Name: how capacitor networks combine charge
Uploaded: 2023-04-30T12:37:58.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

Energy

PHYS.PS3.13

Capacitors in Series and Parallel

Capacitors can be connected in either series or parallel configurations in a circuit.
Consider the capacitors connected in series to a battery; the plate connected to the battery&#39;s positive terminal develops a positive charge while the plate attached to the negative terminal is negatively charged.
An equal magnitude of the charge is induced on the other plates. However, the potential difference across each capacitor varies as the ratio of the charge to its capacitance.
Considering the capacitors as a single equivalent capacitor, the potential difference across it equals the sum of potentials across each capacitor.
Thus, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.
Now, if the capacitors are connected in parallel, the potential difference of each capacitor equals the battery voltage. Therefore, the charge varies as the product of the capacitance of individual capacitors and the potential difference.
The total charge for the equivalent capacitor in a parallel connection is the sum of the charges of the individual capacitors. Therefore, the equivalent capacitance is additive.

capacitors in series and parallel

Multiple capacitors connected serve as electrical components in various applications. These multiple capacitors behave as a single equivalent capacitor, and its total capacitance depends on the capacitance of individual capacitors and the type of connections. Capacitors can be arranged in two - orientations, either in series or parallel connections.
Suppose the capacitors are connected one after the other such that the negative terminal of the first connects to the positive terminal of the second. In that case, it is called a series connection. Each capacitor acquires an equal magnitude of charge Q, when this series combination is connected to a battery with voltage V. The charge on the plate attached to the battery&#39;s positive terminal is +Q, and the charge on the plate connected to the negative terminal is &#8722;Q. Charges are then induced on the other plates so that the sum of the charges on all plates, and the sum of charges on any pair of capacitor plates, is zero.
However, the potential drop on each capacitor varies as the ratio of the charge to its capacitance. The sum of the potential drop across each capacitor equals the total battery voltage. The reciprocal of equivalent capacitance in a series circuit is the sum of reciprocals of individual capacitances. Thus, the capacitor combination resembles a single equivalent capacitor with a capacitance value smaller than the smallest capacitances in a series combination.
When the multiple capacitors are connected such that the positive terminals of all the capacitors are connected to the battery&#39;s positive terminal, and negative terminals are connected to the battery&#39;s negative terminal, it&#39;s called a parallel connection. The voltage drop across each capacitor is the same, but the charge stored varies. The total charge stored by the network is the sum of the charge stored in each capacitor. The equivalent capacitance in a parallel circuit equals the sum of all individual capacitances in the network. Thus, the capacitor combination resembles a single equivalent capacitor with higher capacitance.

Multiple capacitors connected serve as electrical components in various applications. These multiple capacitors behave as a single equivalent capacitor, ...

Education

JoVE Core

Unit 1

Capacitance

KEY TERMS AND CONCEPTS

how capacitor networks combine charge

Capacitor networks combine charge and voltage in different ways, depending on how the capacitors are connected. When several capacitors act together, they can be treated as one equivalent capacitor. The total capacitance depends on the capacitance of each capacitor and on the connection type.

In a series connection, the capacitors are connected one after another. The negative terminal of the first capacitor connects to the positive terminal of the second. When this series group is connected to a battery with voltage V, each capacitor carries the same magnitude of charge Q. The plate attached to the battery’s positive terminal has +Q, and the plate attached to the negative terminal has −Q.

The other plates gain induced charges so that the total charge on all plates is zero. The sum of the charge on any pair of capacitor plates is also zero. The potential drop across each capacitor depends on the ratio of charge to capacitance. The total of these voltage drops equals the battery voltage. For capacitors in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. This makes the equivalent capacitance smaller than the smallest capacitance in the series group.

In a parallel connection, the positive terminals of all capacitors connect to the battery’s positive terminal. Their negative terminals connect to the battery’s negative terminal. Each capacitor has the same voltage drop, but the stored charge can differ. The total charge in the network is the sum of the charge on each capacitor. For capacitors in parallel, the equivalent capacitance is the sum of all individual capacitances. The network then acts like a single capacitor with a larger capacitance.

How Capacitor Networks Combine Charge

capacitors and capacitance

Parallel Plate Capacitors and Stored Charge

Parallel plate capacitors store electric charge between two conducting plates. The plates are separated by a distance, and the space between them is either a vacuum or an insulating material called a dielectric. Capacitors are used in many ways, from reducing static in radio reception to storing energy in heart defibrillators. When the two conductors are identical parallel plates, the device is called a parallel plate capacitor. If a battery is connected to an initially uncharged capacitor,...

spherical and cylindrical capacitor

Capacitance in Spheres and Cylinders

A spherical capacitor uses two concentric conducting spherical shells. The inner shell has radius R1, and the outer shell has radius R2. The shells carry equal and opposite charges, +Q and −Q. For an isolated conducting spherical capacitor, the outer shell can be treated as if it were at infinity. By symmetry, the electric field between the shells points radially outward. Using Gauss’s law on a spherical Gaussian surface of radius r gives the field magnitude between the shells. That electric...

