1. Electric Circuit
- 1.1. Circuit Elements
- - 1.1.1. Active Circuit Elements
  - 1.1.2. Passive Circuit Elements
- 1.2. Ohms Law
- 1.3. Open Circuits
- 1.4. Short Circuits
2. Resistance
- 2.1. Resistance of Circular Wires
- 2.2. Temperature Effect on Resistance
- 2.3. Resistor
- 2.4. Color coding and Standard Resistor Values
- 2.5. Metric Units of Resistance
3. Series DC Circuits
- 3.1. Series Circuit
- 3.2. Circuit Instrumentation
- 3.3. Series Circuit Power Distribution
- 3.4. Series Voltage Sources
- 3.5. Kirchhoffs Voltage Law
- 3.6. Voltage Division in a Series Circuit
- 3.7. Interchanging Series Elements
- 3.8. Circuit Analysis Notation
- - 3.8.1. Single and Double Subscript Notation
- 3.9. Internal Resistance of Voltage Sources
- 3.10. Voltage Regulation
- 3.11. Loading Effects of Instruments
4. Parallel DC Circuits
- 4.1. Parallel Circuits
- 4.2. Power Distribution
- 4.3. Kirchhoffs Current law
- 4.4. Current Divider Rule
- 4.5. Voltage Sources in Parallel
- 4.6. Voltmeter Loading Effect
- 4.7. Troubleshooting Techniques
- 4.8. Parallel DC Circuits Applications
5. Series Parallel Circuits
- 5.1. Reduce and Return Approach
- 5.2. Block Diagram Approach
- 5.3. Ladder Networks
- 5.4. Voltage Divider Supply
- 5.5. Potentiometer Loading
- 5.6. Iron Vane Movement
6. Methods of Analysis
- 6.1. Current Sources
- 6.2. Branch Current Analysis
- 6.3. Mesh Analysis
- 6.4. Mesh Analysis with Current Sources
- 6.5. Nodal Analysis
- 6.6. Nodal Analysis with Voltage Sources
- 6.7. Bridge Networks
- 6.8. Star Delta Transformation
7. Network Theorems
- 7.1. Linearity Property
- 7.2. Superposition Theorem
- 7.3. Thevenins Theorem
- 7.4. Nortons Theorem
- 7.5. Maximum Power Transfer Theorem
- 7.6. Application of Maximum Power Transfer Method
- 7.7. Millmans Theorem
- 7.8. Substitution Theorem
- 7.9. Reciprocity Theorem
8. Capacitors
- 8.1. Capacitance
- 8.2. Types of capacitor
- 8.3. Initial Conditions of capacitor
- 8.4. Capacitor Charging Phase
- 8.5. Capacitor Discharging Phase
- 8.6. Instantaneous Values of Capacitor
- 8.7. Thevenin Equivalent Circuit of Capacitor
- 8.8. Current through capacitor
- 8.9. Capacitors in series and parallel
- 8.10. Energy Stored by a Capacitor
- 8.11. Stray Capacitance
9. Magnetic Circuits
- 9.1. Magnetic Flux Density
- 9.2. Permeability
- 9.3. Magnetic Reluctance
- 9.4. Ohms Law for Magnetic Circuits
- 9.5. Magnetizing Force
- 9.6. Hysteresis Curve
- 9.7. Domain Theory of Magnetism
- 9.8. Amperes Circuital Law
- 9.9. Series Magnetic Circuits
- 9.10. Magnetic Circuit Air Gaps
- 9.11. Series and Parallel Magnetic Circuits
- 9.12. Application of Magnetic circuits
10. Inductors
- 10.1. Faradays Law of Induction
- 10.2. Lenz law
- 10.3. Self Inductance
- 10.4. Types of Inductors
- 10.5. Inductor values
- 10.6. Induced Voltage
- 10.7. Transient Response of RL Circuit
- 10.8. Initial Values of an Inductor
- 10.9. Decay of Current in RL Circuit
- 10.10. Thevenin Equivalent Circuit of Inductor
- 10.11. Inductors in Series and Parallel
- 10.12. RL and RLC Circuits with DC Inputs
- 10.13. Energy Stored by an Inductor
- 10.14. Applications of inductor
11. Sinusoidal Alternating Waveforms
- 11.1. Sinusoidal AC Voltage Generation
- 11.2. Sinusoidal AC Waveform Definitions
- 11.3. The Sine Wave
- 11.4. General Format for the Sinusoidal Voltage or Current
- 11.5. Phase Relationship of a Sinusoidal Waveform
- 11.6. Average Value of Sinusoidal Waveform
- 11.7. Root Mean Square value of Sinusoidal waveform
- 11.8. AC meters and Instruments
