School Science Lessons
2024-06-22
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Capacitors, Dielectrics
Table of contents
31.8.0 Capacitors
31.9.0 Dielectrics
31.8.0 Capacitors
31.8.3.8 Blinking neon bulb
31.8.0.0 Capacitors
31.8.3.6 Capacitor charge and discharge
31.8.1.0 Capacitor discharge
31.8.2.0 Capacitors in AC circuits
31.8.2.1 Capacitive reactance
31.8.2.2 Capacitor, (condenser), capacitance in an AC circuit
31.8.2.3 Capacitors charging
31.8.2.4 Capacitors in series and parallel
31.8.3.5 Electrostatic voltmeters
farad
31.8.3.4 Heat from a capacitor
31.8.3.1 Leyden jar capacitor
31.8.3.3 Light a bulb with a capacitor
31.8.1.3 Parallel plate capacitor
31.8.2.5 Power consumed by a capacitor
31.8.5.0 RC time constants
31.8.3.2 Short a capacitor
31.8.4.0 Types of capacitors
31.9.0 Dielectrics
31.9.2.0 Dielectrics
31.9.2.1 Permittivity
Experiments
31.9.2.5 Attraction of charged plates
31.9.2.7 Bound charge
31.9.2.9 Breath figures
31.9.2.2 Capacitor with dielectrics
31.9.2.11 Displacement current
31.9.2.6 Dissectible condenser
31.9.2.3 Equation Q = CV, electroscope
31.9.2.4 Force on a dielectric
31.9.2.8 Impedance of a dielectric
31.9.2.10 Lichtenberg figures
31.8.4.0 Types of capacitors
Fixed capacitors, dielectric capacitors
31.8.3.1 Leyden jar capacitor
Spark-gap capacitors - morse code
31.8.4.1 Ceramic capacitors
31.8.4.2 Film capacitors
31.8.4.3 Paper capacitors
31.8.4.4 Electrolytic capacitors
31.8.4.5 Mica capacitors
31.8.4.6 Supercapacitors
31.8.4.7 Variable capacitors
31.8.0.0 Capacitors
See diagram 31.8.0.0: Circuit to charge a capacitor.
See diagram 31.8.1.1: Parallel plate capacitor.
See diagram 30.5.1.5: Time variation of power.
See diagram 30.5.2.01c: Ratio of voltage to current.
1. Capacitors
Capacitors store electric charge.
Capacitors contain two parallel electrical conductives, plates, separated by an insulating layer, the dielectric.
Capacitors store electrical energy in the form of an electric field, to be released later.
A capacitor stores energy by separating charge.
A potential difference occurs when charge is placed in a capacitor.
Capacitors were formerly called "condensers".
2. Capacitance
Capacitance, C, is the ability of the capacitor to store charge, Q, source of emf, e.g. a battery, will move charge from one plate to the other until the voltage produced by the charge build-up will equal the battery voltage.
Capacitance is measured in farads, F.
Capacitance is the ratio of the total amount of charge stored on the parallel plates / potential difference between the plates (voltage applied to the plates), C = Q / V.
Capacitance, C = Q coulombs / V volts, measured in farads, F.
So 1 farad, F = 1 CV-1.
(Michael Faraday, England, 1791-1867)
The farad
A farad, F, is the SI derived unit of capacitance as the charge in coulombs a capacitor accepts for the potential across it to change by 1 volt.
1 farad is the capacitance, which stores a charge of 1 coulomb across a potential difference of 1 volt.
The farad, F, is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge.
One farad has a very large capacitance, so the smaller units used are the microfarad, µF, and the picofarad pF.
1 mF, 1 millifarad, one thousandth, 10-3, of a farad = 0.001 F.
1 μF, 1 microfarad, one millionth, 10-6, of a farad = 0.000 001 F, (1 F = 1000000 µF).
1 nF 1 nanofarad, one billionth, 10-9, of a farad.
1 pF 1 picofarad, one trillionth, 10−12, of a farad.
Note: Capacitance, C, is measured in farads, F, but charge, Q, is measured in coulombs, C.
Capacitance = εA / d, where ε= permittivity of material between the plates, A = overlapping area of the plates, d = distance between plates.
Capacitors in parallel C = C1 + C2 + C3.
Capacitors in series C = 1 / C1 + 1 / C2 + 1 / C3.
3. Energy of a capacitor
The work done, W, equals the shaded area under the graph of potential difference between the plates, V, and charge of the plates, Q.
So W= QV.
V is actually the average potential difference the charge moves through.
If V = maximum potential difference, the average potential difference = V /2.
