Name: displacement current in an rc circuit
Uploaded: 2023-09-18T17:11:20.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.PSc.6.5

Ampere-Maxwell's Law: Problem-Solving

Un condensador de placa paralela en vacío está en condiciones de carga. El radio de cada placa es de 5 cm. En un instante, la corriente de conducción que fluye a través de los cables es de 0,4 A. ¿Cuál será la corriente de desplazamiento entre las placas en este momento?
Además, calcule la densidad de corriente de desplazamiento y evalúe la tasa de cambio en el campo eléctrico entre las placas. Calcule el campo magnético inducido entre las placas y represúrelo a una distancia de 1 a 5 cm del eje.
La corriente de desplazamiento se expresa en términos de flujo eléctrico, que a su vez, se puede obtener en términos de carga.
La corriente de desplazamiento es igual a la corriente de conducción que fluye a través de los cables, que es de 0,4 amperios.
Además, se puede calcular la densidad de corriente de desplazamiento.
A medida que el condensador se carga, aumenta el campo eléctrico entre las placas, que se evalúa utilizando la densidad de corriente de desplazamiento y la permitividad del espacio libre.
Según la ley de Ampere-Maxwell, el campo magnético se induce entre las placas del condensador, que se calcula para diferentes distancias del eje y se traza como se muestra.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 2. [Versión web], páginas 94–95. Obtenido de <a href="https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves">https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves</a></li>
</ol>

ley de ampère-maxwell: resolución de problemas

Un condensador de placas paralelas con capacidad C, cuyas placas tienen área A y distancia de separación d, está conectado a una resistencia R y una batería de voltaje V. La corriente comienza a fluir en t = 0. ¿Cuál es la corriente de desplazamiento entre las placas del condensador en el tiempo t? A partir de las propiedades del condensador, ¿cuál es la corriente real correspondiente?

Para resolver el problema, podemos usar las ecuaciones del análisis de un circuito RC y la versión de la ley de Ampère de Maxwell.

Para la primera parte del problema, el voltaje entre las placas en el tiempo t está dado por:

<img alt="Equation1" src="/files/ftp_upload/14207/14207_Equation_1.svg" style="text-align: center; height: 35px;">

Supongamos que el eje z apunta desde la placa positiva hacia la placa negativa. En este caso, la componente z del campo eléctrico entre las placas en función del tiempo t está dada por:

<img alt="Equation2" src="/files/ftp_upload/14207/14207_Equation_2.svg" style="text-align: center; height: 38px;">

Por lo tanto, la componente z de la corriente de desplazamiento Id entre las placas del condensador se puede evaluar como:

<img alt="Equation3" src="/files/ftp_upload/14207/14207_Equation_3.svg" style="text-align: center; height: 37px;">

donde <img alt="Equation 4" src="/files/ftp_upload/14207/14207eq04.png" style="margin: auto;"> se está utilizando la capacitancia C.

Además, para resolver la segunda parte del problema anterior, la corriente hacia el condensador después de que se cierra el circuito se puede obtener por la carga en el condensador, que a su vez se puede evaluar usando la expresión para VC. Como resultado, se encuentra que la corriente real hacia el condensador es igual a la corriente de desplazamiento.

Ley de Ampère-Maxwell: Resolución de problemas

Un condensador de placa paralela con capacitancia C, cuyas placas tienen un área A y una distancia de separación d, se conecta a una resistencia R y a una batería de tensión ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Electromagnetic Induction

Inducción electromagnética

KEY TERMS AND CONCEPTS

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displacement current in an rc circuit

Displacement current in an RC circuit can be found by tracking the charging capacitor. A parallel-plate capacitor with capacitance C, plate area A, and plate separation d is connected to a resistor R and a battery of voltage V. When the current starts to flow at t = 0, the charge and voltage on the capacitor change with time.

The first step is to use the RC-circuit result for the capacitor voltage at time t. With the z-axis pointing from the positive plate to the negative plate, the electric field between the plates has a z-component that follows that same time dependence. The displacement current between the plates is then evaluated from this electric field and the capacitor relation.

The second step is to find the real current into the capacitor after the circuit is closed. This current is obtained from the charge on the capacitor, using the expression for V_C. The result is that the real current into the capacitor is the same as the displacement current.

