School Science Lessons
Physics
2025-11-12

Electroscopes

31.8.0 Capacitors
31.9.0 Dielectrics
31.1.0 Electrophorus
31.2.0 Electroscopes
31.3.0 Lightning, sparks
31.4.0 van de Graaff generator

31.1.0 Electrophorus
31.1.1 Induction coil
31.1.2 Rhumkorff coil
31.1.3 Mutual inductance
31.1.4 Self-inductance
31.1.5 Wimshurst machine
Experiments
31.1.6 Electrophorus
31.1.7 Induction kit
31.1.8 Kelvin water dropper induction generator
31.1.9 Repulsing balloons

31.2.0 Electroscopes
31.2.1 Aluminium foil electroscope
31.2.2 Balloon electroscope
31.2.3 Biot's apparatus electroscope
31.2.4 Charged ebonite rod on electroscope
31.2.5 Chocolate wrapper electroscope
31.2.6 Drink-can electroscope
31.2.7 Gold leaf electroscope
31.2.8 Metal foil ball electroscope
31.2.9 Oppositely-charged electroscopes
31.2.10 Pith ball indicator electroscope
31.2.11 Two kinds of static charge in electroscope
31.2.12 Pith ball plate and flying strings

31.3.0 Lightning
31.3.1 Lightning
Experiments
31.3.5 Finger sparks
31.3.2 Franklin's bell
31.3.3 Rubbed balloon sparks
31.3.4 Saint Elmo's fire

31.4.0 van de Graaff generator
31.4.1 van de Graaff generator
31.4.2 Atmospheric electric field motor
31.4.3 Blow soap bubbles at the van de Graaff generator
31.4.4 Electric pinwheel
31.4.5 Electrostatic voltmeters
31.4.6 Hair on end with van de Graaff generator
31.4.7 Streamers on a van de Graaff generator
31.4.8 van de Graaff generator friction

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 Coulomb's law
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

31.1.1 Induction coil
See diagram 31 5 14: Induction coil.
(H. D. Ruhmkorff, 1803- 1877, Germany, France)
1. An induction coil (spark coil, Ruhmkorff induction coil) is a kind of transformer where low voltage direct current in a primary coil is interrupted to induce higher voltage in the secondary coil.
The induction coil contains a primary circuit (a few turns of thick wire), a switch, a rheostat (variable resistance), a battery, a make-and-break (interrupter), and a condenser in parallel with the make-and- break.
The secondary circuit is many turns of thin wire wound on the primary coil, with a spark gap.
The greatest distance between the spheres of the spark gap is a measure of the induced emf.
An iron core usually consists of a bunch of insulated iron wires, which can be placed within the primary coil.
Changing magnetic field created by the primary circuit can induce a changing voltage and/or current in the secondary circuit.

31.1.2 Rhumkorff coil
IEC Ruhmkorff induction coil, tungsten vibrating points, high quality capacitor reduces arcing, fuse fitted to protect primary winding, secondary winding contains thousands of turns and can be slide from the primary winding to reduce coupling, runs on 6 to 9 volts, spark length 25 - 30 cm, removable and adjustable needle points with insulated handles, 300 mm, 125 mm, 110 mm.
High voltage induction coil with a removable secondary winding.
The fused primary is wound on a laminated electrical-steel coil, it requires 6 to 9V DC, input is via 4 mm banana plugs.
The vibrating contacts are easily adjusted and are made of tungsten.
The coil produces a 25 mm spark between adjustable needle points, which plug into 4 mm sockets, removing the points allows the high voltage to be fed to other equipment.

31.1.3 Mutual inductance
Mutual inductance of two circuits refers to the size of the voltage in the secondary circuit induced by changes in the current of the primary circuit.
The unit of mutual inductance is the henry, H.
Mutual inductance for two adjacent circuits is the emf induced in one circuit caused by the unit rate of change in the current flowing though the other circuit.
In the induction coil, the induced emf is proportional to the number of turns per unit length of the primary circuit to the number of turns in the secondary circuit, and is proportional to the time rate of change of current in the primary circuit.
When an iron core is placed inside the primary coil the currents magnetizes the iron to increase the induced emf in the secondary coil.
The back emf can flow across the gap in the make and break causing a spark.
However, instead this current can charge a condenser in parallel with the make and break.
The charged condenser immediately discharges to send current through the primary circuit in a direction opposite to the original current.
When the change in magnetic flux from the primary coil is experienced by the secondary coil, an emf is induced in the secondary coil.
The emf = M × (change in primary coil current / change in time), or M × (time rate of change in the primary current), where M = the mutual inductance of that 2 coil system.