So energy stored, W = W X V, Q = CV, so energy stored in a capacitor charge Q and potential difference V =
QV = (Q2 / C) = CV2 joule, j.
Experiment
1. When you switch off the power to your computer, the indicator lights keep glowing for a while, because electrical energy has been stored in capacitors.
2. Show that the capacitance of a parallel plate capacitor is inversely proportional to the distance of separation.
Cover the plates of the capacitor with shellac so that they may contact without shorting.
When 9V is applied momentarily to the capacitor, no deflection is noted on the electroscope.
After separating the plates, the electroscope leaves diverge showing that the voltage has increased and the capacitance has decreased.
For a small deflection of the electroscope, about 1000 volts is needed.
C = Q / V, C= A / d.
31.8.2.0 Capacitors in AC circuits
See diagram 30.5.1.0: AC generator and capacitor.
See diagram 30.5.1.3: Time variation of voltage and current for a capacitor.
See diagram 30.5.1.5: Time variation of power for a capacitor.
1. The current in a capacitor in an AC circuit depends on the frequency and is out of phase with the voltage.
The voltage across a capacitor lags the current by 90o.
2. A capacitor stops DC after allowing a brief flow of current that charges it, but lets AC pass though it as the capacitor is charged then discharged in one direction, then charged then discharged in the opposite direction, 50 times per second.
So no current actually passes through a capacitor, because its plates are separated by an insulator.
However, current seems to pass through as the electrons move on and off the plates very rapidly.
So an AC ammeter does register the "passing" of current and the larger the capacitor the greater the current "passed".
3. If a generator, frequency ω, supplies an RMS voltage to a capacitor, capacitance C, RMS current, IRMS, = ωCVRMS.
Experiment
4. Connect a 1000 μF in series with a 20 W globe to a 9 Volt AC source, and observe the brightness of the globe.
If the 1000 μF capacitor is replaced by a 470 μF capacitor, the globe is less bright.
If the 9 Volt AC source is replace by a 9 Volt DC source, the globe will not light.
31.8.2.1 Capacitive reactance
1. Capacitive reactance Xc is the ratio of the voltage to the current in a capacitor.
The equivalent of Ohm's law for a capacitor is Vc = IXc, where Xc is the capacitive reactance in ohm, Vc is the capacitive voltage, and I is the effective current.
So capacitive reactance, Xc = 1 / 2πfC, where f is the frequency of the AC in hertz and C is the capacitance in farad.
However, there is a difference in phase.
The current reaches a maximum, the capacitor has maximum charge, when the current has just finished flowing forwards and is about to start flowing backwards.
So the voltage across the capacitor is 90o, one quarter cycle, behind the current.
So reactance is the ratio of voltage to current when they differ in phase by 90o and resistance is the same ratio when voltage and current are in phase.
2. Also, I RMS = VRMS / Xc, where Xc is called the "capacitive reactance".
It is the "resistance of the capacitor".
So Xc = 1 / ωC, ohm.
3. The capacitive reactance of a 20-F capacitor in a 50 Hz circuit = Xc = 1 / ωC = 1 / (2 π x 50 x 20 x 10-6) = 159 ohm.
4. Capacitive reactance is frequency dependent.
See diagram 30.5.2.2. The ratio of voltage to current in a capacitor decreases with frequency.
Unlike resistance, capacitive reactance depends on frequency of the AC generator.
Reactance is frequency dependent.
When frequency is reduced, the reactance increases and the current decreases.
A capacitor in an AC circuit consumes no energy.
For a capacitor, the ratio of voltage to current decreases with frequency.
When the frequency is halved, but the current amplitude is kept constant, the capacitor has twice as long to charge up, so it generates twice the potential difference.
The lower frequency causes a larger charge, and so a larger Vc.
31.8.2.2 Capacitor (condenser), capacitance in an AC circuit
Capacitance and energy
A capacitor stores energy in the form of an electric field between its oppositely charged plates.
So lines of force of an electric field exist between the plates of a capacitor.
The greater the attractive force between the charges on the opposite plates of a capacitor, the more energy is stored.
Coulomb's law
Coulomb's law states that the force between two charged objects is proportional to the product of the charges and inversely proportional to the square of their separation.
See diagram 31.8.2.2 Capacitance and energy.
* The capacitor in circuit (ii) has double the area of the capacitor in circuit (i), so double the capacitance.
* The capacitor in circuit (iii) has half the separation of the capacitor in circuit (ii), so double the capacitance.
* The identical metal plates in circuit (iv) are connected to the same battery.
