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

抵抗器と単一のエネルギー貯蔵素子(コンデンサまたはインダクタ)を備えた電気回路は、一次回路と呼ばれます。
これらは、入力信号と出力信号に関連する 1 次微分方程式によって記述されます。
RC回路は、ネオンランプ発振器回路のようなリラクゼーション発振器に使用されています。
電圧が印加されると、コンデンサは充電を開始し、ランプは開回路として機能します。コンデンサがネオンガスをイオン化するために必要な電圧に達すると、ランプは短絡します。
コンデンサが放電してフラッシュが発生し、このプロセスが繰り返されます。
点滅の時間間隔は時定数に依存し、R値とC値を調整することで調整できます。
チューブライトでは、RL回路が使用され、チョークをインダクタとして、固有のワイヤ抵抗が抵抗として機能します。
電圧印加時には、チョークは急激な電流増加に抵抗し、印加電圧とともに増加する起電力を生成します。この起電力によりガスがイオン化され、チューブの光が照らされます。
 RL回路では、抵抗に対するインダクタンスは時定数です。

利益相反は宣言されていません。

一次回路

First-Order Circuits

抵抗器と単一のエネルギー蓄積素子 (コンデンサまたはインダクタ) で構成される一次電気回路は、多くの電子システムの基礎です。 これらの回路は、入力信号と出力信号の間の関係を記述する一次微分Figureによって支配されます。

1 次回路の一般的な例の 1 つは、RC (抵抗器 - コンデンサー) 回路です。 これらの回路では、ネオンランプ発振回路などの緩和発振器で使用されます。 RC 回路に電圧が印加されると、コンデンサが充電を開始し、ランプは開回路として動作します。 ランプ内のネオンガスをイオン化するためにコンデンサが必要な電圧まで充電されると、ランプが突然短絡します。 これによりコンデンサが放電し、閃光が発生します。 コンデンサが完全に放電すると、このプロセスが繰り返され、継続的な点滅効果が得られます。

これらのフラッシュ間の時間間隔は回路の時定数によって決まり、抵抗 (R) と静電容量 (C) の値を調整することで調整できます。 これらの値を慎重に選択することで、フラッシュの頻度を制御する事ができます。

チューブライトでは、RL (抵抗インダクター) 回路として知られる、別のタイプの一次回路が利用されます。 チューブライト内のチョークコイルはインダクターとして機能し、ワイヤーの固有抵抗は抵抗として機能します。 電圧が印加されると、チョークは電流の急激な増加に抵抗し、印加電圧とともに上昇する起電力 (emf) を生成します。 この起電力によりチューブライト内のガスがイオン化され、チューブライトが点灯します。

RL 回路では、時定数は抵抗 (R) に対するインダクタンス (L) として定義されます。 この時定数は、回路が入力信号の変化にどれだけ速く応答するかを決定する上で重要な役割を果たします。 時定数が大きいほど回路の応答は遅くなり、その逆も同様です。

抵抗器と単一のエネルギー貯蔵素子(コンデンサまたはインダクタ)を備えた電気回路は、一次回路と呼ばれます。
彼らはによって説明されています...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

First and Second-Order Circuits

一次および二次回路

KEY TERMS AND CONCEPTS

主要な用語と概念

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...

design example: frog muscle response

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...

parallel rlc circuits

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...

second-order op amp circuits

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

First-Order Circuits in Flashing Lamps

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