If we have a number of such condensers we can combine them in “parallel” or in “series.” If all the plates on one side are connected together and also those on the other, the condensers are joined in parallel. If C1, C2, C3, &c., are the separate Systems of condensers. capacities, then Σ(C) = C1 + C2 + C3 + &c., is the total capacity in parallel. If the condensers are so joined that the inner coating of one is connected to the outer coating of the next, they are said to be in series. Since then they are all charged with the same quantity of electricity, and the total over all potential difference V is the sum of each of the individual potential differences V1, V2, V3, &c., we have
The resultant capacity is C = Q/V, and
These rules provide means for calculating the resultant capacity when any number of condensers are joined up in any way.
If one condenser is charged, and then joined in parallel with another uncharged condenser, the charge is divided between them in the ratio of their capacities. For if C1 and C2 are the capacities and Q1 and Q2 are the charges after contact, then Q1/C1 and Q2/C2 are the potential differences of the coatings and must be equal. Hence Q1/C1 = Q2/C2 or Q1/Q2 = C1/C2. It is worth noting that if we have a charged sphere we can perfectly discharge it by introducing it into the interior of another hollow insulated conductor and making contact. The small sphere then becomes part of the interior of the other and loses all charge.
Measurement of Capacity.—Numerous methods have been devised for the measurement of the electrical capacity of conductors in those cases in which it cannot be determined by calculation. Such a measurement may be an absolute determination or a relative one. The dimensions of a capacity in electrostatic measure is a length (see Units, Physical). Thus the capacity of a sphere in electrostatic units (E.S.U.) is the same as the number denoting its radius in centimetres. The unit of electrostatic capacity is therefore that of a sphere of 1 cm. radius.[1] This unit is too small for practical purposes, and hence a unit of capacity 900,000 greater, called a microfarad, is generally employed. Thus for instance the capacity in free space of a sphere 2 metres in diameter would be 100/900,000 = 1/9000 of a microfarad. The electrical capacity of the whole earth considered as a sphere is about 800 microfarads. An absolute measurement of capacity means, therefore, a determination in E.S. units made directly without reference to any other condenser. On the other hand there are numerous methods by which the capacities of condensers may be compared and a relative measurement made in terms of some standard.
One well-known comparison method is that of C. V. de Sauty. The two condensers to be compared are connected in the branches of a Wheatstone’s Bridge (q.v.) and the other two arms completed with variable resistance boxes. These arms Relative deter-minations. are then altered until on raising or depressing the battery key there is no sudden deflection either way of the galvanometer. If R1 and R2 are the arms’ resistances and C1 and C2 the condenser capacities, then when the bridge is balanced we have R1 : R2 = C1 : C2.
Another comparison method much used in submarine cable work is the method of mixtures, originally due to Lord Kelvin and usually called Thomson and Gott’s method. It depends on the principle that if two condensers of capacity C1 and C2 are respectively charged to potentials V1 and V2, and then joined in parallel with terminals of opposite charge together, the resulting potential difference of the two condensers will be V, such that
| V = | (C1V1 − C2V2) |
| (C + C) |
and hence if V is zero we have C1 : C2 = V2 : V1.
The method is carried out by charging the two condensers to be compared at the two sections of a high resistance joining the ends of a battery which is divided into two parts by a movable contact.[2] This contact is shifted until such a point is found by trial that the two condensers charged at the different sections and then joined as above described and tested on a galvanometer show no charge. Various special keys have been invented for performing the electrical operations expeditiously.
A simple method for condenser comparison is to charge the two condensers to the same voltage by a battery and then discharge them successively through a ballistic galvanometer (q.v.) and observe the respective “throws” or deflections of the coil or needle. These are proportional to the capacities. For the various precautions necessary in conducting the above tests special treatises on electrical testing must be consulted.