The charge on the plates separated by an insulator is greater than if separated by air.
Dielectrics concentrate the lines of force of the electric field between the plates and so increase the capacity for storage of energy.
Capacitors are polarized or unpolarized.
Unpolarized capacitors, for less than 1 F, and may be connected with either polarity.
They have high voltage ratings of 50 volts to 250 volts.
They have different types of labels, e.g. 0.1 = 0.1 F = 100 nF, 4 n7 = 4.7 nF.
Very small capacitors have a number code:
First number is 1st digit of the value.
Second number is 2nd digit of the value.
Third number is the number of zeros to give capacitance in pF, e.g. 102 = 1000 pF = 1 nF, 472 J = 4700 pF = 4.7 nF, J = 5% tolerance.
Capacitors are used in filter circuits, because they pass AC (changing) signals, but they block DC (constant) signals.
The time constant measures the time for a capacitor to charge or discharge with a certain resistor.
So capacitors are used with resistors in timing circuits, because it takes a known time for a capacitor to fill with charge.
(Comment: The usual range of capacitors nowadays is 0.47 F (microfarads) to 47 mF (millifarads).
Capacitors for more than 1F are not manufactured, except to special order.
0.5 F and 0.68 F capacitors are found in some computer motherboards instead of the battery that was used to keep the CMOS-based BIOS memory alive.
These capacitors are also used in some modern portable radio, TV tuner memories and high powered audio amplifiers in sporty motor vehicles.
31.8.2.3 Capacitors charging
See diagram 30.5.2.3 Capacitors charging.
The voltage on a capacitor depends on the amount of charge stored on its plates.
The current flowing onto the positive capacitor plate, and the equal current flowing off the negative plate, is the rate at which charge is being stored.
In Diagram 30.5.2.3, the current and the voltage are out of phase.
Vc = q / C.
V = Xc Im sin (ωt -π2).
When charge builds upon a capacitor, a voltage develops across the capacitor, which opposes the charging current.
Voltage across the capacitor V = Q / C, where Q is the amount of charge in coulomb, and C is the capacitance in farad.
The current leads the voltage by a quarter of a cycle, i.e. 90o.
31.8.2.4 Capacitors in series and parallel
The combined capacitance, C, of capacitors in series is less than the smallest capacitor, C1 or C2 or C3.
1 / C = 1 / C1 + 1 / C2 + 1 / C3.
The combined capacitance, C, of capacitors in parallel is as if all the capacitors together behave as one big capacitor.
C = C1 + C2 + C3.
31.8.2.5 Power consumed by a capacitor
See diagram 30.5.2.5: Power consumed by a capacitor.
See diagram 30.5.1.4: Alternating current voltage.
Instantaneous power for any circuit, P = IV.
Diagram 30.5.2.5 shows power that changes with time.
The power is negative when the current and voltage have opposite signs, i.e. between ωt = 0, and ωt = π / 2.
The power is positive when the current and voltage have the same signs, i.e. between ωt = π / 2, and ωt = π.
Between ωt = 0, and ωt = π / 2, the capacitor takes energy from the generator.
Between ωt = π / 2, and ωt = π, the capacitor gives back energy to the generator.
So the power consumed by a capacitor in an AC circuit has an average value of zero watt.
A capacitor in an AC circuit consumes zero net energy.
31.8.4.1 Ceramic capacitors
See diagram Ceramic capacitor.
Ceramic dielectric, metal electrodes
Ceramic capacitors have metal coatings on the sides of ceramics as plates that have very high dielectrics.
Ceramic capacitors have capacitor values 1pF to 0.1 µF.
31.8.4.2 Film capacitors
See diagram Film capacitor.
Film capacitors are named after the dielectric, e.g. polymer film, plastic film, polypropylene film, polycabonate film, polyester film, metallized film, PTE film, polystyrene film.
Polyester capacitors, called green caps, are used mainly in audio circuits.
They have capacitance up to 0.001 uF, are not polarized and may have a colour code like the resistor code.
31.8.4.3 Paper Capacitors
See diagram Paper capacitor.
Paper Capacitors, Waxed paper capacitors, have two strips of tinfoil as plates rolled to form a cylinder with waxed paper insulation, dielectric, between the plates.
They are rated in farads, e.g. 0.1 F.
Paper capacitors have thin sheets of tin foil between sheets of paraffin-impregnated paper with a lead attached to each paper strip.
Paper capacitors are often called "greencaps".
Paper capacitors have capacitor values from 0.001 µF to 1.5 µF.
