group of five, the plates being seen edge on. The plates of each group are connected together, but each group is carefully insulated from the other. In order to get them close together and yet insulated, the plates are often separated by thin sheets of mica or by paper saturated with paraffin wax.

The essential principle as just presented may be summarized as follows: (1) Bringing two oppositely charged conductors near together tends to lower the differ

ence of potential between them. Hence (2) larger charges are re

A

quired in order to produce the same difference of potential.

B

FIG. 324

509. A condenser connected to an alternating-current circuit. A very interesting illustration of the action of a condenser is its use on an alternating-current circuit. If an ordinary telephone condenser of a size marked 2 microfarads (symbolized in Fig. 325 by the two parallel lines at C) is connected through a 25-watt 110-volt tungsten-filament lamp, L, to the alternating-current light-circuit, the lamp will glow. This is an interesting case, for there is not a complete electric circuit in the usual sense. The plates of the condenser

In the alternating-current circuit the difference of potential, or voltage, between the wires is continually changing. At the instant when the wire A is charged positively, the wire B is charged negatively. Then the voltage between them decreases until in a very short time they are at the same potential. Later the wires become charged in the opposite direction, A becoming negative and B positive, and so on, the potential changing to and fro at a rapid rate. Knowing what is happening to the wires A and B, one can next explain why the lamp will glow. When A is positive and B nega

tive, the condenser will become charged. When the difference of potential begins to decrease, that is, when A begins to lose its positive charge, the condenser begins to discharge back through the lamp. Then, as A becomes negative and B positive, the condenser charges up in the opposite direction, the charging current going through the lamp. Hence at each change in the direction of the voltage of the line-at each "oscillation"-the condenser is discharged and then charged oppositely. If the wires A and B are connected to the usual type of alternating circuit, the wire A will be charged positively 60 times a second. Hence the condenser will be fully charged and discharged 120 times a second. On each charge or discharge a current passes through the lamp and gives what we call an alternating current in the lamp.*

If the condenser is connected in a circuit which has a voltage acting always in one direction, -not pulsating nor alternating, there will be no continual charging and discharging through the lamp, and hence the lamp will not glow.

510. Quantitative relation between the charge and the voltage of a condenser. We are now ready to discuss the quantitative relation between the quantity on a condenser, its voltage, and what is called the capacity, or capacitance, of the condenser. That quantitative relations in electricity are very important has been pointed out a number of times, and this case is no exception to the general rule.

In the case of the condenser there is a very simple relation between the charge on the condenser and the voltage between the plates; for the charge, or quantity, is directly proportional to the voltage. For example, if the voltage is doubled, the charge is doubled. This can be expressed algebraically by the equation

where Q represents the charge† and V the voltage, or difference of potential, between the plates. C is a constant for any one condenser.

*When a 2-microfarad condenser and a 25-watt 110-volt lamp are connected to a 110-volt 60-cycle circuit, the current through the lamp is about 0.08 ampere. † By Q, or the charge on a condenser, is meant the charge on one plate only. In symmetrical condensers the charges on the two conductors are equal, but of opposite signs.

✓ 511. Capacity, or capacitance. If the constant C of equation (88) is known for any condenser, the charge Q on the condenser can always be obtained by multiplying the constant by the voltage. Obviously, then, a knowledge of the value of the constant C for a condenser not only gives the student some idea of the size of the condenser but enables him to compute easily the value of Q. In fact, this constant is such a useful and convenient one that it is given a name-the capacity, or capacitance,* of the condenser.

The student needs a word of caution about the use of the term capacity. The most common use, in other than electrical practice, is in connection with the volume measurement of commodities. In such cases the word usually means the total amount the given container will hold. But it does not have that sense in electrical usage nor in some other cases. Consider the case of a tank used to hold compressed air or some other gas. If the gas obeys Boyle's law (sect. 45), the quantity of gas in the tank is given by

Q=kp,

where p is the pressure of the gas, and k is a constant which depends on the size of the tank. If one wishes at any time to know the quantity of gas in the tank, one reads a pressure gauge and then multiplies the pressure by the constant k. The product will give the quantity of gas in the tank. The constant gives one also some idea of the size of the tank, and it may be called the capacity of the tank. It is not, however, the total amount of gas that the tank will hold. Certainly no one would say that the capacity of the tank is the total amount of gas that the tank will hold, for that is an indeterminate quantity. The total amount of gas that it will hold can be determined only by compressing gas into the tank until it bursts.

