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Core - Electrical Engineering

Chapter 5

First and Second-Order Circuits

5.1 : First-Order Circuits

5.1 : First-Order Circuits

Electrical circuits with resistors and a single energy storage element - a capacitor or inductor are called first-order circuits. They are described by a ...

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5.2 : RC Circuit without Source

5.2 : RC Circuit without Source

When a DC source is removed abruptly from an RC circuit, the circuit becomes source-free. Assuming the fully charged capacitor's initial voltage is ...

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5.3 : RC Circuit with Source

5.3 : RC Circuit with Source

When a DC source is applied abruptly to an RC circuit, its voltage is represented as a unit step function. The voltage across the capacitor is the step ...

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5.4 : RL Circuit without Source

5.4 : RL Circuit without Source

When a DC source is suddenly disconnected from an RL circuit, it becomes source-free. Assuming the inductor has an initial current i0, the initial energy ...

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5.5 : RL Circuit with Source

5.5 : RL Circuit with Source

When an RL circuit is connected to a DC source, its complete response is divided into transient and steady-state responses. The transient response is the ...

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5.6 : Design Example: Frog Muscle Response

5.6 : Design Example: Frog Muscle Response

A student uses an RL circuit to study the muscle response of a frog's leg to electrical stimulation. Closing the switch causes a brief muscle ...

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5.7 : Second-Order Circuits

5.7 : Second-Order Circuits

An electrical circuit comprising two irreducible energy storage elements is called a second-order circuit. Some examples include RLC circuits as well as ...

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5.8 : Series RLC Circuit without Source

5.8 : Series RLC Circuit without Source

A source-free RLC circuit a composed of a resistor, an inductor, and a capacitor in series without an external energy source. Here, the initial energy ...

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5.9 : Types of Responses of Series RLC Circuits

5.9 : Types of Responses of Series RLC Circuits

A source-free series RLC circuit is represented by a second-order differential equation. Its complete solution is a linear combination of two distinct ...

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5.10 : Series RLC Circuit with Source

5.10 : Series RLC Circuit with Source

Consider an automobile ignition system that produces high voltage from the battery essential for generating a spark. This system can be modeled as a ...

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5.11 : Parallel RLC Circuits

5.11 : Parallel RLC Circuits

Consider a street lamp with an RLC surge protector to protect its components from sudden voltage spikes. This setup can be approximated by the simplest ...

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5.12 : Second-order Op Amp Circuits

5.12 : Second-order Op Amp Circuits

Consider an audio system that utilizes a second-order low-pass filter to eliminate the undesirable high-frequency noise in the audio signal. This setup ...

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5.13 : Design Example: Underdamped Parallel RLC Circuit

5.13 : Design Example: Underdamped Parallel RLC Circuit

Underdamped parallel RLC circuits can sustain oscillations at a resonant frequency, making them suitable for use in oscillators. An electrical engineer is ...

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