Name: first-order circuits in flashing lamps
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 15 s
Channel: JoVE

I circuiti elettrici con resistori e un singolo elemento di accumulo di energia - un condensatore o un induttore - sono chiamati circuiti del primo ordine.
Sono descritti da un'equazione differenziale del primo ordine che mette in relazione i segnali di ingresso e di uscita.
I circuiti RC sono utilizzati negli oscillatori di rilassamento come i circuiti oscillatori con lampada al neon.
Quando viene applicata la tensione, il condensatore inizia a caricarsi e la lampada agisce come un circuito aperto. Quando il condensatore raggiunge la tensione necessaria per ionizzare il gas neon, la lampada diventa un cortocircuito.
Il condensatore si scarica, creando un flash, e il processo si ripete.
L'intervallo di tempo tra i lampeggi dipende dalla costante di tempo, regolabile regolando i valori R e C.
Nelle luci a tubo, viene utilizzato un circuito RL, con un'induttanza come induttore e la resistenza intrinseca del filo che funge da resistore.
All'applicazione della tensione, l'induttanza resiste a improvvisi aumenti di corrente, generando un campo elettromagnetico che aumenta con la tensione applicata. Questo campo elettromagnetico ionizza il gas, illuminando la luce del tubo.
In un circuito RL l'induttanza rispetto alla resistenza è la costante di tempo.

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circuiti di primo ordine

First-Order Circuits

I circuiti elettrici del primo ordine, che comprendono resistori e un singolo elemento di accumulo dell'energia, un condensatore o un induttore, sono fondamentali per molti sistemi elettronici. Questi circuiti sono governati da un'equazione differenziale del primo ordine, che descrive la relazione tra i segnali di ingresso e di uscita.

Un esempio comune di circuito del primo ordine è il circuito RC (resistenza-condensatore). Questi circuiti sono utilizzati negli oscillatori di rilassamento come i circuiti oscillatori delle lampade al neon. Quando viene applicata tensione a un circuito RC, il condensatore inizia a caricarsi e la lampada si comporta come un circuito aperto. Quando il condensatore si carica fino alla tensione richiesta per ionizzare il gas neon all'interno della lampada, la lampada va improvvisamente in cortocircuito. Ciò fa sì che il condensatore si scarichi, creando un lampo di luce. Una volta che il condensatore si scarica completamente, il processo si ripete, producendo un effetto lampeggiante continuo.

L'intervallo di tempo tra questi lampeggi, dipende dalla costante di tempo del circuito, che può essere sistemata regolando i valori di resistenza (R) e capacità (C). Scegliendo attentamente questi valori, è possibile controllare la frequenza dei lampeggi.

Nelle luci a tubo viene utilizzato un diverso tipo di circuito del primo ordine, noto come circuito RL (resistore-induttore). La bobina d'arresto nel tubo luminoso funge da induttore, mentre la resistenza intrinseca del filo funziona da resistore. All'applicazione della tensione, l'induttanza resiste a un improvviso aumento di corrente, generando una forza elettromotrice (fem), che aumenta con la tensione applicata. Questo ionizza il gas all'interno del tubo luminoso, facendolo illuminare.

In un circuito RL, la costante di tempo è definita come l'induttanza (L) sulla resistenza (R). Questa costante di tempo gioca un ruolo fondamentale nel determinare la rapidità con cui il circuito risponde ai cambiamenti nel segnale di ingresso. Maggiore è la costante di tempo, più lenta è la risposta del circuito e viceversa.

Circuiti di Primo Ordine

I circuiti elettrici con resistori e un singolo elemento di accumulo di energia - un condensatore o un induttore - sono chiamati circuiti del primo ordine.
Sono descritti da un ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

First and Second-Order Circuits

Circuiti del primo e del secondo ordine

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

first-order circuits in flashing lamps

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals.

One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor reaches the voltage needed to ionize the neon gas, the lamp suddenly acts like a short circuit.

That change lets the capacitor discharge, and the lamp flashes. After the capacitor fully discharges, the same cycle begins again. This repeated charge-and-discharge process creates a steady flashing effect. The time between flashes depends on the circuit time constant, which can be adjusted by changing the resistance R and capacitance C. By selecting different values, the flash frequency can be controlled.

Tube lights use another first-order circuit called an RL circuit, which contains a resistor and an inductor. In this case, the choke coil works as the inductor, and the wire resistance acts as the resistor. When voltage is applied, the choke resists a sudden rise in current and produces an electromotive force, or emf, that grows with the applied voltage. This emf helps ionize the gas in the tube light, so the lamp turns on.

