Find the differential equation for the circuit shown in Figure P 9.2-1 using the direct method.
Read more
Table of Contents
1
Electric Circuit Variables
1.2
Electric Circuits and Current
1.3
Systems of Units
1.5
Power and Energy
1.7
How Can We Check . . . ?
2
Circuit Elements
2.1
How Can We Check . . . ?
2.2
Engineering and Linear Models
2.4
Resistors
2.5
Independent Sources
2.6
Voltmeters and Ammeters
2.7
Dependent Sources
2.8
Transducers
2.9
Switches
3
Resistive Circuits
3.2
Kirchhoffs Laws
3.3
Series Resistors and Voltage Division
3.4
Parallel Resistors and Current Division
3.5
Series Voltage Sources and Parallel Current Sources
3.6
Circuit Analysis
3.7
Analyzing Resistive Circuits Using MATLAB
3.8
How Can We Check . . . ?
4
Methods of Analysis of Resistive Circuits
4.11
How Can We Check . . . ?
4.2
Node Voltage Analysis of Circuits with Current Sources
4.3
Node Voltage Analysis of Circuits with Current and Voltage Sources
4.4
Node Voltage Analysis with Dependent Sources
4.5
Mesh Current Analysis with Independent Voltage Sources
4.6
Mesh Current Analysis with Current and Voltage Sources
4.7
Mesh Current Analysis with Dependent Sources
4.8
The Node Voltage Method and Mesh Current Method Compared
4.9
Circuit Analysis Using MATLAB
5
Circuit Theorems
5.2
Source Transformations
5.3
Superposition
5.4
Thevenin s Theorem
5.5
Nortons Equivalent Circuit
5.6
Maximum Power Transfer
5.8
Using PSpice to Determine the Thevenin Equivalent Circuit
5.9
How Can We Check . . . ?
6
The Operational Amplifier
6.1
How Can We Check . . . ?
6.3
The Ideal Operational Amplifier
6.4
Nodal Analysis of Circuits Containing Ideal Operational Amplifiers
6.5
Design Using Operational Amplifiers
6.6
Operational Amplifier Circuits and Linear Algebraic Equations
6.7
Characteristics of Practical Operational Amplifiers
7
Energy Storage Elements
7.11
How Can We Check . . . ?
7.2
Capacitors
7.3
Energy Storage in a Capacitor
7.4
Series and Parallel Capacitors
7.5
Inductors
7.6
Energy Storage in an Inductor
7.7
Series and Parallel Inductors
7.8
Initial Conditions of Switched Circuits
7.9
Operational Amplifier Circuits and Linear Differential Equations
8
The Complete Response of RL and RC Circuits
8.1
How Can We Check . . . ?
8.3
The Response of a First-Order Circuit to a Constant Input
8.4
The Response of a First-Order Circuit to a Constant Input
8.5
Stability of First-Order Circuits
8.6
The Unit Step Source
8.7
The Response of a First-Order Circuit to a Nonconstant Source
9
The Complete Response of Circuits with Two Energy Storage Elements
9.1
Roots in the Complex Plane
9.11
How Can We Check . . . ?
9.2
Differential Equation for Circuits with Two Energy Storage Elements
9.3
Solution of the Second-Order Differential EquationThe Natural Response
9.4
Natural Response of the Unforced Parallel RLC Circuit
9.5
Natural Response of the Critically Damped Unforced Parallel RLC Circuit
9.6
Natural Response of an Underdamped Unforced Parallel RLC Circuit
9.7
Forced Response of an RLC Circuit
9.8
Complete Response of an RLC Circuit
9.9
State Variable Approach to Circuit Analysis
10
Sinusoidal Steady-State Analysis
10.1
Op Amps in AC Circuits
10.11
The Complete Response
10.12
Using MATLAB to Analyze Electric Circuits
10.2
Sinusoidal Sources
10.3
Phasors and Sinusoids
10.4
Impedances
10.5
Series and Parallel Impedances
10.6
Mesh and Node Equations
10.7
Thevenin and Norton Equivalent Circuits
10.8
Superposition
10.9
Phasor Diagrams
11
AC Steady-State Power
11.1
The Ideal Transformer
11.11
How Can We Check . . . ?
11.3
Instantaneous Power and Average Power
11.4
Effective Value of a Periodic Waveform
11.5
Complex Power
11.6
Power Factor
11.7
The Power Superposition Principle
11.8
The Maximum Power Transfer Theorem
11.9
Coupled Inductors
12
Three-Phase Circuits
12.2
Three-Phase Voltages
12.3
The Y-to-Y Circuit
12.4
The D-Connected Source and Load
12.5
The Y-to-D Circuit
12.6
Balanced Three-Phase Circuits
12.7
Instantaneous and Average Power in a Balanced Three-Phase Load
12.8
Two-Wattmeter Power Measurement
12.9
How Can We Check . . . ?
