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Series RLC Circuit without Source01:21

Series RLC Circuit without Source

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Within the field of electrical circuits, source-free RLC circuits present an intriguing domain. These circuits comprise a series arrangement of a resistor, inductor, and capacitor, operating independently of external energy sources. Their initiation hinges upon utilizing the initial energy stored within the capacitor and inductor to instigate their functionality. Their mathematical equation, a second-order differential equation, sets these circuits apart. This equation captures how the...
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Series Resonance01:17

Series Resonance

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The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...
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Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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RL Circuit without Source01:14

RL Circuit without Source

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When a DC source is suddenly disconnected from an RL (Resistor-Inductor) circuit, the circuit becomes source-free. Assuming the inductor has an initial current denoted as I0, the initial energy stored in the inductor can be determined.
Applying Kirchhoff's voltage law around the loop of the circuit and substituting the voltages across the inductor and resistor yields a first-order differential equation. A logarithmic equation is obtained by rearranging the terms in this equation,...
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Thevinin's Theorem01:15

Thevinin's Theorem

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Thévenin's theorem plays a pivotal role in electrical circuit analysis, offering a solution to the challenges posed by variable loads within a circuit. In practical applications, it is common to encounter circuits where certain elements remain fixed while others fluctuate, often referred to as the "load." A typical household electrical outlet serves as a prime example of a variable load, as it can be connected to a variety of appliances, each with its own unique electrical...
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RL Circuit with Source01:14

RL Circuit with Source

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When an RL (Resistor-Inductor) circuit is connected to a DC source, the complete response of the circuit can be divided into two parts: the transient response and the steady-state response.
The transient response of the circuit is its temporary reaction to the sudden application of the DC source. This response is characterized by a current that exponentially decays to zero as time approaches infinity. During this transitional period, the inductor behaves like a short circuit, causing the source...
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First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources.

Entropy (Basel, Switzerland)·2020
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Related Experiment Video

Updated: Jul 12, 2025

Monitoring Leucine-Rich Repeat Containing 8 Channel (LRRC8/VRAC) Activity Using Sensitized-Emission Förster Resonance Energy Transfer (SE-FRET)
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Monitoring Leucine-Rich Repeat Containing 8 Channel (LRRC8/VRAC) Activity Using Sensitized-Emission Förster Resonance Energy Transfer (SE-FRET)

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Variable-Length Resolvability for General Sources and Channels.

Hideki Yagi1, Te Sun Han2

  • 1Department of Computer and Network Engineering, The University of Electro-Communications, Tokyo 182-8585, Japan.

Entropy (Basel, Switzerland)
|October 28, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces variable-length (VL) source resolvability, defining the minimum average length for approximating probability distributions using VL uniform random numbers. It analyzes this rate using variational distance and divergence measures, finding they coincide for exact approximations.

Keywords:
channel resolvabilityoutput approximationrandom number generationsource resolvabilityvariable-length resolvability

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Area of Science:

  • Information Theory
  • Probability Theory
  • Computer Science

Background:

  • The approximation of probability distributions is fundamental in information theory.
  • Variable-length coding is crucial for efficient data representation.

Purpose of the Study:

  • To introduce and analyze the concept of variable-length (VL) source resolvability.
  • To investigate the minimum average length rate for approximating probability distributions using VL uniform random numbers.
  • To extend the analysis to channel resolvability.

Main Methods:

  • Analysis of VL resolvability using variational distance as an approximation measure.
  • Investigation of VL resolvability with divergence as an approximation measure.
  • Extension of source resolvability to channel resolvability.
  • Analysis of second-order VL resolvability.

Main Results:

  • The asymptotically minimum average length rate, termed VL resolvability, is investigated.
  • It is shown that resolvability under variational distance and divergence measures coincides when asymptotically exact approximation is required.
  • A general characterization of channel resolvability is obtained, reducing to source resolvability formulas for identity channels.

Conclusions:

  • VL source resolvability provides a new framework for understanding information approximation.
  • The findings unify different approximation measures under specific conditions.
  • The generalization to channel resolvability offers broader applicability in communication systems.