 |
| Fig. 2. |
In the absolute determination of capacity we have to measure the ratio of the charge of a condenser to its plate potential difference. One of the best methods for doing this is to charge the condenser by the known voltage of a battery, and then Absolute deter-minations. discharge it through a galvanometer and repeat this process rapidly and successively. If a condenser of capacity C is charged to potential V, and discharged n times per second through a galvanometer, this series of intermittent discharges is equivalent to a current nCV. Hence if the galvanometer is calibrated by a potentiometer (q.v.) we can determine the value of this current in amperes, and knowing the value of n and V thus determine C. Various forms of commutator have been devised for effecting this charge and discharge rapidly by J. J. Thomson, R. T. Glazebrook, J. A. Fleming and W. C. Clinton and others.[3] One form consists of a tuning-fork electrically maintained in vibration of known period, which closes an electric contact at every vibration and sets another electromagnet in operation, which reverses a switch and moves over one terminal of the condenser from a battery to a galvanometer contact. In another form, a revolving contact is used driven by an electric motor, which consists of an insulating disk having on its surface slips of metal and three wire brushes a, b, c (see fig. 2) pressing against them. The metal slips are so placed that, as the disk revolves, the middle brush, connected to one terminal of the condenser C, is alternately put in conductive connexion with first one and then the other outside brush, which are joined respectively to the battery B and galvanometer G terminals. From the speed of this motor the number of commutations per second can be determined. The above method is especially useful for the determinations of very small capacities of the order of 100 electrostatic units or so and upwards.
Dielectric constant.—Since all electric charge consists in a state of strain or polarization of the dielectric, it is evident that the physical state and chemical composition of the insulator must be of great importance in determining electrical phenomena. Cavendish and subsequently Faraday discovered this fact, and the latter gave the name “specific inductive capacity,” or “dielectric constant,” to that quality of an insulator which determines the charge taken by a conductor embedded in it when charged to a given potential. The simplest method of determining it numerically is, therefore, that adopted by Faraday.[4]
Table I.—Dielectric Constants (K) of Solids (K for Air = 1).
| Substance. | K. | Authority. |
| Glass, double extra dense flint, density 4.5 | 9.896 | J. Hopkinson |
| Glass, light flint, density 3.2 | 6.72 | ” |
| Glass, hard crown, density 2.485 | 6.61 | ” |
| Sulphur | 2.24 | M. Faraday |
| 2.88 | Coullner | |
| 3.84 | L. Boltzmann | |
| 4.0 | P. J. Curie | |
| 2.94 | P. R. Blondlot | |
| Ebonite | 2.05 | Rosetti |
| 3.15 | Boltzmann | |
| 2.21 | Schiller | |
| 2.86 | Elsas | |
| India-rubber, pure brown | 2.12 | Schiller |
| India-rubber, vulcanized, grey | 2.69 | ” |
| Gutta-percha | 2.462 | J. E. H. Gordon |
| Paraffin | 1.977 | Gibson and Barclay |
| 2.32 | Boltzmann | |
| 2.29 | J. Hopkinson | |
| 1.99 | Gordon | |
| Shellac | 2.95 | Wällner |
| 2.74 | Gordon | |
| 3.04 | A. A. Winkelmann | |
| Mica | 6.64 | I. Klemenčič |
| 8.00 | P. J. Curie | |
| 7.98 | E. M. L. Bouty | |
| 5.97 | Elsas | |
| Quartz— | ||
| along optic axis | 4.55 | P. J. Curie |
| perp. to optic axis | 4.49 | P. J. Curie |
| Ice at −23° | 78.0 | Bouty |
- ↑ It is an interesting fact that Cavendish measured capacity in “globular inches,” using as his unit the capacity of a metal ball, 1 in. in diameter. Hence multiplication of his values for capacities by 2.54 reduces them to E.S. units in the C.G.S. system. See Elec. Res. p. 347.
- ↑ For fuller details of these methods of comparison of capacities see J. A. Fleming, A Handbook for the Electrical Laboratory and Testing Room, vol. ii. ch. ii. (London, 1903).
- ↑ See Fleming, Handbook for the Electrical Laboratory, vol. ii. p. 130.
- ↑ Faraday, Experimental Researches on Electricity, vol. i. § 1252. For a very complete set of tables of dielectric constants of solids, liquids and gases see A. Winkelmann, Handbuch der Physik, vol. iv. pp. 98-148 (Breslau, 1905); also see Landolt and Börnstein’s Tables of Physical Constants (Berlin, 1894).
