine Vx in the circuit of Fig. 10.62 using...Ch. 10 - Calculate the voltage at nodes 1 and 2 in the...Ch. 10 - Solve for the current I in the circuit of Fig....Ch. 10 - Use nodal analysis to find Vx in the circuit shown...Ch. 10 - By nodal analysis, obtain current Io in the...Ch. 10 - Use nodal analysis to obtain Vo in the circuit of...Ch. 10 - Obtain Vo in Fig. 10.68 using nodal analysis.Ch. 10 - Refer to Fig. 10.69. If vs (t) = Vm sin t and vo...Ch. 10 - For each of the circuits in Fig. 10.70, find Vo/Vi...Ch. 10 - For the circuit in Fig. 10.71, determine Vo/Vs....Ch. 10 - Using nodal analysis obtain V in the circuit of...Ch. 10 - Design a problem to help other students better...Ch. 10 - Solve for io in Fig. 10.73 using mesh analysis....Ch. 10 - Use mesh analysis to find current io in the...Ch. 10 - Using mesh analysis, find I1 and I2 in the circuit...Ch. 10 - In the circuit of Fig. 10.76, determine the mesh...Ch. 10 - Using Fig. 10.77, design a problem help other...Ch. 10 - Use mesh analysis to find vo in the circuit of...Ch. 10 - Use mesh analysis to determine current Io in the...Ch. 10 - Determine Vo and Io in the circuit of Fig. 10.80...Ch. 10 - Compute I in Prob. 10.15 using mesh analysis....Ch. 10 - Use mesh analysis to find Io in Fig. 10.28 (for...Ch. 10 - Calculate Io in Fig. 10.30 (for Practice Prob....Ch. 10 - Compute Vo in the circuit of Fig. 10.81 using mesh...Ch. 10 - Use mesh analysis to find currents I1, I2, and I3...Ch. 10 - Using mesh analysis, obtain Io in the circuit...Ch. 10 - Find I1, I2, I3, and Ix in the circuit of Fig....Ch. 10 - Find io in the circuit shown in Fig. 10.85 using...Ch. 10 - Find vo for the circuit in Fig. 10.86, assuming...Ch. 10 - Using Fig. 10.87, design a problem to help other...Ch. 10 - Using the superposition principle, find ix in the...Ch. 10 - Use the superposition principle to obtain vx in...Ch. 10 - Use superposition to find i(t) in the circuit of...Ch. 10 - Solve for vo(t) in the circuit of Fig. 10.91 using...Ch. 10 - Determine io in the circuit of Fig. 10.92, using...Ch. 10 - Find io in the circuit of Fig. 10.93 using...Ch. 10 - Using source transformation, find i in the circuit...Ch. 10 - Using Fig. 10.95, design a problem to help other...Ch. 10 - Use source transformation to find Io in the...Ch. 10 - Use the concept of source transformation to find...Ch. 10 - Rework Prob. 10.7 using source transformation. Use...Ch. 10 - Find the Thevenin and Norton equivalent circuits...Ch. 10 - For each of the circuits in Fig. 10.99, obtain...Ch. 10 - Using Fig. 10.100, design a problem to help other...Ch. 10 - For the circuit depicted in Fig. 10.101, find the...Ch. 10 - Calculate the output impedance of the circuit...Ch. 10 - Find the Thevenin equivalent of the circuit in...Ch. 10 - Using Thevenins theorem, find vo in the circuit of...Ch. 10 - Obtain the Norton equivalent of the circuit...Ch. 10 - For the circuit shown in Fig. 10.107, find the...Ch. 10 - Using Fig. 10.108, design a problem to help other...Ch. 10 - At terminals a-b, obtain Thevenin and Norton...Ch. 10 - Find the Thevenin and Norton equivalent circuits...Ch. 10 - Find the Thevenin equivalent at terminals ab in...Ch. 10 - For the integrator shown in Fig. 10.112, obtain...Ch. 10 - Using Fig. 10.113, design a problem to help other...Ch. 10 - Find vo in the op amp circuit of Fig. 10.114....Ch. 10 - Compute io(t) in the op amp circuit in Fig. 10.115...Ch. 10 - If the input impedance is defined as Zin = Vs/Is,...Ch. 10 - Evaluate the voltage gain Av = Vo/Vs in the op amp...Ch. 10 - In the op amp circuit of Fig. 10.118, find the...Ch. 10 - Determine Vo and Io in the op amp circuit of Fig....Ch. 10 - Compute the closed-loop gain Vo/Vs for the op amp...Ch. 10 - Determine vo(t) in the op amp circuit in Fig....Ch. 10 - For the op amp circuit in Fig. 10.122, obtain Vo....Ch. 10 - Obtain vo(t) for the op amp circuit in Fig. 10.123...Ch. 10 - Use PSpice or MultiSim to determine Vo in the...Ch. 10 - Solve Prob. 10.19 using PSpice or MultiSim. Obtain...Ch. 10 - Use PSpice or MultiSim to find vo(t) in the...Ch. 10 - Obtain Vo in the circuit of Fig. 10.126 using...Ch. 10 - Using Fig. 10.127, design a problem to help other...Ch. 10 - Use PSpice or MultiSim to find V1, V2, and V3 in...Ch. 10 - Determine V1, V2, and V3 in the circuit of Fig....Ch. 10 - Use PSpice or MultiSim to find vo and io in the...Ch. 10 - The op amp circuit in Fig. 10.131 is called an...Ch. 10 - Figure 10.132 shows a Wien-bridge network. Show...Ch. 10 - Consider the oscillator in Fig. 10.133. (a)...Ch. 10 - The oscillator circuit in Fig. 10.134 uses an...Ch. 10 - Figure 10.135 shows a Colpitts oscillator. Show...Ch. 10 - Design a Colpitts oscillator that will operate at...Ch. 10 - Figure 10.136 shows a Hartley oscillator. Show...Ch. 10 - Refer to the oscillator in Fig. 10.137. (a) Show...
Knowledge Booster
Electrical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
    • SEE MORE QUESTIONS
    Recommended textbooks for you
  • Introductory Circuit Analysis (13th Edition)
    Electrical Engineering
    ISBN:9780133923605
    Author:Robert L. Boylestad
    Publisher:PEARSON
    Delmar's Standard Textbook Of Electricity
    Electrical Engineering
    ISBN:9781337900348
    Author:Stephen L. Herman
    Publisher:Cengage Learning
    Programmable Logic Controllers
    Electrical Engineering
    ISBN:9780073373843
    Author:Frank D. Petruzella
    Publisher:McGraw-Hill Education
  • Fundamentals of Electric Circuits
    Electrical Engineering
    ISBN:9780078028229
    Author:Charles K Alexander, Matthew Sadiku
    Publisher:McGraw-Hill Education
    Electric Circuits. (11th Edition)
    Electrical Engineering
    ISBN:9780134746968
    Author:James W. Nilsson, Susan Riedel
    Publisher:PEARSON
    Engineering Electromagnetics
    Electrical Engineering
    ISBN:9780078028151
    Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
    Publisher:Mcgraw-hill Education,
  • Introductory Circuit Analysis (13th Edition)
    Electrical Engineering
    ISBN:9780133923605
    Author:Robert L. Boylestad
    Publisher:PEARSON
    Delmar's Standard Textbook Of Electricity
    Electrical Engineering
    ISBN:9781337900348
    Author:Stephen L. Herman
    Publisher:Cengage Learning
    Programmable Logic Controllers
    Electrical Engineering
    ISBN:9780073373843
    Author:Frank D. Petruzella
    Publisher:McGraw-Hill Education
    Fundamentals of Electric Circuits
    Electrical Engineering
    ISBN:9780078028229
    Author:Charles K Alexander, Matthew Sadiku
    Publisher:McGraw-Hill Education
    Electric Circuits. (11th Edition)
    Electrical Engineering
    ISBN:9780134746968
    Author:James W. Nilsson, Susan Riedel
    Publisher:PEARSON
    Engineering Electromagnetics
    Electrical Engineering
    ISBN:9780078028151
    Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
    Publisher:Mcgraw-hill Education,
    Current Divider Rule; Author: Neso Academy;https://www.youtube.com/watch?v=hRU1mKWUehY;License: Standard YouTube License, CC-BY