31.1.4 Self-inductance
See diagram 31.5.15: Self-inductance.
Self-inductance refers to a circuit creating changing magnetic flux through itself, which can induce an opposing voltage in itself.
The unit of self-inductance is the henry.
When current is started or stopped in a conductor, an induced emf occurs in that conductor, self-induction, with direction such as to oppose the change (Lenz's law).
So when the current starts to flow, the self-induced emf opposes the rise in current, back emf.
When the current is broken, the back emf tends to cause the current to keep flowing to cause the current to falls gradually to zero instead of falling instantly.
The unit of self-inductance, the henry, is the self-inductance of a circuit in which the back emf is 1 volt when the current alters at the rate of 1 ampere per second.
When AC passes through a coil, the changing magnetic flux induces a back emf in the coil, which opposes the changing current.
Self-inductance of the coil is measured in henry, L.
The current lags behind the emf by a quarter of a cycle, 90^o.
Self-inductance, inductance, occurs when a coil with a changing current induces an emf, in itself.
So = L ( I / t) henry (H), where 1 H = 1 V.s / A.
Coils are turns of insulated copper wire to increase inductance depending on how many turns, distance between turns, diameter of the oil, and what they are wound on.
For inductance, self inductance, L, in an AC circuit, when the AC passes through the coil the changing magnetic flux induces a "back emf " in the coil that opposes the changing current.
While magnetic flux is changing inside a coil, a back emf is induced, which opposes the changing current.
emf = L × (change in current / change in time) = L × (rate of change of current), where L = self-inductance constant of the coil.
The unit of self-inductance is the henry, H.
One 1 henry, H, = emf of 1 volt induced in a circuit by electric current change of 1 ampere per second.
Self-inductance occurs when AC passes through a coil, because, if the current in a coil changes, the magnetic flux through the coil caused by the current also changes, so the changing current induces an emf in the same coil.
The current lags behind the emf by a quarter of a cycle (90^o).
Back emf, E = -L I / t, where I / t is the rate of change of the current, and L is the self inductance of the coil measured in henry, H.

31.1.5 Wimshurst machine
Wimshurst machine induction generator
See diagram 31.6.1: Wimshurst machine.
"Two parallel plates rotate in opposite directions.
Charge due to friction in collected by combs then stored in two integrated high voltage capacitors, Leyden jars, connected in parallel to an adjustable spark gap up to 30 mm.
The Wimshurst electrostatic generator consists of a system of electrophorus plates that operate in a continuous fashion to accumulate large amounts of positive and negative charge.
If positive charge on a disk on one plate A an opposite negative charge is induced on the nearest metal disk on the contra-rotating second plate B.
The connecting rods transfer an induced positive charge to disks on a diametrically opposite position of Plate A.
As the plates rotate the second plate B moves to a position where it induces a positive charge on the disk opposite it on plate A via the second set of connecting rods.
With continuous rotation positive charges accumulate at position A and negative charges at B.
Experiment
Attach a 3 m long wood bar at one end to one terminal of a static machine, with the other end grounded or insulated, then attach electroscopes along the bar to show flow of charge and potential drop.
Attach two ends of a dry stick to a static machine then measure with an electrostatic voltmeter and micro-ammeter.