Displacement Current in an RC Circuit

induction

Magnetic Flux and Induced Current

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ampere-maxwell's law: problem-solving

Displacement current in an RC circuit can be found by tracking the charging capacitor. A parallel-plate capacitor with capacitance C, plate area A, and plate separation d is connected to a resistor R and a battery of voltage V. When the current starts to flow at t = 0, the charge and voltage on the capacitor change with time. The first step is to use the RC-circuit result for the capacitor voltage at time t. With the z-axis pointing from the positive plate to the negative plate, the electric...

differential form of maxwell's equations

Maxwell’s Equations at a Point

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Eddy Currents and Magnetic Braking

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Magnetic Flux and Induced Emf

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lenz's law

Magnet Motion and Induced Current

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faraday disk dynamo

Faraday Disk Dynamo and DC Output

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induced electric fields: applications

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displacement current

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Maxwell’s correction to Ampère’s law explains how changing electric fields can create magnetic fields. The key idea is the displacement current, Id, which Maxwell added to the real conduction current, I. This extra term helps the law work when current is not steady. The displacement current is defined using the permittivity of free space, ε0, and the electric flux, ΦE. It is not a real flow of charge. Instead, it is an added term in Maxwell’s equations that acts like current in Ampère’s law. <br...

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electromagnetic fields

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key terms and concepts

See how displacement current is found in a charging parallel-plate capacitor using RC circuit relations and Maxwell’s version of Ampère’s law.

Displacement Current in an RC Circuit | JoVE K12

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JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

PS.Phy.5.2

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HIgh School

PS.9

PS.9.e

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

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Instantaneous Velocity - I

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Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

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Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

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Analyze and interpret data to explain the motion of an object moving with a constant velocity or that is accelerating.

PS.PSc.4.1

Electrical Current

Electrical current is defined as the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large ...

Drift Velocity

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced ...

Current Density

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, ...

Resistivity

When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The ...

Resistance

When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known ...

Ohm's Law

Many materials exhibit a simple relationship between the values of current, voltage, and resistance, known as Ohm&#8217;s law. The current that flows ...

Non-ohmic Devices

In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and ...

Construct an explanation to compare simple series and parallel circuits in terms of Ohm's Law.

PS.PSc.6.2

Continuity Equation

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area ...

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current ...

Electrical Conductivity

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Theory of Metallic Conduction

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the ...

Obtain, evaluate, and communicate information to explain how current is affected by changes in composition, length, temperature, and diameter of wire.

PS.PSc.6.3

Magnetism

Magnets are commonly found in everyday objects, such as toys, hangers, elevators, doorbells, and computer devices. Experimentation on these magnets shows ...

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

motion-of-a-charged-particle-in-a-magnetic-field

Motion Of A Charged Particle In A Magnetic Field

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

magnetic-force-on-a-current-carrying-conductor

Magnetic Force On A Current-Carrying Conductor

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor ...

magnetic-force-on-current-carrying-wires-example

Magnetic Force On Current-Carrying Wires: Example

In a magnetic field, moving charges encounter a force. If a wire contains these moving charges, i.e., if the wire is carrying a current, then a force acts ...

force-on-a-current-loop-in-a-magnetic-field

Force On A Current Loop In A Magnetic Field

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical ...

torque-on-a-current-loop-in-a-magnetic-field

Torque On A Current Loop In A Magnetic Field

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Consider a point charge moving with a ...

Biot-Savart Law

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Biot-Savart Law: Problem-Solving

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Consider a mobile phone battery ...

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the ...

magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the ...

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the ...

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot&#8211;Savart Law can be expressed as follows:

To evaluate the divergence of the ...

Ampere's Law

A fundamental property of a static magnetic field is that it is not conservative, unlike an electrostatic field. Instead, there is a relationship between ...

Ampere's Law: Problem-Solving

Ampere&#x27;s law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the ...

Solenoids

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field for a solenoid is the ...

Use models to explain magnetism in terms of domains, interactions of poles, and magnetic fields.

PS.PSc.6.4

Analyze motion in terms of speed, velocity, acceleration, and momentum.

Displacement Current in an RC Circuit

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