31.8.4.4 Electrolytic capacitors
See diagram Paper capacitor.
See diagram 30.5.6.5 Charging an electrolytic capacitor.
DC power, Aluminium, Tantalum bead, Niobium name after material in anode
Charging an electrolytic capacitor
Electrolytic capacitors have a thin layer of aluminium oxide as dielectric between two strips of aluminium foil as plates, e.g. 0.1 F (100, 000 F).
One plate is marked + and should be charged positively.
In diagram 30.5.6.5, electrons flow from the negative terminal of the battery to plate Y of the capacitor, and from plate X of the capacitor to the positive terminal of the battery.
Positive charge builds up on the X plate and negative charge builds up on the Y plate, until the potential difference between the plates is equal and opposite to the potential difference of the battery, i.e. 1.5 V.
Electron flow then stops and the meters, which had shown equal flicks during the charging, return to zero.
The capacitor now has charge Q, i.e. one plate has charge +Q and the other plate has charge -Q.
If V = 1.5 V and C = 500 F (farad), Q = VC,
= 1.5 V x 500 F,
= 1.5 x 500 x 10-6,
= 750 x 10-6 coulombs.
Electrolytic capacitors usually consist of two rolls of aluminium foil.
The positive plate roll has a layer of aluminium oxide dielectric on its surface.
The foil layers are separated by paper soaked in electrolyte.
Electrolytic capacitors have capacitor values from 0.47 µF to 2500 µF.
Electrolytic capacitors are polarized capacitors, for more than 1 F.
They must be connected with correct polarity.
Axial electrolytic capacitors have leads are attached to each end.
Radial electrolytic capacitors have both leads are at the same end for use on printed circuit boards and to take less space.
The value of electrolytic capacitors are printed on them showing capacitance and voltage rating, e.g. 6 volts.
Electrolytic capacitors contain an electrolyte.
If the voltage rating is exceeded, the capacitor can be damaged.
The capacitor should have with a rating greater than the circuit's power supply voltage, e.g. 25 volts.
The capacitors in which the anode is present in it such a way that it possesses a layer of oxidized material which acts as the dielectric.
Hence these are known as the Electrolytic capacitors.
These are preferred in the DC power application circuits.
Symbol of Electrolytic Capacitor
Tantalum bead capacitors are used where a large capacitance, 0.1 muF to 100 muF, is needed in a small size and are usually polarized.
Use in place of electrolytic capacitors of the same values.
(Comment: Tantalum capacitors should NOT be used in place of electrolytics, because in electrolytics quite different design and application rules.
s operate best when close to their rated voltage, but tantalums fail as a power of the applied voltage, so they are best used at small proportions of the rated voltage.)
31.8.4.5 Mica capacitors
See diagram Mica capacitor.
Mica capacitors and Silver Mica capacitors, glass, silicon, air-gap, vacuum, are named after the dielectric.
Mica capacitors have thin sheets of mica as dielectric between sheets of metal foil connected together to form two plates.
Mica capacitors have capacitor values from 20 pF to 700pF.
31.8.4.7 Variable capacitors, trimmer and tunable
Variable capacitors have one set of plates that can moves relative to the other, e.g. in the tuning circuit of transistor radios.
Variable air capacitors have two parallel sets of metal plates, a fixed set and a moving set.
Tuners vary the capacitance by rotating the plates of the moving set between the plates of the fixed set and so change the capacitance.
The maximum capacitance with the plates fully interleaved is about 0.0005 F.
Radio and television tuners use low resistance RLC circuits to distinguish sharply between frequencies of different radio and television transmitters.
Some announcers still say "Stayed tuned!" just before an advertisement starts.
Variable capacitors can be varied by moving a rotating shaft.
Usually used with a tuning dial with the radio stations marked.
The smaller "trimmer capacitors" from 1.5 pf to 160 pF are used with larger fixed value capacitor.
The larger are used in transistor radios, used to tune different radio stations.
(Comment: The physical size is related to the applied voltage.
The capacitance is related to the operating frequency.
So large variable capacitors are used in broadcast transmitters.
Small variable capacitors are used in transistorized portable receivers.
High capacity is used for low frequency.
Small capacity is used for higher frequencies or as trimmers for larger capacitors.)
31.8.1.0 Capacitor discharge
See diagram 31.8.1.0: Discharge curve of a capacitor.
As a capacitor charges, a potential difference accumulates between the parallel plates and it becomes fully charged when the potential difference across the plates is equal to the electromotive force of the source.
If the capacitor is disconnected from this source, it can be used to make a current flow around a circuit.