31.1.6 Electrophorus
See diagram 31.1.8.1: Electrophorus.
See diagram 31.147: Many charges from one source.
An electrophorus is used to repeatedly generate static electricity by induction.
Discharge of an electrophorus shows the actual movement of charge.
Alessandro Giuseppe Antonio Anastasio Volta (1745 - 1827), was the Italian experimenter who invented the "electroforo perpetuo", electrophorus, described in 1775.
Luigi Galvani (1737 - 1798), another Italian experimenter did the first work on the twitching of frogs' legs by electric current.
Volta took up the study of frogs' legs and showed Galvani that he was wrong about "animal electricity".
Experiments
1. The electrophorus has a flat metal disc A, with an insulating handle H, and a flat ebonite disc B, on an earthed metal sole S.
Rub plate B is rubbed with cats fur so that it acquires a negative charge.
Place disc A on disc B.
Neither A nor B are perfectly flat so contact between the discs is only at a few points.
So surfaces of the discs are mainly separated by a thin layer of air.
Disc A has charges induced on it.
Earth disc A by touching while it is still resting on B.
Electrons flow from disc A it to earth leaving a net positive charge on disc A.
This net charge can be used as a source of charge so the above procedure can be repeated many times to build up charge on B, because in each charging cycle no charge is removed from B.
The electrophorus works better if first dried in front of a radiator.
2. The electrophorus consists of a flat metal disc with an insulated glass handle, a flat dielectric disc, e.g. ebonite, on an earthed metal sole.
If the flat dielectric disc is rubbed with silk it becomes positively charged by friction.
When the flat metal disc is placed near or on the dielectric disc the lower surface of the metal disc become negatively charged by induction and so the upper surface of the metal disc becomes positively charged.
The upper surface of the metal disc is lightly touched with a finger to earth it and neutralize the positive charges.
Electrons cannot flow from the dielectric disc to the metal disk, because the dielectric disk is an insulator.
The metal disc now has a negative charge and can be lifted away with the insulated handle.
The two discs are not perfectly flat so these two discs touch at only a few places leaving a thin layer of air between them.
So the charging is mainly by induction and not by contact.
The procedure can be repeated many times to build up charge on the metal disc, because no charge has been removed from the dielectric disc.
More work is required to lift the charged metal disc than if it were uncharged, because a force of attraction occurs between the charged metal disc and the oppositely charged dielectric disk.
A spark occurs between a finger and the disc and this can occur again after the disc is recharged.
The energy required comes from the person who lifts the disc, because more energy is needed the lift the charged disc than an uncharged disc, because of the force of attraction between the charged disc and the uncharged ebonite dielectric.
3. Finger electrophorus shows electric field.
Charge an electrophorus then trace a circle on it with your finger and probe the resulting field with a pith ball on a long thread.
4. Use a neon discharge tube to show a flash by holding one end on the electrophorus and then touching the other end.
5. Suspend an electrophorus by raising it off the plate with an attached helical spring.
Touch the disc to remove induced charge and see the spring lengthen.
6. You can use a plastic gramophone record to make an electrophorus, but it slips about in use.
Also, some records contain materials that do not take the same charge consistently.
You can use a block of sulfur as an electrophorus. but handling it is difficult, because it tends to crumble.
Brass, copper and aluminium work as well as a copper plate.
Use short Perspex handles for convenience in storage with no metal screws protruding through the Perspex.
It will nor work without a nearly perfect insulator for a handle.
Nylon clothes may crackle when pulled over the head in dry weather, because nylon on is an insulator.
Friction with dry hair or even dry clothing electrifies the clothing.
In dry weather, the charges accumulate and, when earthed, cause noisy little sparks.
If the weather is humid, the charges generated can be conducted off the Perspex, through water vapour, on to the table and on to earth.
In damp weather dry the electrophorus with a radiator before use.
7. Rub a sheet of Perspex, or slab of solidified sulfur or a plastic gramophone record, with fur.
The rubbing action wipes loose surface electrons off the Perspex onto the fur, so the Perspex becomes positively charged.
Hold a flat sheet of copper by an insulated handle on the charged Perspex.
The copper sheet and Perspex touch at only a few points although both seem flat.
The copper conductor has electrons that can move from atom to atom, unlike an insulator.
Positive charges from excess protons in the Perspex attract electrons from the flat sheet of copper when it comes into the electric field of the charged Perspex.
Unlike charges attract, so the underside of the copper disc becomes negatively charged, because it has extra electrons attracted to it, leaving the upper side with fewer electrons.
Touch the top of the sheet of copper with the finger.
The human body is damp and an electrical conductor, so when you touch the copper plate, electrons flow through your body to the top of the sheet of copper.
These electrons replace the electrons lost when the electrons in the sheet of copper flowed down to the Perspex.
When you remove your finger from the copper, these replacement electrons are left on the copper plate.
The electrons lost from your body are replaced by electrons moving up your body from the earth, if you are not wearing insulating rubber-soled shoes.
When you lift the copper plate, the extra electrons are trapped on it.
You can produce a spark between the charged copper plate and your knuckle or the metal burner, because so many excess electrons are repelling each other on the charged plate that they can be "pushed off" the plate.
If you touch the plate with one end of a conducting copper wire, and touch the other end to your finger or to the burner, these excess electrons quickly flow through the wire and form an electric current.
An electric current through a wire is simply a movement of and electrons.
When all the excess electrons have flowed from the plate through the wire, the current will stop.
When the charged plate is surrounded by dry air there is no conductor through which the excess electrons can flow to earth.
When the plate is brought close to a conducting object such as the metal of the burner, the excess electrons on the plate first repel any free or conduction electrons in the burner as far as possible away from that part of the metal closest to the charged plate.
This part of the metal then becomes positively charged.
Electrons now on the plate try to push each other and are attracted to the positive part of the metal burner.
Some electrons leap from the charged plate through the air to the burner, knocking electrons out of air molecules and these join in the electric current passing from plate to burner, producing a quick spark and a sharp cracking noise.
In a charged electrophorus, charge leaks away due to conduction of electrons by moisture on the surface of the apparatus.
The original energy comes from you, because work is done in lifting the plate off against the attraction caused by the electric field.
Pulling the charged copper disc away from the oppositely charged Perspex sheet takes energy from you.
When you put your finger, which is "earthed", on the copper, some electrons wiped off the Perspex get back to the Perspex where the copper touches the electrophorus.
However, the points of contact are few on these two surfaces so the electrons cannot spread all over the Perspex, because it is a non-conductor.
8. Electrophorus lights a Bunsen burner.
Use electrons trapped on the electrophorus to make a spark and to light the gas in a Bunsen burner.
Bring the copper plate of a charged electrophorus near your knuckle and see if you can detect a spark as the electrons jump across the gap to your body and back to "earth" from where they came.
The electron flow is from the surplus to the deficiency, that is, a current of electrons flows from negative to positive.
Charge the plate again by laying it on the charged Perspex, touching the topside with a finger and lifting the plate off.
This time, turn the gas on a little and nearly touch the Bunsen burner with the copper plate.
If you can make a long spark, it will light the gas.
Electrons running from a charged copper plate can momentarily light up a fluorescent tube.
The electron flow is from the surplus to the deficiency, i.e. a current of electrons flows from negative too positive.
9. Electrophorus lights electric lamp.
Charge the copper disc of the electrophorus.
Hold the end of the lamp in one hand and touch the terminal of the other end with the copper disc.
You may need to darken the room slightly to be able to notice the flash.
To measure the amount of charge stored on an electrophorus, repeat the experiment.
How many times you can cause the lamp to flash without recharging the plastic plate?
If the original charge on the plastic does not leak away, the lamp can be flashed many times.
10. Many charges from one source.
Use a flat bottom aluminium foil pie dish.
Push a drawing pin up through the centre of the pie dish.
Press a rubber eraser down onto the upturned point of the drawing pin.
Rub the bottom of a flat polystyrene dish with wool.
Hold onto the end of the eraser and use it as a handle to lift up the pie dish then place it in the polystyrene bowl.
The head of the drawing pin now connects the aluminium pie dish with the polystyrene bowl.
Touch the aluminium pie dish with your finger then lift it up using the rubber eraser handle.
Touch the aluminium pie dish again.
A spark may jump between your finger and the pie dish each time you touch it.
11. Use a piece of aluminium or a cake tin.
Heat the metal evenly over a flame.
Touch a wax candle to the centre of the aluminium until it melts and sticks solidly to it as a handle.
Use a plastic dish pan or bowl larger than the cake tin.
Put the bowl or pan on a table and stroke the inside bottom of the pan briskly with a piece of fur or flannel for half a minute.
Put the aluminium on the plastic and press it down hard with your fingers.
Remove the aluminium pan, put your finger near the metal and see a spark.
You can take many charges from the plastic without more rubbing.
Press the metal against the plastic, press with your fingers and lift by the handle.
12. Many charges from one source
See diagram 31.1.8.1: Many charges from one source, electrophorus.
Use a piece of aluminium or a cake tin.
Heat the metal evenly over a flame.
Touch a wax candle to the centre of the aluminium until it melts and sticks solidly to it as a handle.
Use a plastic dish pan or bowl larger than the cake tin.
Put the bowl or pan on a table and stroke the inside bottom of the pan briskly with a piece of fur or flannel for half a minute.
Put the aluminium on the plastic and press it down hard with your fingers.
Remove the aluminium pan, put a finger near the metal to get a spark.
You can take many charges from the plastic without more rubbing.
Press the metal against the plastic, press with your fingers and lift by the handle.