12. Basic Elements of AC Circuit and Phasors
- 12.1. The Derivative of Sinusoidal Waveform
- 12.2. Response of Resistor to a Sinusoidal Voltage
- 12.3. Response of Inductor to a Sinusoidal Voltage
- 12.4. Response of Capacitor to a Sinusoidal Voltage
- 12.5. Frequency Effects on L and C in DC Circuits
- 12.6. Frequency Response of the Basic Elements
- 12.7. Average Power of Sinusoidal Voltage
- 12.8. AC Power Factor
- 12.9. Complex Numbers
- 12.10. Phasors
13. Series and Parallel ac Circuits
- 13.1. Impedance and the Phasor Diagram
- 13.2. AC Series Configuration
- 13.3. AC Voltage Divider Rule
- 13.4. Frequency Response of the RC Circuit
- 13.5. SUMMARY of Series AC Circuits
- 13.6. Admittance and Susceptance
- 13.7. Parallel ac Networks
- 13.8. Current Divider Rule of ac Circuits
- 13.9. Frequency Response of Parallel RL Network
- 13.10. Parallel ac Networks Summary
- 13.11. AC Equivalent Circuit
- 13.12. Phase Shift Measurement with Dual Trace Oscilloscope
- 13.13. Application of Series and Parallel ac Circuits
- - 13.13.1. Home Wiring
  - 13.13.2. Speaker Systems
14. Methods of Analysis of AC Network
- 14.1. Independent Versus Dependent Controlled Sources
- 14.2. Source Conversion of ac Circuits
- 14.3. Mesh Analysis for ac Circuits
- 14.4. Nodal Analysis for ac Circuits
- 14.5. AC Bridge Networks
- 14.6. Star Delta Transformation (AC)
15. Network Theorem (AC)
- 15.1. Superposition Theorem (ac)
- 15.2. Thevenins Theorem (ac)
- 15.3. Nortons Theorem (ac)
- 15.4. Maximum Power Transfer Theorem (ac)
16. Power (AC)
- 16.1. Resistive (AC) Circuit Power Calculation
- 16.2. Apparent Power
- 16.3. Reactive Power in Inductive Circuit
- 16.4. Reactive Power in Capacitive Circuit
- 16.5. The Power Triangle
- 16.6. The Total Apparent, Active and Reactive Power
- 16.7. Power Factor Correction
- 16.8. Wattmeters and Power Factor Meters
- 16.9. Effective Resistance
17. Resonance
- 17.1. Series Resonant Circuit
- 17.2. The Quality Factor (Q)
- 17.3. Total Impedance Versus Frequency
- 17.4. Selectivity of Frequency
- 17.5. Magnitudes of Voltages across RLC versus Frequency
- 17.6. Examples of Series Resonance Circuits
- 17.7. Parallel Resonant Circuit
- - 17.7.1. Resonace Frequency of a Parallel Resonant Circuit
- 17.8. Selectivity Curve for Parallel Resonant Circuits
- 17.9. Effect of Quality Factor greater than or Equal to 10
- 17.10. Examples of Parallel Resonance
- 17.11. Applications of Resonance Circuits
18. Transformer
- 18.1. Mutual Inductance
- 18.2. The Iron Core Transformer
- 18.3. Reflected Impedance and Power
- - 18.3.1. Transformer as a Impedance Matching
  - 18.3.2. Transformer as an Isolation Device
- 18.4. Iron Core Transformer Equivalent Circuit
- 18.5. Transformer Frequency Considerations
- 18.6. Series Connection of Mutually Coupled Coils
- 18.7. Air Core Transformer
- 18.8. Transformer Nameplate Data
- 18.9. Types of Transformers
- 18.10. Tapped and Multiple Load Transformers
- 18.11. Networks with Magnetically Coupled Coils
- 18.12. Applications of Transformer
- - 18.12.1. Transformer for Low Voltage Compensation
  - 18.12.2. Ballast Transformer
19. Polyphase Systems
- 19.1. The Three Phase Generator
- 19.2. The Y Connected Generator
- - 19.2.1. Phase Sequence (Y CONNECTED GENERATOR)
  - 19.2.2. Y connected Generator connected to a Y connected load
- 19.3. The Y Delta System
- 19.4. The Delta Connected Generator
- 19.5. The Delta Delta, Delta Y Three Phase Systems
- 19.6. Power Calculation of Y Connected Balanced Load
