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

Uno studente utilizza un circuito RL per studiare la risposta muscolare della zampa di una rana alla stimolazione elettrica.
La chiusura dell'interruttore provoca una breve contrazione muscolare mentre l'apertura innesca un'attività muscolare sostenuta per 0,01 secondi.
Lo studente modella la zampa della rana come un resistore per determinarne la resistenza, supponendo che una corrente di 20 milliampere induca la risposta muscolare sostenuta.
Quando l'interruttore è chiuso, l'induttore agisce come un cortocircuito in uno stato stazionario, bypassando il resistore e provocando una lieve contrazione muscolare.
Applicando la legge di Ohm al resistore da 60 ohm si ottiene la corrente iniziale.
Quando l'interruttore viene aperto, il circuito diventa un circuito RL privo di sorgente. La corrente ora scorre attraverso il resistore, causando un'attività muscolare sostenuta.
La costante di tempo è uguale al rapporto tra induttanza e resistenza e la corrente che passa attraverso l'induttore è espressa utilizzando la corrente iniziale e la costante di tempo calcolate.
I valori attuali e temporali corrispondenti all'attività muscolare sostenuta vengono sostituiti nell'equazione corrente. Risolvendo l'equazione si ottiene il valore della resistenza incognita.

Nessun conflitto di interessi dichiarato.

esempio di progettazione: progettazione di circuiti rl

Uno studente ha il compito di lavorare su un esperimento intrigante che coinvolge un circuito RL (Resistore-Induttore) per studiare la risposta muscolare della zampa di una rana alla stimolazione elettrica. Il circuito RL svolge un ruolo cruciale in questo esperimento, fornendo i mezzi per controllare e misurare gli impulsi elettrici che innescano la contrazione muscolare.

Quando l'interruttore che collega il circuito RL è chiuso, si osserva una breve contrazione muscolare. Questo perché, in condizioni stazionarie, l'induttore si comporta come un cortocircuito, bypassando il resistore e provocando una lieve e breve contrazione nella zampa della rana. Applicando la legge di Ohm al resistore da 60 ohm, lo studente può calcolare la corrente iniziale che passa attraverso il circuito.

All'apertura dell'interruttore, il circuito RL diventa privo di sorgente. Ora la corrente scorre attraverso il resistore, che lo studente modella come la zampa di rana. Questo cambiamento provoca un'attività muscolare prolungata che dura dieci secondi.

Lo studente presuppone che sia una corrente di 20 milliampere la responsabile dell'induzione di questa risposta muscolare sostenuta. Per verificare questa ipotesi, utilizza la costante di tempo del circuito RL, che è uguale al rapporto tra induttanza e resistenza. La corrente che passa attraverso l'induttore può essere espressa utilizzando la corrente iniziale calcolata e questa costante di tempo.

Sostituendo i valori attuali e temporali corrispondenti all'attività muscolare sostenuta nell'equazione corrente, lo studente può risolvere la resistenza sconosciuta. Questo valore di resistenza rappresenta la resistenza modellata della zampa della rana.

Questo esperimento serve come dimostrazione pratica di come i circuiti RL possano essere utilizzati per studiare le risposte fisiologiche. Illustra i principi fondamentali che governano questi circuiti, come le risposte transitorie e stazionarie e il concetto di costante di tempo. Tracciando paralleli tra circuiti elettrici e sistemi biologici, evidenzia anche la natura interdisciplinare della scienza, colmando il divario tra fisica e biologia.

Esempio di Progettazione: Progettazione di Circuiti RL

Uno studente utilizza un circuito RL per studiare la risposta muscolare della zampa di una rana alla stimolazione elettrica.
La chiusura dell'interruttore provoca un corto ...

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

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

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

Correlation and Causation

Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A ...

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

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy ...

Demonstrating the Scientific Method with Tree Branches
ExpandObtain branches containing a few dozen typical leaves from five different local tree species. ...

Observation and Background Research
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Problem-Solving

A problem-solving strategy is a plan of action used to find a solution. It involves trial and error, algorithms, heuristics, and insights. Effective ...

Problem Definition

Problem definition is the initial and the most essential step in research.
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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Electrical Safety

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Working with Centrifuges

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Working with Hot and Cold Sources

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Guidelines in Case of a Laboratory Emergency

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Chemical Storage: Categories, Hazards And Compatibilities

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Safe Handling of Mineral Acids

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Handling Chemical Spills

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Proper Use of Autoclaves

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Fume Hoods and Laminar Flow Cabinets

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Fume hoods and laminar flow cabinets are engineering controls ...

Decontamination for Laboratory Biosafety

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Proper Waste Disposal

Robert M. Rioux and Taslima A. Zaman, Pennsylvania State University, Pennsylvania, PA

Users are responsible for the proper disposal of the waste ...

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

Source: Laboratory of Dr. Neal Abrams &#8212; SUNY College of Environmental Science and Forestry
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Proper Lab Notebook Keeping

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	Nitration of Methyl BenzoateExpand
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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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Ogive Graph

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Histogram

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Relative Frequency Histogram

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Scatter Plot

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Time-Series Graph

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Bar Graph

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Multiple Bar Graph

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Pareto Chart

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Pie Chart

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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.

Modeling and Similitude

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Models, Theories, and Laws

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112.51.c.1.G.

Scientific Laws and Theories

Scientific Laws

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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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