31.1.7 Induction Kit
Two movable coils with a removable iron core, the primary inner core has 450 turns of heavy wire, it sits within a secondary coil of 1300 turns of fine wire.
Ideal for magnetic field and induction experiments to demonstrate that an induced potential is produced either by:
the movement of a permanent magnet or an electromagnet,
or by the change of current in one coil.
Outer coil 125 mm x 50 mm.
Experiment See diagram 31.5.14a: Mutual inductance.
1. Two coils face each other, one attached to a galvanometer, the other to a battery and tap switch.
Coupling can be increased with various cores.
Aluminium, laminated iron, and other solid iron cores are available.

31.1.8 Kelvin water dropper induction generator
See diagram 31.7.4.3: Water dropper induction generator.
See diagram 31.7.4.3a: Droppers.
Two droppers produce two fine jets of water from the upper container.
Valves A and B break the two fine jets of water drops before passing through rings C and D.
The drops fall into containers E and F connected to an adjustable spark gap G.
A Neon globe can be attached to one of the electrodes of the spark gap so that it flashes every 10 seconds.
The distance between the spark gap electrodes can be enlarged and an electrostatic voltmeter can be connected into the circuit.
The voltmeter will read full scale in a short time, because the apparatus can produce voltages > 6000V.
During operation of the generator the containers E and F do not remain at exactly the same potential.
If one container, say the container at the right becomes positive, electrical charges on the container will induce opposite charges on the jet.
A negative container induces positive charge on the jet, so positive charged drops break off and fall into the positive container, making it still more positive.
At the other side the positive container induces negative drops to make the negative container still more negative.
So charges build up very rapidly.

31.1.9 Repulsing balloons
Blow up two balloons and tie with strings one metre long.
Rub each balloon with fur.
Hold the strings together and note how they repel.
Put your hand between them and note what happens.
Bring one balloon near your face.
Repeat, using three balloons.

31.2.1 Aluminium foil electroscope
See diagram 31.3.8: Aluminium foil electroscope.
Use a plastic or glass jar with a metal cap.
Punch two holes in the lid to hold a wire inside the jar.
Cut two leaves of metalled paper or light aluminium foil so that they can swing freely over a hook at the end of the wire.
Use the electroscope for testing electrostatic charges.
Rub the PVC rod (- ve), with the wool felt and touch the electroscope.
Rub the acrylic rod (+ ve), with cellophane and touch the electroscope.

31.2.2 Balloon electroscope
A helium-filled balloon can be painted with aluminium and charged with a van de Graaff generator.

31.2.3 Biot's apparatus, electroscope
See diagram 31.7.23: Biot's apparatus.
To show that the charge resides on the surface of a statically-charged conductor, an iron sphere is charged and placed on a conductor.
Two thin brass covers with glass handles are the same shape as the iron sphere and are placed on it.
The covers are removed and are shown to have the same charge as the sphere, which has lost its charge.
This experiment shows that charge rests on the surface of a conductor.

31.2.4 Charged ebonite rod on electroscope
Charge an ebonite rod negatively by rubbing it with wool.
Roll the charged rod on the metal lid of an electroscope.
Some electrons transfer to the lid.
When the ebonite rod is removed, the electroscope is left with excess electrons.
Electrons can move through the metal lid, wire and leaves.
Both leaves of the electroscope become negatively charged.

