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

Ein Schüler verwendet einen RL-Schaltkreis, um die Muskelreaktion eines Froschschenkels auf elektrische Stimulation zu untersuchen.
Das Schließen des Schalters bewirkt eine kurze Muskelkontraktion, während das Öffnen eine anhaltende Muskelaktivität für 0,01 Sekunden auslöst.
Der Student modelliert das Froschschenkel als Widerstand, um seinen Widerstand zu bestimmen, wobei er davon ausgeht, dass ein Strom von 20 Milliampere die anhaltende Muskelreaktion induziert.
Wenn der Schalter geschlossen ist, wirkt die Induktivität im stationären Zustand wie ein Kurzschluss, der den Widerstand umgeht und eine leichte Muskelkontraktion verursacht.
Wendet man das Ohmsche Gesetz auf den 60-Ohm-Widerstand an, erhält man den Anfangsstrom.
Wenn der Schalter geöffnet wird, wird die Schaltung zu einer quellenfreien RL-Schaltung. Durch den Widerstand fließt nun Strom, was zu einer anhaltenden Muskelaktivität führt.
Die Zeitkonstante entspricht dem Verhältnis von Induktivität zu Widerstand, und der durch die Induktivität fließende Strom wird mit dem berechneten Anfangsstrom und der Zeitkonstante ausgedrückt.
Die aktuellen und zeitlichen Werte, die der anhaltenden Muskelaktivität entsprechen, werden in die aktuelle Gleichung eingesetzt. Das Lösen der Gleichung ergibt den Wert des unbekannten Widerstands.

Es wurden keine Interessenkonflikte angegeben.

entwurfsbeispiel: entwurf einer rl-schaltung

Ein Student hat die Aufgabe, an einem faszinierenden Experiment mit einer RL-Schaltung (Widerstand-Induktor) zu arbeiten, um die Muskelreaktion eines Froschbeins auf elektrische Stimulation zu untersuchen. Der RL-Schaltkreis spielt in diesem Experiment eine entscheidende Rolle, da er die Möglichkeit bietet, die elektrischen Impulse zu steuern und zu messen, die eine Muskelkontraktion auslösen. Wenn der Schalter, der den RL-Kreis verbindet, geschlossen ist, ist eine kurze Muskelkontraktion zu beobachten. Dies liegt daran, dass die Induktivität im eingeschwungenen Zustand wie ein Kurzschluss wirkt, den Widerstand umgeht und eine leichte, kurze Kontraktion im Froschschenkel verursacht. Durch die Anwendung des Ohmschen Gesetzes auf den 60-Ohm-Widerstand kann der Schüler den anfänglichen Strom berechnen, der durch den Stromkreis fließt. Beim Öffnen des Schalters wird der RL-Kreis quellenfrei. Nun fließt der Strom durch den Widerstand, den der Schüler als Froschschenkel modelliert. Diese Veränderung führt zu einer anhaltenden Muskelaktivität von zehn Sekunden. Der Student geht davon aus, dass ein Strom von 20 Milliampere für die Auslösung dieser anhaltenden Muskelreaktion verantwortlich ist. Um diese Annahme zu überprüfen, verwenden sie die Zeitkonstante der RL-Schaltung, die dem Verhältnis von Induktivität zu Widerstand entspricht. Der durch die Induktivität fließende Strom kann mithilfe des berechneten Anfangsstroms und dieser Zeitkonstante ausgedrückt werden. Durch Einsetzen der Strom- und Zeitwerte, die der anhaltenden Muskelaktivität entsprechen, in die aktuelle Gleichung kann der Schüler den unbekannten Widerstand ermitteln. Dieser Widerstandswert stellt den modellierten Widerstand des Froschschenkels dar. Dieses Experiment dient als praktische Demonstration, wie RL-Schaltkreise zur Untersuchung physiologischer Reaktionen verwendet werden können. Es veranschaulicht die Grundprinzipien dieser Schaltkreise, wie z. B. transiente und stationäre Reaktionen und das Konzept der Zeitkonstante. Indem es Parallelen zwischen elektrischen Schaltkreisen und biologischen Systemen zieht, unterstreicht es auch den interdisziplinären Charakter der Wissenschaft und überbrückt die Lücke zwischen Physik und Biologie.

Entwurfsbeispiel: Entwurf einer RL-Schaltung

Ein Schüler verwendet einen RL-Schaltkreis, um die Muskelreaktion eines Froschschenkels auf elektrische Stimulation zu untersuchen.
Das Schließen des Schalters bewirkt einen kurzen Muskel ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

First and Second-Order Circuits

Schaltungen erster und zweiter Ordnung

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 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

The Scientific Method

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Inductive Reasoning

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Deductive Reasoning

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Correlation and Causation

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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.

Scientific Method

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Demonstrating the Scientific Method with Tree Branches
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Observation and Background Research
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Problem-Solving

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Problem Definition

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The researcher identifies and explains the specific issue or gap to be ...

Apply science practices related to specialized topics of study to plan and conduct investigations or use engineering practices to design solutions to problems;

112.51.c.1.B.

Proper Personal Protective Equipment

Robert M. Rioux &#38; William A Elliott, Pennsylvania State University, University Park, PA
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Emergency Eyewash and Shower Stations

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Working with Centrifuges

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Working with Hot and Cold Sources

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Safe Handling of Mineral Acids

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Proper Use of Autoclaves

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Decontamination for Laboratory Biosafety

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Proper Waste Disposal

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Use appropriate safety equipment and practices during laboratory, classroom, and field investigations as outlined in Texas Education Agency-approved safety standards;

112.51.c.1.C.

Common Lab Glassware and Uses

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Proper Lab Notebook Keeping

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112.51.c.1.D.

SI Units: 2019 Redefinition

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Measurement: Standard Units

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Measurement: Derived Units

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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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What is a Frequency Distribution

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Cumulative Frequency Distribution

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Relative Frequency Histogram

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Multiple Bar Graph

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Organize quantitative or qualitative data using representations appropriate to the specialized topic of study such as scatter plots, line graphs, bar graphs, charts, data tables, diagrams, scientific drawings, and student-prepared models;

112.51.c.1.F.

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112.51.c.1.G.

Scientific Laws and Theories

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Distinguish among scientific hypotheses, theories, and laws as appropriate to the specialized topic of study.

112.51.c.1.H.

Identify advantages and limitations of models such as their size, scale, properties, and materials as appropriate to the specialized topic of study;

112.51.c.2.A.

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112.51.c.2.B.

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RL Circuit and Frog Leg Current Response

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