In electrical terminology the word capacity is used in the sense just explained in the case of the gas tank. It does not mean the total amount of electricity the conductor will hold. A little reflection will convince one that the total amount of electricity that a conductor can hold is indeterminate. One may keep adding charges until something smashes or until a spark breaks down the insulation.

The quantitative definition of the capacitance, or capacity, of a condenser may be stated in either one of two ways. Both are based on equation (88). From this equation it is readily seen that

Hence the capacitance is equal to the ratio between the charge and the voltage of the condenser. Another way is to take a special case -one where the voltage is unity (that is, where V = 1). In this case C = Q. Hence the capacitance of a condenser is equal to its charge when the charging voltage is equal to unity.

512. Capacitance dependent on physical dimensions. In section 508 an experiment was described in which moving two plates together decreased their voltage. In this case the plates were insulated, and the quantity of electricity on them remained constant. This experiment shows that moving the plates together increases the capacitance; for since Q was constant, V decreased, and C is equal to Q/V, it follows that C was increased. In general, moving two conductors nearer together increases the capacitance of the pair.

A simple experiment with a roll of tin foil shows that an increase in the charged area increases the capacitance. The foil is rolled on a tube or rod made of some insulating material. While rolled up, it is charged and then touched to an electroscope or electrostatic voltmeter. The size of the deflection will give some idea of the potential of the foil. If the foil is partly unrolled without discharging it, one will find by again touching it to the electroscope that its potential is now less; as we saw in the last paragraph, this means that the capacitance is greater. When the tin foil is rolled up again, it will be found to have again a larger potential and hence a smaller capacitance.

Any charged conductor (such as a roll of tin foil) may be regarded as part of a condenser, the other part being the walls, floor, table, etc., where there will be an equal and opposite induced charge. In the experiment of measuring the potential of the foil, what was really measured was the difference of potential between the foil, on the one hand, and the walls, floor, table, etc., on the other.

513. Capacitance dependent on the medium between the plates. If instead of using air as the insulator between the two plates of a condenser, one uses a sheet of glass, hard rubber, or some other insulating medium, the capacitance of the condenser becomes larger.

This is easily shown experimentally. In Fig. 326 the plate A is connected to an electroscope or electrostatic voltmeter and then charged. The plate B is connected to the ground. When a plate of glass or some other insulating material is slipped between the two plates, the leaves of the electroscope will fall. When the plate of insulating material is withdrawn, the leaves will again diverge. The electroscope thus shows that the potential of A is decreased by the insertion of the glass plate. As before, a lowering of the difference of potential, with the charge Q remaining constant, means, since C = Q/V, that the capacitance has become larger.

BI

++++++

A

FIG. 326

something to do with the electrical action. Indeed, from this experiment it is possible to deduce the fact that two charges of electricity, when submerged in some insulating oil, should attract each other with a very different force from that exerted in air. It was such experiments as this that suggested the "strain" theory referred to in section 393. It led physicists to think more about the medium in which electric and magnetic fields are produced. It ultimately led to the discovery of electromagnetic waves, which today are so commonly used in wireless telegraphy and telephony.

The medium between the conductors of a condenser is usually called the dielectric. Different dielectrics do not behave alike: some change the potential and capacitance more than others. The dielectric constant k, which is used to measure the relative effects of the different dielectrics, is defined as follows: The dielectric constant of any substance is equal to the ratio of the capacitance of a condenser when that substance is used as the dielectric to the capacitance when there is a vacuum between the conductors (for all practical purposes air at ordinary pressures may be used instead of a vacuum). The numerical values of the dielectric constants of a number of substances are given on the next page.