But as charge flows during the discharge, the potential difference across the capacitor drops, so the capacitor can only supply a "burst" of energy.
31.8.1.3 Parallel plate capacitor
See diagram 31.8.1.3: Parallel plate capacitor.
Charge is spread evenly over the plate with an electric field uniform in direction and magnitude except near the edge of the plate.
The electric field is at right angles to the plate and its size is independent of the distance from the plate.
A parallel plate capacitor consists of two identical conducting plates separated by a distance.
So the electric field should be uniform between the plate, but does not exist outside the plates.
The capacitance of a parallel plate capacitor is inversely proportional to the distance of separation of the plates.
Experiment
1. Mix semolina (wheat middlings) or grass seeds in castor oil.
Pour the oil mixture between the plates of a parallel plate capacitor.
When a potential difference is applied between the two plates, the seeds show the directions of the electric field lines.
Before use, electrolytic capacitors should be correctly connected across the battery for minute to ensure that the plates are formed.
Charge a large capacitor, e.g. 500 muF (50 V working) with no resistor in the circuit.
Connect 4 volts from a 12 volt battery or power pack to the two plates of the capacitor through two galvanometers, or microammeter, each side of the capacitor.
When the switch is closed, see the momentary pulses of current, positive charge to one plate and negative charge to the other plate, then no more current.
Remove the battery from the circuit with the flying lead to discharge the capacitor and observe momentary current in the opposite directions.
3. Charge a 500 muF capacitor through a high resistor.
Repeat 1. with a high resistance, e.g. 4.7 kohm in series with the capacitor.
Observe the slow charging process as the current dies exponentially as the charge rises to full value.
Remove the battery from the circuit with the flying lead to discharge the capacitor and observe momentary current in the opposite directions.
You can see the same current patterns using 5 kV from a power pack to charge 0.001 muF (20 kV working) capacitor.
4. Charge a 0-001 muF capacitor using a van de Graaff generator and then short circuit it.
Charge the 0.001 muF capacitor by holding the capacitor horizontally in a clamp and connecting the stud mounting end to the earthed negative terminal of the power supply.
Connect the positive terminal to the capacitor through a 100 ohm resistor.
Include a very high resistance in series to avoid damaging the capacitor, e.g. wet string.
Connect the end of the resistor to the top of the capacitor with an insulated flexible lead held by hand.
After a few seconds, remove this flexible lead.
Use another insulated lead to short circuit the capacitor.
Hold the insulated flying lead by hand against the sphere so that it can readily be removed from contact and used to short circuit the capacitor.
Be careful! Two cm sparks can be obtained from a capacitor charged in this way!
This experiment shows that the charged capacitor can produce sparks when it has been charged from an electrostatic source.
The capacitors may not be designed for use at these voltages and may
breakdown.
5. Change the spacing of a charged parallel plate capacitor while it is attached to an electroscope.
See diagram 31.8.1.5: Spacing of a charged parallel plate capacitor.
* Vary the spacing of a charged parallel plate capacitor while the voltage is measured with an electroscope field and voltage.
* Charge a simple capacitor of two parallel movable plates and the divergence of electroscope leaves varies as the plates are moved.
* Charge parallel plates with a rod watch and the electroscope as the distance between the plates is changed.
6. The relationship between capacitance and plate separation for a parallel plate capacitor, C = κ εoA/d, i.e. capacitance is inversely proportional to separation distance.
Test this relationship by using increasing the numbers of sheets of paper or plastic or other dielectric material.
However, the inverse relationship (C X 1/d) may not hold, because of the air between the sheets.
To remove the air effect, add weights to the capacitor or increase the width of the plastic, e.g. use builder's plastic, thickness 50 μm, 100 μm, and 150 μm, so there is no air gap.
31.9.2.0 Dielectrics
See diagram 31.8.2.0: Effect of a dielectric.
A dielectric is a non-conductor of electric charge, i.e. an insulator.
It can be a solid, liquid or gas that can keep an electric field constant.
Dielectrics are used in electric cables, electric terminals and capacitors.
The dielectric constant, K, relative permittivity, of a material measures how effectively it reduces an electric field across it.
The dielectric strength of a material expressed in volts per millimetre indicates the maximum potential difference gradient that can be applied to it before it breaks down and starts conducting electrons across it.
Non-conductors do not allow a flow of charge, but there is still a displacement of charge within them when a potential difference is applied.
Insulation material includes alcohol, quartz, dry gases, glass, pure water, sulfur, whereas conductors include aluminium, copper and silver.