For an RL circuit, the time constant is L divided by R, where L is inductance and R is resistance. This value shows how quickly the circuit responds to changes in the input signal. A larger time constant means a slower response, while a smaller one means a faster response.

First-Order Circuits in Flashing Lamps

first-order circuits

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals. One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor...

rc circuit without source

RC Capacitor Discharge After Power Loss

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit. Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in...

rc circuit with source

RC Circuit Charging After a DC Step

An RC circuit with a DC source shows how a capacitor charges after a sudden voltage step. The applied source is treated as a unit step function, and the capacitor voltage is the step response of the circuit. This response describes how the circuit reacts right after the input changes. A capacitor cannot change its voltage instantly. So, immediately after the switch closes at t=0, the capacitor voltage stays at its initial value. Kirchhoff’s current law is then applied at that moment and...

rl circuit without source

RL Circuit Decay After Source Removal

An RL circuit begins to decay after the DC source is removed. At that moment, the circuit becomes source-free. If the inductor has an initial current, I0, it also stores initial energy. That stored energy drives the natural response of the circuit. Kirchhoff’s voltage law is applied around the loop. The inductor voltage and resistor voltage are substituted into the equation. This gives a first-order differential equation for the current. Rearranging the terms produces a logarithmic form, which...

rl circuit with source

RL Step Response Under a DC Source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied. During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source...

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RL Circuit and Frog Leg Current Response

An RL circuit is used to model the frog leg’s response to electrical stimulation. In this setup, the student studies how current changes in a resistor-inductor circuit can trigger muscle contraction. The circuit provides a way to control and measure the electrical impulses involved in the experiment. When the switch is closed, the frog’s leg shows a brief contraction. At steady state, the inductor acts like a short circuit. That lets current bypass the resistor and produces a mild, short...

second-order circuits

RLC Damping and Resonant Frequency

Second-order circuits use two energy storage elements, such as a capacitor and an inductor, to shape how current and voltage change over time. These circuits include RLC circuits, along with RC and RL circuits that have two capacitors or two inductors. Their behavior is described by second-order differential equations that connect the input signal to the output signal. The input usually comes from a voltage source or a current source. The output is often the voltage across the capacitor, the...

series rlc circuit without source

Natural Response of a Source-Free RLC Circuit

A source-free RLC circuit is a series circuit with a resistor, inductor, and capacitor, but no external energy source. It begins with the energy already stored in the capacitor and inductor. That stored energy drives the circuit at first. The circuit is described by a second-order differential equation. This equation shows how the resistor, inductor, and capacitor interact over time. The resistor removes energy from the circuit, so the solution has an exponential form. When the exponential...

types of responses of series rlc circuits

types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

A source-free series RLC circuit shows three response patterns based on damping. The circuit is described by a second-order differential equation. Its complete solution is made from two distinct solutions. Those solutions depend on the roots, which are written in terms of the damping factor and the resonant frequency. When the damping factor is greater than the resonant frequency, both roots are real and negative. This gives an overdamped response. The circuit output decays slowly over time. <br...

series rlc circuit with source

Forced Response in a Series RLC Circuit

A series RLC circuit with a DC source can model an automobile ignition system. The circuit shows how a battery can produce the high voltage needed for a spark. In this case, the input DC voltage acts like a forcing step function. Applying Kirchhoff's voltage law leads to a second-order differential equation. A second-order differential equation is an equation with a term for the second derivative. The form of this equation is very similar to the one used for a source-free RLC circuit, so the...

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Parallel RLC Step Response in Surge Protectors

Parallel RLC circuits help explain how a surge protector works in a street lamp. The circuit model uses a DC input source that creates a step response when the switch is turned on. This setup shows how the lamp’s components can be protected from sudden voltage spikes. When the switch closes, Kirchhoff’s current law is applied to the parallel RLC circuit. That leads to a second-order differential equation. The solution has two parts: a transient response and a steady-state response. The...

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Second-Order Op Amp Low-Pass Filters

Second-order op-amp low-pass filters remove unwanted high-frequency noise from audio signals. They are used in audio systems to refine sound quality. These filters are often built as voltage followers and have two nodes with storage elements. The circuit analysis follows the same basic method used for second-order RLC circuits. In practice, bulky inductors are usually avoided because of their size and weight. For that reason, the focus here is on RC second-order op-amp circuits, which are...

design example: underdamped parallel rlc circuit

design-example-underdamped-parallel-rlc-circuit

Oscillator Design with a Parallel RLC Circuit

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design. The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance...

key terms and concepts

Explore RC and RL first-order circuits through neon lamps and tube lights. Learn how time constant, resistance, capacitance, and inductance control circuit response.

First-Order Circuits in Flashing Lamps | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

First-Order Circuits in Flashing Lamps

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