Other Types of Capacitors

Spherical capacitor

Consists of two concentric conducting spherical shells of radii R1(inner shell) and R2(Outer shell)

These shells are given equal and opposite charges +Q and -Q, respectively.

symmetry, radially outward

From ________, the electrical field between the shells is directed ________________.

By applying Gauss’ law over a spherical Gaussian surface of radius r concentric with the shell; The enclosed charge is Q.

How to obtain the magnitude of the Electrical field of the Spherical capacitors.

∮ E•n̂dA = E(4πr^2) = Q/ε0

Complete applied equation of the Gauss’ law for the Spherical capacitor.

E = (1/4πε0)*(Q/r^2)r̂

Formula to find the Electrical field between the conductors of the Spherical conductor.

This gets substituted in the E of the first formula of the parallel plate capacitors to and l becomes r̂dr

C = Q/V = (4πε0)*((R1*R2)/R2 - R1)

Formula to find the capacitance of the spherical conductor.

(1/4πε0)*(Q/R1)

Q/4πε0 ∫(from R1 to +∞ ) dr/r^2 = ?

[The Magnitude of the potential difference between the surface of an isolated spheres and infinity]

C = Q/V = Q*(4πε0R1/Q) = 4πε0R1

Equation of the capacitance of an isolated sphere with its derivation.

Cylindrical capacitor

Consists of two concentric, conducting cylinders

Inner cylinder of radius R1, may either be a shell or be completely solid

Outer cylinder is a shell of inner radius R2

Assumed that the length of each cylinder is l and that the

charges +Q and -Q reside on the inner and outer cylinders respectively

∮ E•n̂dA = E(2πrl) = Q/ε0

Complete applied equation of the Gauss’ law for the Cylindrical capacitor.

E = (1/2πε0)*(Q/rl)r̂

Formula to find the Electrical field between the conductors of the cylindrical conductor. (r̂ is the unit radial vector along the radius of the cylinder)

This gets substituted in the E of the first formula of the parallel plate capacitors to and l becomes r̂dr

C = Q/V = 2πε0l/ln(R2/R1)

Formula to find the capacitance of the cylindrical conductor.

Also an important application to determine the capacitance per unit length of the coaxial cable.

geometry

In other cases, capacitance only depends on the ________ of the conductor arrangement.

opposite, outer

In the coaxial cable, current flows in the _________ directions in the inner and outer conductors, with the _____ conductor usually grounded.

C/l = 2πε0/ln(R2/R1)

Equation for the capacitance per unit length of the coaxial cable

metal foil, two, insulation

Common capacitors are often made of two small pieces of __________ separated by ___ small pieces of __________.

Yes, it is true

Is it true that the metal foil and insulation are encased in a protective coating, and two metal leads are used for connecting the foils to an external circuit.

Mica, ceramic, paper, Teflon^TM non-stick coating.

4 common insulting materials in the capacitors.

Electrolytic capacitor

Capacitor type that consists of an oxidized metal in a conducting paste.

Its high capacitance relative to other common types of capacitance is its main advantage

Aluminium electrolytic capacitor

Capacitor whose capacitance can be as high as 1.0 F.

Because it only functions correctly when the metal foil is at a higher potential than the conducting paste. When reverse polarization occurs, electrolytic action destroys the oxide film.

Why you must be careful when using an electrolytic capacitor in a circuit?

Conduction paste

A soft, sticky, electrically conductive material inside an electrolytic capacitor.

Helps to ensure good contact between the foil and the lead wires, allowing electricity to flow smoothly and reducing resistance at those contact points.

Without it the capacitor’s performance could drop or become unstable.

Reverse polarization

Connecting a polarized component, like an electrolytic capacitor, the wrong way around

(negative lead is connected to the higher voltage and positive lead is connected to the lower voltage)

It causes electrolytic action to destroy the oxide film, leading to failure.

Oxide film

A very thin insulating layer on the metal foil in an electrolytic capacitor. It’s formed with the correct voltage and destroyed if voltage is applied backwards.

Electrolytic action

A chemical process inside the electrolytic capacitor where the electrolytes react with the metal foil. In reverse polarization, it dissolves the thin oxide insulating layer

Because half of the time, ac voltage would have the wrong polarity, as an alternating current reverses its polarity.

Why is the electrolytic capacitors cannot be connected across an alternating current source?

Variable air capacitor

Capacitor that has two sets of parallel plates.

By turning the shaft, the cross-sectional area in the overlap of the plates can be changed.

Capacitance of this system can be tuned to a desired value

Stator

(1)

The fixed set of plates

Rotor

(2)

The set of plates attached to a shaft that is rotatable.

Applications of the capacitor tuning.

Radio transmission and in receiving radio signals from electronic devices. For example, tuning the car radio to someone’s favorite station.

Symbol of a common capacitor

Symbol of an electrolytic capacitor

Symbol of a variable-capacitance capacitor

cell biology, plasma membrane, living cell

An interesting applied example of a capacitor model comes from ____________ and deals with the electrical potential in the _______________ of a ___________.

Cell membrane

______________ separate cells from their surroundings but allow some selected ions to pass in or out of the cell.

70 mV

The potential difference across a cell membrane is about how much?

7 to 10 nm

Estimated thickness of a cell membrane.

nano-sized capacitor, 7*10^6 V/m

Treating the cell membrane as a ____________________, the estimated smallest electrical field strength across its plate will be __________ which great enough to create an electrical sparkle in the air.

Coulomb force

Diffusion transfers the ions in the cell until halted by the…

Na+

The type of ion to which most cell membranes are impermeable towards. This ion crosses only through voltage-gated channels in muscles or neurons or through the (name of the ion)-potassium pumps.

Ernest Everett Just

An American biologist who discovered the role of the cell membrane in the reproductive fertilization.

Wave of negativity

A sudden change in the egg’s electrical charge that happens instantly when it fuses with a sperm cell, making the inside more negative.

Fast block

A quick electrical change in the egg’s membrane after sperm entry, preventing any more sperm from fusing with the egg.

Series combination (1/Cs); (V = Q/Cs)

The reciprocal equivalent of the capacitance

Where all the capacitors carry the same charge but the voltage divides among them

Parallel combination (Cp); Q = CpV

The equivalent of the capacitance

Where all the capacitors have the same voltage but the charge divides among them.