Capacitor networks combine charge and voltage in different ways, depending on how the capacitors are connected. When several capacitors act together, they can be treated as one equivalent capacitor. The total capacitance depends on the capacitance of each capacitor and on the connection type. In a series connection, the capacitors are connected one after another. The negative terminal of the first capacitor connects to the positive terminal of the second. When this series group is connected to...

equivalent capacitance

Finding Net Capacitance in Capacitor Networks

Capacitor networks can be arranged in series or parallel, and the connection type changes how charge and voltage are shared. When the network is connected to a battery, the potential drop across each capacitor and the charge stored in each one depend on that arrangement. The full network can then be replaced by one equivalent capacitor that stores the same charge for the same potential difference. To find the net capacitance, a capacitor network is grouped into series and parallel parts. A...

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Capacitor Charging and Stored Electric Energy

A charged capacitor stores electric potential energy by doing work during charging. This idea is similar to an archer pulling back a bowstring and storing elastic potential energy. When the arrow is released, that stored energy becomes motion. In the same way, the work put into a capacitor is stored as electric potential energy. For a parallel plate capacitor, the process starts when it is connected to a battery. The plate attached to the negative side of the battery gains extra electrons.

energy stored in a capacitor: problem solving

energy-stored-in-a-capacitor-problem-solving

Capacitor Energy and CDI Ignition

Capacitors store electric potential energy, and that energy can be released over a short time. This makes them useful in a range of applications. Benjamin Franklin coined the word battery in 1749 for a series of capacitors connected to store energy. One common use is capacitor-discharge ignition, or CDI, in small engines. In a CDI system, the energy from a capacitor ignites an induction coil, which then fires the spark plug. To find the energy stored in a typical CDI capacitor, at least two of...

capacitor with a dielectric

How Dielectrics Boost Capacitor Storage

A dielectric can help a parallel plate capacitor store more charge. In a basic capacitor, two conducting plates are separated by a set distance. Keeping the plates parallel can be mechanically difficult, especially when the plates are large and cannot touch each other. A dielectric is a non-conducting material with no free or loosely bound electrons. Placing this material between the plates creates a small gap and helps hold the plates together. It also increases the capacitor’s capacitance,...

dielectric polarization in a capacitor

How Dielectrics Change Capacitor Fields

Dielectrics change the electric field, voltage, and capacitance in a capacitor. A dielectric is an insulating material placed between the plates. Its presence affects how the field behaves inside the capacitor. Dielectrics are usually described as polar or nonpolar. In a polar dielectric, positive and negative charges are already separated, so each molecule has a permanent dipole moment. In a nonpolar dielectric, that charge separation is not present until an external electric field acts on...

gauss's law in dielectrics

Dielectric Effects on Electric Fields

Dielectric effects on electric fields explain how an insulating material changes the field between capacitor plates. When a polar dielectric is placed in an external field, its dipoles line up with the field. The opposite charges on nearby dipoles cancel each other, so the dielectric as a whole remains neutral. When the dielectric is inserted between the plates of a capacitor, bound charges appear near the edges of the dielectric and at the metal surface. These induced surface charges create...

potential due to a polarized object

Bound Charges in Polarized Dielectrics

Polarized dielectrics form when charges inside atoms or molecules shift slightly in an electric field. A neutral atom has a positive nucleus and a negative electron cloud. An external electric field pulls them in opposite directions. The pull is balanced by the attraction between the nucleus and electrons, so the atom becomes polarized. Some molecules, such as water, already have separated positive and negative sides. In a uniform electric field, the forces on those sides cancel. Even so, a...

susceptibility, permittivity and dielectric constant

susceptibility-permittivity-and-dielectric-constant

Dielectric Polarization and Capacitance

Dielectric polarization explains how a material responds to an external electric field. When a dielectric is placed in the field, its charges shift so the material becomes polarized. The charge density in the dielectric is the sum of bound and free charge densities, and the total charge density can also be written in terms of the total electric field. The bound charge density can be measured using polarization. This leads to a link between electric displacement and polarization. For linear...

electrostatic boundary conditions in dielectrics

electrostatic-boundary-conditions-in-dielectrics

Field Behavior at Dielectric Interfaces

Field behavior at dielectric interfaces changes when an electric field crosses from one homogeneous medium into another. That change creates a discontinuity, or sudden jump, in the field. The boundary conditions depend on which materials meet at the interface. When the two sides are different dielectric materials, the electric field and the electric displacement are linked through the material’s permittivity. Replacing the electric field with the electric displacement in the boundary...

key terms and concepts

Learn how capacitors combine in series and parallel, including charge, voltage drop, and equivalent capacitance for high school physics.

How Capacitor Networks Combine Charge | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Virginia  Standards of Learning

HIgh School

Physical Science

PS.9

PS.9.a

PH.8

PH.8.a

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Resistance

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Ohm's Law

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PHYS.PS3.11

Kirchhoff's Rules

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PHYS.PS3.12

Capacitors and Capacitance

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Equivalent Capacitance

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Electric Field of Parallel Conducting Plates

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PHYS.PS3.14

Electromagnetic Waves

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PHYS.PS3.15

How Capacitor Networks Combine Charge

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