Capacitance

Page 1-B

This text is meant to accompany class discussions. It is not everything there is to know about the basics of torque and the two conditions of equilibrium. It is meant as a prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Click for the questions that go with this reading

Capacitance

Take two metal flat metal plates of equal size. Position them such that they are parallel to each other. Connect one plate to the negative side of a battery and the opposite plate to the positive side of a battery. An equal amount of charge will move off of one plate and onto the the other plate. As this happens an electric field will build between the plates. This will not continue forever. once the potential difference across the plates equals the potential difference of the battery, the charges will stop moving. Given enough time the plate that is connected to the positive side of the battery will positively charged and the side connected to the negative side will be negatively charged. The potential difference will match the potential difference of the battery.

PArallel Plate Capacitor

Because these two plates have a potential difference, the charged plates are energy storage devices. This is called a parallel plate capacitor.

Capacitance is defined as the ratio of the charge on the plates, measured in Coulombs, to the potential difference, measured in Volts. Capacitance is measured in farads -abbreviated with a capital "F" because it is named in honor of Michael Faraday.

C is the capacitance [ Farads: F ]
Q is the charge on one the plates [ Coulomb: C ]
V is the potential difference across the plates [ Volts: V ]

Each plate has the same charge on it just with an opposite sign. When physicists talk about the charge on this simple capacitor, they are referring to the charge on one plate. This is the "Q" in the formula for capacitance.

Sometimes it is convenient to think of the equation above by isolating the charge on the plates.

This shows that the charge, Q, is directly proportional to the potential difference, ΔV.

Parallel Plate Capacitor

Furthermore, for a parallel plate capacitor, the formula for determining the capacitance.

ε_o describes the ability to store energy in the presence of an electric field. Sometimes a polarizable material such as glass, mylar, paper, etcetera. These materials are called a dielectric and they increase the capacitance of a capacitor. The dielectric constant, K, measures how the permitivity constant is affected. A higher dielectric constant means a higher capacitance and therefore a higher amount of energy can be stored.

Every dielectric has a limit to how much energized charge is can hold back. The breakdown voltage is the amount of voltage needed to turn the normally insulating dielectric into a conductor. In a capacitor if the dielectric breakdown voltage is reached, the capacitor usually shorts out and becomes nothing more than wire. Some capacitors can explode and spray their electrolytes out. These electrolytes are dangerous and can harm your skin or blind you if they get in your eye.

Material	Dielectric Constant	Breakdown Voltage (V/m)
Vacuum	1	-
Pyrex Glass	5.6	14 x 10⁶
Mylar	3.1	430 x 10⁶
Air	1	3 x 10⁶
Teflon	2.1	60 x 10⁶
Paper	3.7	16 x 10⁶
Polyethylene	2.25	50 x 10⁶

Example 1

Question
Solution

When accounting for the amount of humidity in the air, the breakdown voltage of air is between 20,000 and 70,000 V/inch. On a clear, dry, day in the winter time, it is not unusual for the air's breakdown voltage to be 50,000 V/inch. If you rub the fur of a pet and then as you touch a door knob get an spark of between your hand and the door knob that is 1/2 an inch long, then what is the potential difference between the two ends of the arc of electricity?

When accounting for the amount of humidity in the air, the breakdown voltage of air is between 20,000 and 70,000 V/inch. On a clear, dry, day in the winter time, it is not unusual for the air's breakdown voltage to be 50,000 V/inch. If you rub the fur of a pet and then as you touch a door knob get an spark of between your hand and the door knob that is 1/2 an inch long, then what is the potential difference between the two ends of the arc of electricity?

This question is solved using the breakdown voltage and dimensional analysis.

Givens
V_breakdown =50,000^V/_in

d = 0.5 inches

Example 2

Question
Solution

A typical capacitor is made from two pieces of metal seperated by some distance with a dielectic between them. In a home made capacitor, two plates with an area of 3.00 cm² each is seperated by a 0.100 mm. The capacitor is measured to have a capacitance of 5.5755 x 10^-11 F. Using the table above, determine which material was used as the dielectric between the plates.

Strategy

Use the basic equation for the definition of capacitance.
Rearrange to isolate the dielectric.
Compare answer to the table above.

Example 3

Question
Hint
Solution

A "super" or "ultra" capacitor is made a little different from a typical capacitor. The two metal plates a covered wtih a carbon coating to increase the surface area that charges can attach to. It is also made from a setup that behave a like a double set of capacitors.This means double the area. There a a couple different types but typically the two plates are the diameter of a molecule apart from each other. What is the capcitance of a super capacitor if it has the same area as the example 2, above, for each plate. The dielectic is air.

The diameter of a cabon atom will need to be reseached on the Internet.

The diameter of a carbon atom can be found on Hyperphysics 2.2 x 10^-8 cm = 2.2x10^-11m.

Example 4

Question
Hint
Solution

A paralle plate capacitor has air between the two plates. The capacitor has a value of 5.00 x 10^-6 F. Each plate has a charge of 1.00x10⁷ C on it. What is the strength of the electric field betwen the plates if they are seperated by 0.500 mm.

Convert every measurement to SI units.
Solve for the potential difference using the definition of capcitance, (above.)
Use this with what you what was learned in past units about parallel plates and electric fields.

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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