31.2.5 Chocolate wrapper electroscope
Push a piece of copper wire through a hole in the lid of a jam jar.
Bend the end of the wire into a hook and hang a folded strip of aluminium foil, or "silver paper" from a chocolate wrapper, over the hook.
Rub a plastic spoon, or ball pen casing with wool or comb the hair with a plastic comb.
Touch the top of the wire with these charged objects.
The ends of the foil strip move apart.
Electrons flowed from the charged objects through the wire to the ends of the strip that now have the same negative charge and so move away from each other.

31.2.6 Drink-can electroscope
See diagram 31.3.3: Drink-can electroscope.
The tab of the soft drink can supports the electroscope leaves in this simple version.

31.2.7 Gold leaf electroscope
Gold Leaf Electroscope, (Commercial).
See diagram 31.5.3: Gold leaf electroscope.
The gold leaf electroscope is used for detecting and measuring electric charges.
It consists of two gold leaves attached to a brass rod in a glass vessel.
A metal cap is attached to the end of the rod.
When the leaves have charges of the same sign they repel each another like an inverted V and separate more widely if the charge is increased or fall together if the charge is decreased.
The gold leaves may be charged by induction or by contact.
Suppose that they are charged negatively.
The sign of the charge on any charged body may be found by bringing it up to the terminal of the electroscope.
If a positively charged body is held close to the terminal, electrons from the leaves will be attracted up to the terminal by the positive charge, and the charge on the leaves will be decreased and they will fall together.
If a negatively charged body is held close to the terminal, electrons will leave the terminal and go down to the gold leaves to increase their charges and so the leaves will separate more than before.
So if the gold leaves are charged together negatively, they fall together for a positively charged body, and separate for a negatively charged body.
To use a negatively charged body to charge the gold leaf electroscope positively, place the negatively charged body near the terminal so that electrons will flow down to the gold leaves, leaving the terminal positively charged.
When the rod is earthed, grounded by touching with the finger, electrons flow from the leaves to the earth, leaving the leaves neutral.
When the earth connection is broken, and the charging body then removed, the positive charge from the terminal distributes over the terminal and leaves, leaving the electroscope with a net charge of opposite polarity to the charged body.
To use a negatively charged body to charge the gold leaf electroscope negatively, place the negatively charged body on the terminal to make direct contact between the terminal and charged body.
An electroscope used for measuring electric charges may have only one leaf.
The case is metal and is also charged.
The movement of the leaf indicating the magnitude of the charge or potential measured.

31.2.8 Metal foil ball electroscope, Kolbe electroscope
Gold Leaf Electroscope, (Commercial).
See diagram 31.47: Metal foil ball electroscope.
An electroscope is used to detect electricity in the air by ionization of air molecules.
1. Use a light weight sphere hanging by a nylon thread to show that like charges repel each other, when electric charges distribute equably over the sphere's surface soon after the sphere is charged.
Fasten the top of the nylon thread on a pen, and then put the pen upon a wide mouth bottle.
Use the wax to join the nylon thread and the sphere.
The sphere can be made of a piece of 6 cm²metal foil, shaped and pressed into a sphere.
Use a table tennis ball, or popcorn to make the sphere with a layer of metal membrane packed around the sphere.
Smearing a liquid containing egg white and aluminium powder or scrap iron evenly on the surface of the sphere.
When a rubbed plastic ruler approaches the light conductor sphere, the sphere will jump.
2. Roll metal aluminium foil from a chocolate packet into a ball.
Use adhesive tape to attach a piece of thread to the ball.
Tie the free end of the thread to a plastic ball pen sleeve.
Place the ball pen sleeve across the mouth of a container so that the ball of foil hangs in the centre of the container, clear of the sides.
Bring a charged body near the metal ball.
At first the charged body attracts the ball then the ball jumps away.
Rub another ball pen sleeve on a plastic protractor.
Hold the pen near the ball and let it take a charge.
Bring the protractor near the charged ball.

31.2.9 Oppositely-charged electroscopes
Investigate equal and opposite charge.
Two electroscope are charged equal and opposite then the charge is transferred from one to the other.
If tape is pulled off an electroscope plate charge will result and the tape will also charge a second electroscope with the opposite charge.

31.2.10 Pith ball indicator, electroscope
Pith balls, (Commercial).
Use the white pith from inside a plant stem.
Dry the pith thoroughly and then press it tightly into small balls 5 mm in diameter.
Coat the pith balls with aluminium powder in egg white, colloidal graphite or metal paint.
Attach each pith ball to a silk thread or fishing line 15 cm in length.
Bring objects rubbed with silk, fur or flannel near the pith ball and note how it behaves.
This equipment is an electroscope.
In place of pith balls, use grains of puffed wheat, puffed rice, expanded polystyrene, Styrofoam balls, ping-pong balls, or any light object.

