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Oscillations In An LC Circuit

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

RLC Circuit as a Damped Oscillator

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

Current Growth And Decay In RL Circuits

Current Growth And Decay In RL Circuits

The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...

Design Example: Underdamped Parallel RLC Circuit

Design Example: Underdamped Parallel RLC Circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...

Second-Order Circuits

Second-Order Circuits

Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...

Forced Oscillations

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

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Related Experiment Video

Updated: Sep 28, 2025

Rewiring Neuronal Circuits: A New Method for Fast Neurite Extension and Functional Neuronal Connection

Rewiring Neuronal Circuits: A New Method for Fast Neurite Extension and Functional Neuronal Connection

Published on: June 13, 2017

Adaptive rewiring in nonuniform coupled oscillators.

MohamamdHossein Manuel Haqiqatkhah^1,2, Cees van Leeuwen^1,3

¹Brain and Cognition Research Unit, KU Leuven, Leuven, Belgium.

Network Neuroscience (Cambridge, Mass.)

|March 31, 2022

Summary

This summary is machine-generated.

Brain network rewiring can develop complex structures even with varied connection strengths. This adaptive rewiring supports information processing in neural networks, suggesting robustness in biological and artificial systems.

Keywords:

Complexity Dynamical systems Evolving neural networks Neural oscillators

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Area of Science:

Neuroscience
Complex Systems
Computational Biology

Background:

Brain structural plasticity involves adaptive rewiring based on network activity synchronization.
Adaptive rewiring transforms random networks into complex, modular small-world networks with rich-club effects.
Previous studies focused on uniform coupling strengths, neglecting amplitude and connection nonuniformities.

Purpose of the Study:

To investigate if nonuniformities in oscillator amplitude or connection strength can coexist with adaptive rewiring.
To determine the impact of these nonuniformities on the development of network complexity and information processing.

Main Methods:

Simulated network evolution with adaptive rewiring.
Introduced subsets of oscillators with differing amplitudes or connection strengths.
Analyzed network structure, modularity, and connectivity under these perturbed conditions.

Main Results:

Nonuniformities led to the formation of distinct structural and functional communities.
These communities generally maintained network connectivity, allowing complexity development.
Network complexity and adaptive rewiring robustly developed despite amplitude or connection strength variations.
Pathological network development occurred only in a small fraction of simulations.

Conclusions:

Adaptive rewiring is robust and can operate alongside information processing functions in neural networks.
Nonuniformities in amplitude and connection strength do not necessarily impede the development of complex network structures.
Findings support the potential for adaptive rewiring in both biological and artificial neural systems.