Although there is no sharp division between conductors and insulators, electrical conductivity, specific conductance, is a measure of current-carrying
ability of a material when an electrical potential difference is placed across it and an electric current flows through it.
Electrical conductivity, symbol σ, is the ratio of current density to
electric field strength and is measured in the derived unit
siemens per metre, S m-1.
Examples include silver, best metal conductor, 63.0 × 106
S m-1, copper 58.6 × 106 S m-1, gold 45.2
× 106 S m-1,
deionized water 5.5 × 10-6 S m-1, and
air 0.3 to 0.8 × 10-14 S m-1.
Semiconductors, e.g. silicon, germanium, have electrical conductivity
in the range 103 to 10-7 S m-1.
The electrical conductivity of solutions used in hydroponics, aquaculture
and water quality control is measured with an EC meter
(electrical conductivity meter).
31.9.2.1 Permittivity
1. Permittivity measures the ability of a material to "permit", i.e. transmit, an electric field.
Permittivity, ε0,
represents the permittivity of free space, i.e. in a vacuum.
If the charges are surrounded by a material, e.g. air, induced charges
in the material decrease the force between the charges.
Permittivity, symbol ε, is measured in farads per metre, F / m.
Vacuum permittivity, symbol ε, permittivity of free space, electric constant = 8.8541878 × 10-12 farads per metre, F / m
Relative permittivity, symbol εr, dielectric constant, includes
for vacuum = 1 (by definition), and approximately:
air = 1.0006., PTFE / Teflon 2.1, Pyrex glass 4.7, rubber 7, silicon 12, ethylene glycol 37, porcelain is × 7 relative permittivity for air.
2. Dielectric constant is an important parameter for characterizing capacitors.
The term dielectric indicates the energy storing capacity of a material
by polarization.
The larger the dielectric constant, the more charge can be stored.
So capacitance is maximized if the dielectric constant is maximized,
and the capacitor plates have large area and are placed as close
together as possible.
If a metal was used for the dielectric instead of an insulator the field
inside the metal would be zero, corresponding to an infinite
dielectric constant.
The dielectric usually fills the entire space between the capacitor plates.
Dielectric constant, K, relative permittivity = permittivity of a material, absolute permittivity, ε(ω) / permittivity of free space, ε0 =
ε(ω) / ε0.
Charts of dielectric constants are issued for most useful materials:
vacuum 1, air (1 atmosphere) 1.00059, polystyrene 2.6, rubber 3.0, paper 3.6, water 80.4.
31.9.2.2 Capacitor with dielectrics
1. Place a dielectric between the plates and push the plated against the dielectric.
Turn on the power supply to charge the plates.
Disconnect ground lead BEFORE turning the supply off.
Slide the dielectric out of he plates and observe how the electroscope
changes.
Insert other dielectrics.
2. Insert and remove a dielectric from a charged parallel plate capacitor
while it is attached to an electroscope.
The voltage is measured with an electroscope as dielectrics are inserted
between parallel plates of a charged capacitor.
Various dielectrics are inserted between two charged metal plates to show
the difference in deflection on an electroscope.
Bring a charged rod close to an electroscope and interpose various materials
between the two.
31.9.2.3 Equation Q = CV, electroscope
The bottom of a parallel plate capacitor is mounted on an electroscope.
Charge the top plate touch the bottom.
Lift off the top.
31.9.2.4 Force on a dielectric
A counterbalanced acrylic dielectric is pulled down between parallel
plates when they are charged with a small Wimshurst generator.
A microscope slide is pulled into the gap between parallel plates of a
capacitor.
Elongated paraffin ellipsoid in a parallel plate capacitor turns when
the field is turned on.
Kerosene climbs between parallel plates.
31.9.2.5 Attraction of
charged plates
A brass plate fitted with an insulating handle can lift a lithographic
stone plate when dc is applied.
Fix the top plate of a parallel plate capacitor on a triple beam balance
to measure the force with and without dielectrics as the voltage
is varied.
Measure the permittivity of free space with a Mettler balance to find
the force between the plates of a parallel plate capacitor.
31.9.2.6 Dissectible condenser
A capacitor is charged disassembled passed around assembled and discharged
with a spark.
The inner and outer conductors of a charged Leyden jar are removed and
brought into contact then reassembled and discharged.
Charge a capacitor and show the discharge then charge again and take
it apart.
31.9.2.7 Bound charge
Grind the two coatings of a Leyden jar successively without much loss
of charge.
A discharge occurs when you connect the two coatings.
31.9.2.8 Impedance of a
dielectric
Place a small parallel plate capacitor in series with a phonograph pickup.