31.2.11 Two kinds of static charge, electroscope
See diagram 31.146A: Positive and negative charges attract each another.
Negative charges repel each another.
See diagram 31.146B: Use an uncharged pith ball electroscope.
See diagram 31.146C: Use a charged pith ball electroscope.
The basic observations of electrostatics are as follows:
Observation 1. Rub a plastic comb with fur.
The plastic comb becomes -ve and the fur becomes +ve.
Observation 2. Rub a glass rod with silk.
The glass rod becomes +ve and silk becomes -ve.
1. Like static charges repel each other and unlike charges attract each other.
Make a turntable by driving a long nail through a wood base.
Push a test-tube into a hole made in a large flat cork.
File the end of the nail to a sharp point and invert the test-tube over it.
Set pins in the top surface of the cork, they brace the objects you put on the turntable.
Use two test-tubes or glass rods, a piece of silk, two plastic combs, an ebonite rod, some wool, and a piece of fur or flannel.
Rub a comb with fur and set it on the turntable.
Rub the other comb with fur and bring it near the comb on the turntable.
2. Rub a glass rod with silk and put it on the turntable.
Again rub a comb with fur and bring it near the glass rod.
Repeat until you are sure of your observations.
When you rub the comb with fur, the plastic takes a negative charge of electricity and the fur takes a positive charge.
When you rub glass with silk, the glass takes a positive charge and the silk a negative charge.
3. Rub an ebonite rod with a piece of wool and bring the rod near an uncharged pith ball electroscope.
Note that the pith ball is first attracted and then repelled.
4. Rub a glass rod with a piece of silk and bring the rod near an uncharged pith ball electroscope.
The pith ball is at first attracted to the glass rod and then repelled.
5. Charge a pith ball negatively by touching it with an ebonite rod rubbed with wool.
When you bring a negatively charged plastic comb near the negatively charged pith ball, they repel each other.
When you bring a positively charged glass near the negatively charged pith ball, they attract each other.

31.2.12 Pith ball plate and flying strings
Pith balls, (Commercial).
1. Place a plate with pith ball hanging on strings on an electrostatic generator.
2. Place a cup filled with Styrofoam balls on an electrostatic generator.

31.3.1 Lightningt
See diagram 31.1.5: Lightning conductor.
1. Lightning bolt
Lightning is a discharge of electrons from a point where there is a surplus of electrons to a point where there are fewer electrons.
Lightning can be discharged from one part of the cloud to another (in-cloud), from cloud to cloud (from negative part of one cloud to positive part of another cloud), from cloud to the atmosphere, from cloud to earth (lightning bolt).
A lighting bolt starts when a forking stream of charge with sharp points goes down from the cloud towards the earth.
Before it reaches the ground an upward stream of positive charge (upward streamer) reaches one of the points and the lightning bolt lights up from the bottom (return stroke).
So a lightning bolt "moves up and down".
Lightning flickers when other sources of charge in the same cloud use the same channel as the first lightning bolt.
A distinctive lightning bolt is sometimes called fork lightning or chain lightning, compared to "sheet lightning", but they are the same, except that sheet lightning is a lightning bolt (forked lightning), hidden by cloud, so you only see the diffused reflection.
2. Electrophorus and lightning
The electrophorus experiment explains lightning, which is the same effect occurring on a much larger scale.
In the atmospheric disturbances of a heavy storm, clouds often become strongly charged electrically.
Just as the copper plate in the electrophorus experiment they might have an excess of electrons produced by the atmospheric disturbances.
If the charged cloud approaches another cloud that is not so heavily charged giant sparks can jump from one cloud to the other.
This is a flash of lightning with the accompanying noise of thunder.
3. Lightning rod
Lightning usually strikes tall objects on featureless surfaces, e.g. trees on a golf course.
However, lightning can strike water, e.g. swimming pools, where the electrical charge remains on the surface and spreads out in all directions.
If the cloud is low, electrons may jump between the cloud and a building on the ground.
The building is struck by lightning.
Tall buildings usually have a long metal lightning rod running from the ground vertically up the side of the building and extending higher than the building.
The long metal rod, lightning conductor, protects the building from being struck by lightning.
The lightning rod has a sharply pointed tip so that an intense electric field forms at the tip during an electrical storm and electric charge flows into the atmosphere preventing a strike on the building by a bolt of lightning.
If a lightning strike does occur, it is conducted to the earth through the lightning rod.
If electrons jump from a charged cloud overhead to the building, they can pass through the conducting rod to earth leaving the building free from damage.
Lightning conductors end in trident points, because points discharge electrons from the earth into the clouds easier than any other shape.
Lightning conductors may also have a metal ball to help electrons to land on in case of discharge is from cloud to earth.
4. Lightning safety
It is not true that lightning does not strike twice in the same place, so do not try to run away from it if you are caught in a thunderstorm.
If lightning hits a tree nearby, electricity may flow into a runner, because the body conducts the electricity better than the ground.
Avoid lightning by sitting with feet together in a depression in the ground.
Individual trees can be protected from lightning in exposed places, e.g. golf courses, by an LPS system, lightning protection for trees, where the trees receive individual lightning conductors.
The "30: 30 safety rule" is if you hear thunder within 30 seconds of lightning, take shelter for 30 minutes.
5. Aircraft and lightning
An aircraft may become charged electrically in flight due to friction with the air.
Most of the charge is removed while the plane is in flight with graphite coated nylon rods fitted with tungsten points placed at the extremities of the aircraft and linked by metal strips.
On landing, the plane is completely discharged by a wire spring coil fitted between the wheels that strikes the ground to allow electrons either to flow on to, or away from, the aircraft.
Otherwise passengers would risk an electric shock when alighting and a fire when refuelling caused by a spark due to discharge.
6. Benjamin Franklin (1706-1790)
He showed that lightning is a discharge of static electricity in 1752 by raising a kite and attaching a key to the end of the string.
A dangerous experiment!
A spark jumped from the key to his hand, because electricity was conducted along the wet string.
Some people who imitated this dangerous experiment were killed by the lightning.
7. Trees and lightning
Examine the lightning strike of trees.
Some trees with rough bark, e.g. oak, are more likely to be struck, because of water in the bark.
Other smooth bark species, e.g. beech, are less likely to be struck.

