Name: rl circuit and frog leg current response
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.2.D.

Design Example: Frog Muscle Response

学生はRL回路を使用して、電気刺激に対するカエルの足の筋肉反応を研究します。
スイッチを閉じると短時間の筋肉収縮が起こり、スイッチを開くと0.01秒間持続的な筋肉活動が引き起こされます。
学生は、カエルの足を抵抗としてモデル化し、20ミリアンペアの電流が持続的な筋肉反応を誘発すると仮定して、その抵抗を決定します。
スイッチが閉じられると、インダクタは定常状態で短絡として機能し、抵抗をバイパスして軽度の筋肉収縮を引き起こします。
60Ωの抵抗器にオームの法則を適用すると、初期電流が得られます。
スイッチを開くと、回路はソースフリーのRL回路になります。電流が抵抗器を流れるようになり、持続的な筋肉活動を引き起こします。
時定数はインダクタンスと抵抗の比に等しく、インダクタを通過する電流は、計算された初期電流と時定数を使用して表されます。
持続的な筋肉活動に対応する現在の値と時間の値は、現在の方程式に代入されます。方程式を解くと、未知の抵抗の値が得られます。

利益相反は宣言されていません。

rl 回路設計

学生は、電気刺激に対するカエルの脚の筋肉反応を研究するための RL (抵抗インダクター) 回路を含む興味深い実験に取り組む課題があります。 RL 回路はこの実験で重要な役割を果たし、筋肉の収縮を引き起こす電気インパルスを制御および測定する手段を提供します。

RL 回路に接続しているスイッチを閉じると、短い筋肉の収縮が観察されます。 これは、定常状態ではインダクターが短絡のように動作し、抵抗器をバイパスし、カエルの足に穏やかな短時間の収縮を引き起こすためです。 オームの法則を 60 オームの抵抗器に適用すると、生徒は回路を流れる初期電流を計算できます。

スイッチを開くと、RL 回路はソースフリーになります。 ここで、生徒がカエルの足に見立てた抵抗器に電流が流れます。 この変化により、筋肉の活動が 10 秒間持続します。

学生は、20 ミリアンペアの電流がこの持続的な筋肉反応を引き起こす原因であると想定しています。 この仮定を検証するために、彼らは、インダクタンスと抵抗の比に等しい RL 回路の時定数を使用しました。 インダクターに流れる電流は、計算された初期電流とこの時定数を用いて表すことができます。

持続的な筋肉活動に対応する電流値と時間値を電流Figureに代入すると、生徒は未知の抵抗を解くことができます。 この抵抗値は、カエルの足のモデル化された抵抗を表します。

この実験は、RL 回路を使用して生理学的反応を研究する方法を実際にデモンストレーションするために役立ちます。 これは、過渡応答および定常状態応答、時定数の概念など、これらの回路を支配する基本原理を示しています。 電気回路と生物学的システムの類似点を描くことで、物理学と生物学の間のギャップを埋める、科学の学際的な性質も強調します。

RL 回路設計

学生はRL回路を使用して、電気刺激に対するカエルの足の筋肉反応を研究します。
スイッチを閉じると一瞬筋肉が...

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

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 muscle response. The student uses Ohm’s law with the 60-ohm resistor to find the initial current in the circuit.

When the switch is opened, the RL circuit becomes source-free. The current then flows through the resistor, which is modeled as the frog’s leg. This change leads to sustained muscle activity that lasts for ten seconds. The student assumes that 20 milliamperes is the current needed for this response.

To test that assumption, the student uses the RL time constant. The time constant is the inductance divided by the resistance. The current in the inductor is written using the initial current and this time constant. By substituting the current and time values for the sustained muscle activity, the student solves for the unknown resistance. That value represents the modeled resistance of the frog’s leg.

This experiment shows how RL circuits can be used to study physiological responses. It also connects transient and steady-state behavior with the idea of a time constant. By linking physics and biology, the setup shows how electrical circuit ideas can help explain a living system.

RL Circuit and Frog Leg Current Response

first-order circuits

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...

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

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 how an RL circuit models frog leg muscle response, from brief contraction to sustained activity, using current, time constant, and resistance.

RL Circuit and Frog Leg Current Response | 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

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Ask questions and define problems related to specialized topics of study based on observations or information from text, phenomena, models, or investigations;

112.51.c.1.A.

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112.51.c.1.B.

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112.51.c.1.C.

Common Lab Glassware and Uses

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112.51.c.1.D.

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Collect quantitative data using the International System of Units (SI) or qualitative data as evidence as appropriate to the specialized topic of study;

112.51.c.1.E.

Review and Preview

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112.51.c.1.F.

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112.51.c.1.G.

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112.51.c.1.H.

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RL Circuit and Frog Leg Current Response

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