Insert different dielectrics.
High dielectrics have low impedance.
31.9.2.9 Breath figures
Blow on a glass plate that has been polarized with the image of a coin.
31.9.2.10 Lichtenberg
figures
Trace a pattern on a dielectric from the two polarities of a charged
Leyden jar.
Litharge and flowers of sulfur sprinkled on adhere to the areas traced
out with the different polarities.
31.9.2.11 Displacement
current
A toroidal coil is either placed around a wire leading to a large pair
of capacitor plates to show Ampere's law or inserted between the
capacitor plates to show displacement current.
Measure the displacement current in a barium titanate capacitor.
(Comment: The experiment in has nothing to do with displacement current in Maxwell's sense!)
31.8.3.1 Leyden jar capacitor
See diagram 31.8.3.1: Leyden jar.
1. A Leyden jar is a glass jar with metal foil on inside and outside
surfaces invented in the Netherlands' town of Leyden about 1745.
It was the early form of a capacitor and can act as a high voltage capacitor, e.g. 2000 pF.
Put aluminium foil into a 250 mL wide mouth glass jar to one third of
the height of the jar.
Cover the jar externally with aluminium foil to the same height as the
internal foil.
Push a large nail through a cork.
Use pliers to twist the end of the nail to form a hook.
Make a hole in the plastic lid of the glass jar so that the cork fits
tightly through it.
Fix the cork into the hole in the lid.
Connect a chain of paper clips to the hook.
Touch the head of the nail with a plastic rod rubbed with fur.
Repeat this action ten times to accumulate electric energy to the Leyden
jar.
The paper clip chain carries charge from the nail head to the aluminium
foil in the jar.
The plastic lid of the glass jar is an insulator.
When the jar is fully charged, use an insulated wire to connect the nail head with the
external aluminium foil.
A spark bounces out from the point of the contact.
2. Make a grounded Leyden jar.
Sparks from a Wimshurst machine are no longer, but are much more intense
when a Leyden jar is connected.
Charge a capacitor with a Wimshurst machine and ground each side separately.
Make a spark to show that the charge is still there.
3. Make series and parallel condensers.
Charge four Leyden jars in parallel and discharge singly and with three
together.
Next charge three in series with one in parallel and discharge singly
and three in series.
Compare the length and intensity of sparks.
Charge a single capacitor two series capacitors and two parallel capacitors
to the same potential and discharge through a ballistic
galvanometer.
4. Show the addition of potentials.
Charge Leyden jars in parallel and discharge charge in parallel again
and connect in series before discharging.
Compare length and intensity of the sparks.
5. Show residual charge.
Charge and discharge a Leyden jar.
Wait a few seconds and discharge it again.
After charging a Leyden jar, light a neon tube up to 100 times.
Also show the polarity of charge on the dielectric with a triode residual
charge.
6. Use Leyden jars with a Toepler-Holtz machine.
The Toepler-Holtz machine produces weak sparks without the Leyden jars
and strong less frequent sparks with the jars connected.
7. Water cup spark collector
See diagram 31.1.4: Water cup spark collector.
Put a plastic cup 3 / 4 full of water into a plastic container containing
water the same height as the water in the cup.
Bend two pieces of bare copper wire at on end so that they can stand
upright.
Put one piece of copper wire in the cup and the other in the plastic
container.
Rub a glass rod with a piece of silk then touch the copper wire standing
in the plastic cup.
When you repeat this action 10 times, you are charging the capacitor.
Hold the end of the copper wire in the outer container with a clothes
peg and move it towards to the centre copper wire.
Observe a spark jumping between the two copper wires.
It is similar to the Leyden jar except the collecting surfaces are water separated by plastic instead of aluminium separated by glass to store charges.
When a glass rod is rubbed with a piece of silk, the centre wire water
accumulates positive charges.
When a plastic rod is rubbed with fur, the centre wire accumulates negative
charges.
31.8.3.2 Short a capacitor
See diagram 31.8.3.2: Short a capacitor.
Turn on the power supply to charge the 5600 μF capacitor through
the power resistor to 120 V and short with a screwdriver.
Remove the leads from the capacitor without touching the binding posts.
Short the posts with the shaft of the screwdriver, (not the tip).
31.8.3.3 Light a bulb with a capacitor
Charge a large electrolytic capacitor, e.g. 5600 microF, to 120 V then
discharge it through a light bulb.
Turn on the power supply to charge the capacitor through the power resistor.
Turn off the power and disconnect the power supply.
To discharge the capacitor, connect to the light bulb only.