31.3.2 Franklin's bell, lightning warning device
See diagram 31.43: Franklin's bell.
Place the bell apparatus beneath the van de Graaff generator dome.
Start the generator to simulate a storm passing overhead.
The high voltage generated present rings the bell.

31.4.47 Metal foil ball electroscope
See diagram 31.47: Metal foil ball electroscope.
1. Hang a strip of aluminium foil, or folded piece of tissue paper, over the ball pen sleeve so that they do not touch the sides of the container.
Bring a charged body near the ball pen sleeve.
The leaves of the paper fly apart, because they have the same kind of charge.
2. Roll metal aluminium foil from a chocolate packet into a ball.
Use adhesive tape to attach a piece of thread to the ball.
Tie the free end of the thread to a plastic ball pen sleeve.
Place the ball pen sleeve across the mouth of a container so that the ball of foil hangs in the centre of the container, clear of the sides.
Bring a charged body near the metal ball.
At first the charged body attracts the ball then the ball jumps away.
Rub another ball pen sleeve on a plastic protractor.
Hold the pen near the ball and let it take a charge.
Bring the protractor near the charged ball.

31.3.3 Rubbed balloon sparks
See diagram 31.2.7: Rubbed balloon sparks.
1. Use a box cover made of metal.
Rub off the paint on its surface with sand paper.
Make a handle by fixing a candle in the centre of the cover.
Use a balloon that has no oil or dirt on its surface.
Pump air into the balloon, then rub the surface of the balloon with strength by a piece of dry wool cloth.
Hold the candle by your right hand to put the cover on the surface of a rubbed balloon.
Then touch the upper surface of the metal cover with the left hand index finger.
Then will probably be a small spark on your finger.
First remove the left hand finger, then take off the metal cover from the balloon, still touch the metal cover by left hand finger, but this time the finger is near the edges of the cover, immediately is a beam of electric spark jumps up between the finger and edge of the cover.
2. Make balloon sparks.
Rub a tightly blown up balloon strongly against your woollen sweater then quickly press the balloon against your ear.
Hear the crackling noise of the sparks between the balloon and your ear.
Make a balloon spark.
Put a metal tray on glass.
Rub a balloon with wool sweater and put it on the tray.
Hold your finger near the edge of the tray.
A spark jumps between the metal tray and your finger.

31.3.5 Finger sparks
Inflate a balloon and rub it with wool.
Attach a candle to a candle holder.
Put the candle holder on the rubbed surface of the balloon, using the candle as a handle.
Touch the upper side of the candle holder with a fingertip.
Observe a small spark jumping to your finger.
Lift the candle holder from the balloon by holding on to the candle.
Touch the bottom edge of the candle holder with a fingertip.
Observe a small spark jumping to your finger.
Rubbing the balloon with the wool leaves the balloon negatively charged.
Bringing the candle holder near the charged balloon pushes all negative charges to the upper side of the candle holder.
Touching the upper side of the candle holder removes the negative charges leaving a positive induced charge on the electrophorus.
Negative charges will jump from the finger when brought near the bottom edge of the electrophorus.

31.3.4 Saint Elmo's fire
See diagram 31.7.4.1b Saint Elmo's fire (University of Melbourne).
Glow seen around ship's masts, aeroplanes propellers and pointed objects on a dark night during electrical storms when steams of charge are given off.
The sailors of sailing ships thought it heralded good luck.
Place a model plane in an evacuation chamber and attach a Tesla coil.
Observe the discharge as the vacuum increases as it changes from streamers from the wing tips and other point objects to a continuous glow.

31.4.1 van de Graaff generator
(van de Graaff, 1901-1967, USA)
van de Graaff generator (Commercial).
This machine generates an electric charge with a vertical endless belt, which conducts charge from a source of voltage and carries it up to the inside surface of a metal dome to produce a high voltage on the dome.
The endless belt is made of insulating material, e.g. rubber or plastic, which is pulled over a Perspex roller by an electric motor.
The upper end of the endless belt is inside a large metal dome.
The moving belt forced charges onto the dome so that it gets to a very high voltage.
1. Attach a wire to a needle.
Touch the other end of the wire to the metal dome and point the needle at a candle flame.
The flame appears to be blown away by a wind.
2. Bring a small metal sphere near the metal dome and note the "lightning" spark.
3. Touch the metal dome and note your hair standing on end.