13
Frequency Response
13.2
Gain, Phase Shift, and the Network Function
13.3
Bode Plots
13.4
Resonant Circuits
13.6
Plotting Bode Plots Using MATLAB
13.8
How Can We Check . . . ?
14
The Laplace Transform
14.1
Stability
14.11
Partial Fraction Expansion Using MATLAB
14.12
How Can We Check . . . ?
14.2
Laplace Transform
14.3
Pulse Inputs
14.4
Inverse Laplace Transform
14.5
Initial and Final Value Theorems
14.6
Solution of Differential Equations Describing a Circuit
14.7
Circuit Analysis Using Impedance and Initial Conditions
14.8
Transfer Functions
14.9
Convolution
15
Fourier Series and Fourier Transform
15.12
Convolution and Circuit Response
15.14
How Can We Check . . . ?
15.2
The Fourier Series
15.3
Symmetry of the Function f (t)
15.5
Exponential Form of the Fourier Series
15.6
The Fourier Spectrum
15.7
Circuits and Fourier Series
15.9
The Fourier Transform
16
Filter Circuits
16.3
Filters
16.4
Second-Order Filters
16.5
High-Order Filters
16.7
How Can We Check . . . ?
17
Two-Port and Three-Port Networks
17.2
T-to-P Transformation and Two-Port Three-Terminal Networks
17.3
Equations of Two-Port Networks
17.4
Z and Y Parameters for a Circuit with Dependent Sources
17.5
Hybrid and Transmission Parameters
17.6
Relationships Between Two-Port Parameters
17.7
Interconnection of Two-Port Networks
17.8
How Can We Check . . . ?
Textbook Solutions for Introduction to Electric Circuits
Chapter 9.2 Problem P9.2-10
Question
The input to the circuit shown in Figure P 9.2-10 is the voltage of the voltage source, \(v_s\). The output is the capacitor voltage v(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0.
Hint: Find a Thevenin equivalent circuit.
Solution
The first step in solving 9.2 problem number 10 trying to solve the problem we have to refer to the textbook question: The input to the circuit shown in Figure P 9.2-10 is the voltage of the voltage source, \(v_s\). The output is the capacitor voltage v(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Find a Thevenin equivalent circuit.
From the textbook chapter Differential Equation for Circuits with Two Energy Storage Elements you will find a few key concepts needed to solve this.
Visible to paid subscribers only
Step 3 of 7)Visible to paid subscribers only
Subscribe to view the
full solution
full solution
Title
Introduction to Electric Circuits 9
Author
James A. Svoboda, Richard C. Dorf
ISBN
9781118477502
The input to the circuit shown in Figure P 9.2-10 is the voltage of the voltage source
Chapter 9.2 textbook questions
-
Chapter 9: Problem 0 Introduction to Electric Circuits 9
-
Chapter 9: Problem 0 Introduction to Electric Circuits 9
Find the differential equation for the circuit shown in Figure P 9.2-2 using the operator method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
Find the differential equation for \(i_L\)(t) for t > 0 for the circuit of Figure P 9.2-3.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-4 is the voltage of the voltage source, \(V_s\). The output is the inductor current i(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t> 0. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-5 is the voltage of the voltage source, \(v_s\). The output is the capacitor voltage v(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-6 is the voltage of the voltage source, \(v_s\). The output is the inductor current i(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-7 is the voltage of the voltage source, \(v_s\). The output is the inductor current \(i_2\)(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Use the operator method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-8 is the voltage of the voltage source, \(v_s\). The output is the capacitor voltage \(v_2\)(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Use the operator method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-9 is the voltage of the voltage source, \(v_s\). The output is the capacitor voltage v(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-10 is the voltage of the voltage source, \(v_s\). The output is the capacitor voltage v(t). Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. Hint: Find a Thevenin equivalent circuit.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-11 is the voltage of the voltage source, \(v_s\)(t). The output is the voltage \(v_2\)(t). Derive the second-order differential equation that shows how the output of this circuit is related to the input. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-12 is the voltage of the voltage source, \(v_s\)(t). The output is the voltage \(v_o\)(t). Derive the second-order differential equation that shows how the output of this circuit is related to the input. Hint: Use the operator method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-13 is the voltage of the voltage source, \(v_s\)(t). The output is the voltage \(v_o\)(t). Derive the second-order differential equation that shows how the output of this circuit is related to the input. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure P 9.2-14 is the voltage of the voltage source, \(v_s\)(t). The output is the voltage \(v_2\)(t). Derive the second-order differential equation that shows how the output of this circuit is related to the input. Hint: Use the direct method.
Read more -
Chapter 9: Problem 0 Introduction to Electric Circuits 9
Find the second-order differential equation for \(i_2\) for the circuit of Figure P 9.2-15 using the operator method. Recall that the operator for the integral is 1 / s.
Read more