Do not short the capacitor.
The 60W bulb lights for about 3 seconds.
A 7.5 W bulb lights for about 20 seconds.
31.8.3.4 Heat from a capacitor
Use a capacitor with a calorimeter.
Discharge a capacitor into a resistor in an aluminium block with an embedded thermistor to measure the temperature increase.
31.8.3.5 Electrostatic voltmeters
Hand-held, non-contacting electrostatic voltmeter instruments (ESV) are used where surface contact on conductive or insulative objects must be avoided.
They are insensitive to variations in probe-to-surface distances, and prevent arc-over between the probe and measured surface.
A surface DC voltmeter measures voltage with no electron transfer and so there is no charge transfer.
The instrument may measures surface potential 3000 volts without contacting the measured surface.
31.8.3.6 Capacitor charge and discharge
See diagram 38.4.1: Capacitors, charge and discharge.
A capacitor stores energy in the form of an electric field between the oppositely charged plates.
A capacitor has two conducting metal plates separated by a non-conducting material, a dielectric.
When electricity supply is applied to the capacitor the electrons start moving from one plate to the other and start accumulating on the other plate, because the dielectric in between does not conduct electricity.
So one plate has many positive charges and other plate has few negative charges, which causes an electric field to form between the two plates.
The electric field makes the molecules in the dielectric get aligned towards the field in a direction which prevents the charge carriers from moving across.
The capacitor is said to be fully charged.
If a load is connected between the two metal plates, the capacitor discharges.
Experiment
1. Capacitance of a capacitor = charge on each plate per voltage between plates, C = Q / V.
The SI unit of capacitance the farad, F, is equivalent to 1 coulomb per volt.
Use an ammeter with deflection in either direction, e.g. 10-0-10 mA, note deflection and whether capacitor keeps or loses its charge:
* before flying lead connected,
* flying lead connected for charging,
* then flying lead disconnected,
* flying lead connected again for charging,
* then flying lead disconnected,
* flying lead connected for discharging.
2. Capacitor charge and discharge with cathode ray oscilloscope, CRO
See diagram 38.4.2: Capacitors, charge and discharge.
Set variable capacitor at about 50 muF and variable resistance at about 50 k ohms.
Set CRO at slowest time -base and sensitivity 1 V / cm.
Connect the earthed Y-input socket to low potential side of the capacitor.
When slow trace starts to cross screen, connect flying lead for charging to see trace showing voltage across capacitor changing with time as capacitor charges, i.e. a graph of voltage against time.
Disconnect flying lead.
When slow trace starts to cross screen, connect flying lead for discharging.
See graph.
Disconnect flying lead.
3. Bulb dims as the capacitor charges.
A 5600 μF capacitor, a light bulb, and a 120 V dc supply in series show a long time constant where the bulb dims as the capacitor charges.
Similarly when current is switched off to a device containing light bulbs.
The bulbs continue to grow after switching off, because of current stored in the capacitors.
4. Use a neon flasher circuit to show the combination rules for series and parallel combinations of resistance and capacitance by timing light flashes.
Measure a capacitance or frequency with a Wien bridge.
31.8.3.8 Blinking neon bulb
Use a neon bulb in parallel with a capacitor to light periodically as the capacitor charges and discharges.
31.8.5.0 RC time constants
See diagram: 31.8.5.0 Charging and discharging curve for a capacitor.
The RC time constant, tau or T, is the time constant in seconds of an RC circuit = circuit resistance (in ohms) X circuit capacitance (in farads).
The RC time constant is the time taken by a capacitor to charge from an initial charge voltage of zero about 63% of the voltage charging it.
If a capacitor is already fully charged, the RC time constant is the time it taken for it discharge to 63% of its fully charged voltage.
The larger the resistance in the circuit, the longer the charge / discharge time.
Charging and discharging a capacitor follows a non-linear curve.
Time constant (τ) ( in seconds) = RC, where R is the resistance value of the resistor and C is the capacitance of the capacitor.
Time constant is affected by the resistance of the resistor and the capacitance of the capacitor.
The larger the resistance or the capacitance the longer it takes for a capacitor to charge or discharge.
The smaller the resistance and capacitor values, the shorter time it takes for a capacitor to charge or discharge.
In a circuit where a 9-volt battery is charging a 1000µF capacitor through a 3KΩ resistor:
Time constant, RC = (10KΩ) X (100µF) = 3 seconds, when the capacitor is charged to 63% of the 9 volts from the battery, i.e. about 5.67 volts.
For the circuit in diagram 31.8.5.0, the RC time constant is 1 second