31.4.2 Atmospheric electric field motor
Electret type and corona type motor for operation from the earth's electric field.
(Electret is a permanently polarized piece of dielectric material having the same function as a permanent magnet.)

31.4.3 Blow soap bubbles at a van de Graaff generator
Blow neutral soap bubbles at a van de Graaff generator for intriguing induction effects.
Try double bubbles.

31.4.4 Electric pinwheel, a simple electrostatic motor
See diagram 31.42: Electric pinwheel.
Place the electric pinwheel on top of a van de Graaff generator dome.
Start the generator then the wheel rotates.
A bluish light and a hissing sound may come from the points of the pinwheel.
The air is ionized in the high electrical field of the points.
The ions and the points have the same sign of charge and thus repel each other.

31.4.5 Electrostatic voltmeters
ESV, Charge Sensor, (Commercial).
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.

31.4.6 Hair on end with van de Graaff generator
1. While standing on an insulated stool charge yourself up with a van de Graaff generator.
2. In very cold countries wear a wool cap outside the house, enter the house then pull off the wool cap.
Your hair stands out and up.
The wool in the wool cap scrapes electrons from the outer layers of your hair so each hair has a net positive charge.
The hair strands all positively charges d so they try to move apart.
However, small hairs close to the negatively charged skin lay down on the skin.

31.4.7 Streamers on a van de Graaff generator
Attach ribbon streamers to the top of a van de Graaff generator.
Fray the end of a nylon clothes-line and charge with an electrostatic machine to show repulsion.
A bunch of hanging nylon strings are charged by stroking with cellophane causing repulsion.
Charge a mop of insulating strings.

31.4.8 van de Graaff friction
van de Graaff generator (Commercial).
See diagram 31.4.40: van de Graaff generator.
A van de Graaff Generator, 200 kV, 220 / 240 V AC, variable speed, acrylic tube design, drive pulley inside lower housing, AV ball bearing motor drive with electronic speed control, metallic upper pulley with ball races mounted on a bracket that also retains the one piece aluminium terminal with magnetic catch, discharge ball with parking position, 4 mm socket terminal for connecting the base housing to a solid earth point, with earth cable and spare charging ball, also replacement belt.
Voltage is produced by rubbing two materials together.
The least used of the six methods is friction.
Its main application is in van de Graaff generators, used by some laboratories to produce high voltages.
Friction electricity (static electricity) is usually a nuisance.
For example, a flying aircraft may accumulate electric charges from the friction between its skin and the passing air.
These charges may interfere with radio communication.
Sliding across dry seat covers or walking across dry carpets, and then contacting other objects may give a mild electric shock.
The van de Graaff generator has an endless belt made of insulating material, e.g. rubber or plastic, that is pulled over a Perspex roller by an electric motor.
The upper end of the endless belt is inside a large metal dome.
The moving belt forced charges onto the dome so that it gets to a very high voltage.
This electrically driven generator with a 200 mm conducting sphere, capacity 15 pF, can be used to generate high direct voltages of 15 to 200 KV using a high speed fabric belt to accumulate charge in a large Faraday cage, i.e. the conducting sphere.
A charge is applied to the belt from a point below, then carried up into the hollow sphere where a collector removes the charge from the belt and stores it on the sphere.
Examine sparks from a van de Graaff generator to a nearby grounded ball.
1. Attach a wire to a needle.
Touch the other end of the wire to the metal dome and point the needle at a candle flame.
The flame appears to be blown away by a wind.
Bring a small metal sphere near the metal dome and note the "lightning" spark.
Touch the metal dome and note your hair standing on end.
Hold a fluorescent tube close to the dome of the van de Graaff generator.
The high voltage gradient lights the tube.
2. Student stands on platform and places hand on top of van de Graaff generator.
Do not remove hand from the surface.
Turn on the van de Graaff generator and observe their hair.
Turn off the van de Graaff generator.
Use grounding wire attached to base of generator to discharge the sphere, then allow student to withdraw hand.
Place various equipment items in kit one at a time on top on the van de Graaff generator and turn it on.
3. Remove pointed metal items such as keys and microphones.
Stand on the insulated stool.
With the variable control fully counter-clockwise, turn the power on.
Hold the pointed probe against the sphere while turning up the motor.
Place your other hand on the sphere before removing the probe.
Do not remove your hand and stay away from anything metal.
Allow yourself to charge up.
Fine, clean, dry hair stands on end the best.
Try pointing at a student or the electrified strings.
To discharge without shocks, hold pointed probe against the sphere, remove other hand and turn off motor.
4. Hold a ball close to a VDG and then bring a point close.

31.8.0.0 Capacitors
See diagram 30.5.6.5: Charging an electrolytic capacitor
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 fo a capacitor.
See diagram 30.5.2.5: Time variation of voltage and current for a capacitor.
See diagram 30.5.2.01c: The ratio of voltage to current in a capacitor decreases with frequency.

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 30.5.2.0c. 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.
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.

31.8.22Coulomb'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.
See diagram 30.5.2.5 Time variation of voltage and current for a capacitor.
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