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

A student uses an RL circuit to study the muscle response of a frog&#39;s leg to electrical stimulation.
Closing the switch causes a brief muscle contraction while opening it triggers sustained muscle activity for 0.01 seconds.
The student models the frog&#39;s leg as a resistor to determine its resistance, assuming that a current of 20 milliamperes induces the sustained muscle response.
When the switch is closed, the inductor acts as a short circuit at a steady state, bypassing the resistor and causing a mild muscle contraction.
Applying Ohm&#39;s law to the 60 ohm resistor gives the initial current.
When the switch is opened, the circuit becomes a source-free RL circuit. Current now flows through the resistor, causing sustained muscle activity.
The time constant equals the ratio of inductance to resistance, and the current passing through the inductor is expressed using the calculated initial current and time constant.
The current and time values corresponding to the sustained muscle activity are substituted into the current equation. Solving the equation gives the value of the unknown resistance.

design example: frog muscle response

A student is tasked to work on an intriguing experiment involving an RL (Resistor-Inductor) circuit to study the muscle response of a frog&#39;s leg to electrical stimulation. The RL circuit plays a crucial role in this experiment, providing the means to control and measure the electrical impulses that trigger muscle contraction.
When the switch connecting the RL circuit is closed, a brief muscle contraction is observed. This is because, at a steady state, the inductor acts like a short circuit, bypassing the resistor and causing a mild, brief contraction in the frog&#39;s leg. Applying Ohm&#39;s law to the 60-ohm resistor, the student can calculate the initial current passing through the circuit.
Upon opening the switch, the RL circuit becomes source-free. Now, the current flows through the resistor, which the student models as the frog&#39;s leg. This change causes sustained muscle activity lasting for ten seconds.
The student assumes that a current of 20 milliamperes is responsible for inducing this sustained muscle response. To verify this assumption, they use the time constant of the RL circuit, which equals the ratio of inductance to resistance. The current passing through the inductor can be expressed using the calculated initial current and this time constant.
Substituting the current and time values corresponding to the sustained muscle activity into the current equation, the student can solve for the unknown resistance. This resistance value represents the modeled resistance of the frog&#39;s leg.
This experiment serves as a practical demonstration of how RL circuits can be used to study physiological responses. It illustrates the fundamental principles governing these circuits, such as transient and steady-state responses and the concept of the time constant. By drawing parallels between electrical circuits and biological systems, it also highlights the interdisciplinary nature of science, bridging the gap between physics and biology.

A student uses an RL circuit to study the muscle response of a frog&#39;s leg to electrical stimulation.
Closing the switch causes a brief muscle ...

Education

JoVE Core

Electrical Engineering

Unit 1

First and Second-Order Circuits

KEY TERMS AND CONCEPTS

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...

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

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112.51.c.1.A.

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112.51.c.1.B.

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112.51.c.1.C.

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112.51.c.1.D.

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112.51.c.1.E.

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RL Circuit and Frog Leg Current Response

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