- 19.7. Power Calculation of Delta Connected Balanced Load
- 19.8. The Three Wattmeter Method
- 19.9. The Two Wattmeter Method
- 19.10. Unbalanced Three phase Four wire, Y Connected Load
- 19.11. Unbalanced, Three phase, Three wire, Y Connected Load
20. Frequency Response
- 20.1. Logarithm
- 20.2. Decibels
- 20.3. Transfer Function
- 20.4. Filters
- 20.5. Bode Plots
- - 20.5.1. High Pass RC Filter
  - 20.5.2. Low Pass RC Filter
- 20.6. Sketching the Bode Response
- 20.7. Low Pass Filter with Limited Attenuation
- 20.8. High Pass Filter with Limited Attenuation
- 20.9. Crossover Networks
- 20.10. Application of Filters
- - 20.10.1. Attenuators
  - 20.10.2. Noise Filters
21. Pulse Waveform and the RC Response
- 21.1. Ideal versus Actual Pulse Waveform
- 21.2. Properties of a Pulse Waveform
- 21.3. Pulse Repetition Rate and Duty Cycle
- 21.4. Average Value of a Pulse Waveform
- 21.5. Transient in RC Network
- 21.6. RC Response to Square Wave Inputs
- 21.7. Oscilloscope Attenuator
- 21.8. Compensating Attenuator Probe
- 21.9. Application of Pulse Waveform
22. The Laplace Transform
- 22.1. Properties of The Laplace Transform
- 22.2. List of the Properties of The Laplace Transform
- 22.3. Examples of The Laplace Transform
- 22.4. The Inverse Laplace Transform
- 22.5. Examples of The Inverse Laplace Transform
- 22.6. Circuit Application of The Laplace Transform
- 22.7. Transfer Function of The Laplace Transform
- 22.8. The Convolution Integral
- 22.9. Application to Integrodifferential Equations
- 22.10. Application of The Laplace Transform to the Network Stability
- 22.11. Application of The Laplace Transform to the Network Synthesis
23. The Fourier Series
- 23.1. Trigonometric Fourier Series
- 23.2. Symmetry Considerations of The Fourier Series
- 23.3. Common Functions of The Fourier Series
- 23.4. Circuit Application of The Fourier Series
- 23.5. Average Power and RMS Values of The Fourier Series
- 23.6. Exponential Fourier Series
- 23.7. Application of the Fourier Series to Spectrum Analyzers
- 23.8. Application of the Fourier Series to Filters
24. Fourier Transform
- 24.1. Properties of the Fourier Transform
- 24.2. Examples of the Fourier Transform
- 24.3. Examples of the Inverse Fourier Transform
- 24.4. Circuit Application of the Fourier Transform
- 24.5. Parsevals Theorem
- 24.6. Comparing the Fourier and Laplace Transform
- 24.7. Application of the Fourier Transform to the Amplitude Modulation
- 24.8. Application of the Fourier Transform to the Sampling
25. Two Port Networks
- 25.1. Impedance Parameters
- 25.2. Admittance Parameters
- 25.3. Hybrid Parameters
- 25.4. Transmission Parameters
- 25.5. Relationships between Parameters
- 25.6. Interconnection of Networks
- 25.7. Application of the Two Port Networks to the Transistor Circuits
- 25.8. Application of the Two Port Networks to the Ladder Network Synthesis
26. Nonsinusoidal Circuits
- 26.1. Circuit Response to a Nonsinusoidal Input
- 26.2. Addition and Subtraction of Nonsinusoidal Waveforms

Properties of The Laplace Transform

Electrical Circuit Analysis > The Laplace Transform

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The properties of the Laplace transform help us to obtain transform pairs without directly using Eq. (1) $$\mathcal{L}[f(t)]=F(s)=\int_{0-}^{\infty} f(t) e^{-s t} d t \tag{1}$$ as we did in Examples 1 and 2. As we derive each of these properties, we should keep in mind the definition of the Laplace transform in Eq. (1).

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