Figs. 542 and 543.--Diagrams showing hydraulic analogy illustrating the difference between amperes and coulombs. The rate of current flow of one ampere in fig. 543 may be compared to the rate of discharge of a pump as in fig. 542. Assuming the pump to be of such size that it discharges a gallon per stroke and is making 60 strokes per minute, the quantity of water discharged per hour (coulombs in fig. 543) is 1 × 60 × 60 = 3,600 gallons. Following the analogy further (in fig. 543), the pressure of one volt is required to force the electricity through the resistance of one ohm between the terminals A and B. In fig. 542, the boiler must furnish steam pressure on the pump piston to overcome the friction (resistance) offered by the pipe and raise the water from the lower level A' to the higher level B'. The difference of pressure between A and B in the electric circuit corresponds to the difference of pressure between A' and B'. The cell furnishes the energy to move the current by maintaining a difference of pressure at its terminals C and D; similarly, the boiler furnishes energy to raise the water by maintaining a difference of pressure between the steam pipe C and exhaust pipe D'.
Fig. 543. If the current strength in fig. 543 be one ampere, the quantity of electricity passing any point in the circuit per hour is 1 × 60 × 60 = 3,600 coulombs.
Current Measurement.--It is necessary to adopt some arbitrary standard in order to compare currents of different strengths. The term strength of a current, or current strength means the rate of flow past any point in the circuit in a given unit of time. The unit of current, called the ampere, is defined as the unvarying current which, when passed through a solution of nitrate of silver in water (15 per cent. by weight of the nitrate) deposits silver at the rate of .001118 gramme per second.
Fig. 544.--Queen weight voltameter for determining the strength of current by the weight of metal deposited in a given time. The two outside plates form the anode and are joined together and to one binding post, while the cathode is placed between them and connected to the other binding post. The cathode thus receives a deposit on both sides. An adjustable arm serves to lower the plates into the electrolyte. To calculate the strength of an unknown current which has passed through a weight voltameter, divide the gain in weight by the number of seconds the current flows through the instrument and by the weight deposited by one ampere in one second. That is, current strength in amperes = gain in weight ÷ (time in seconds × .0003286).
Ques. How much copper or zinc will one ampere deposit in one second?
Ans. .0003286 gramme of copper in a copper voltameter, or .0003386 gramme of zinc in a zinc voltameter.
Ques. What is the difference between an ampere and a coulomb?
Ans. An ampere is the unit rate of flow of the current, and a coulomb is the unit quantity of electricity, that is, the ampere is the rate of current flow that will deposit .0003286 grammes of copper in one second and a coulomb is the quantity of electricity that passes a given point in one second when the current strength is one ampere. In other words a coulomb is one ampere second.
Fig. 545.--Gas voltameter for determining the strength of current by the volume of gas evolved. To use, connect up as shown in the illustration. Adjust so that the zero position of the burette is about one-half inch below the level of the top of the U tube. Pour acidulated water into the mouth of the burette till the water in the U tube is about one-half inch from the top. With the electrodes inserted through the corks, carefully place each one in position by giving a slight twist to the right as the cork enters. The water level in the U tube and burette should now be the same, or further adjustment must be made to attain this result. The level in the burette does not necessarily have to correspond with the zero graduation, but must not be below it. Unclamp the burette and hold it nearly horizontal. The liquid will not run out if the corks be tight, so that this is the air leakage test. Attach the connectors and wires from the current source (which should have a pressure of 2 or more volts) placing a switch in the circuit. When the switch is closed, bubbles of gas will rise in the U tube from both electrodes, displacing the water and forcing it up the burette. Hydrogen will be liberated over the negative electrode, and oxygen over the positive electrode in the proportion of twice as much hydrogen as oxygen. To calculate the current strength, divide the volume of gas liberated by the time in seconds, and by the volume of gas liberated (in cubic centimeters) by one ampere in one second and by .1733; that is: amperes = volume of gas liberated ÷ (time in seconds × .1733).
EXAMPLE.--If an arc lamp require a current of 8 amperes, how much electricity does it consume per hour?
Since one coulomb = one ampere second, the quantity of electricity consumed per hour is
8 amperes × ( 60 × 60 ) = 28,800 coulombs.
Voltameter.--A voltameter is an electrolytic cell employed to measure an electric current by the amount of chemical decomposition the current causes in passing through the cell. There are two classes of voltameter:
Ques. What is the difference between these two classes of voltameter?
Ans. In one, the current strength is determined by the weight of metal deposited or weight of water decomposed, and in the other by the volume of gas liberated.
Ques. How should the plates of a weight voltameter be treated before use?
Ans. They must be thoroughly cleaned and polished with sandpaper, the sand being afterwards removed by placing them in running water. The fingers must not be placed on any part of the plate which is to receive the deposit.
Ques. What form of voltameter has been selected to measure the International ampere?
Ans. The silver voltameter arranged as here specified:
The cathode on which the silver is to be deposited shall take the form of a platinum bowl, not less than 10 cms. in diameter, and from 4 to 5 cms. in depth.
The anode shall be a disc or plate of pure silver some 30 sq. cms. in area, and 2 or 3 cms. in thickness. This shall be supported horizontally in the liquid near the top of the solution by a silver rod riveted through its center.
To prevent the disintegrated silver which is formed on the anode falling upon the cathode, the anode shall be wrapped around with pure filter paper, secured at the back by suitable folding.
The liquid shall consist of a neutral solution of pure silver nitrate containing about 15 parts by weight of the nitrate to 85 parts of water.
Ques. What is the value of the International ampere as measured with the silver voltameter?
Ans. The International ampere is represented sufficiently well for practical use by the unvarying current which, when passed through a silver voltameter (as described above) deposits silver at the rate of .001118 gramme per second.
Fig. 546.--Single contact and short circuiting key. This key is intended especially for use with D'Arsonval galvanometers in zero deflection methods. The key is connected in circuit with the galvanometer so that whenever the key is not depressed, the galvanometer is short circuited, and its oscillations quickly damped out by the currents induced in its coil. The back end of the spring is held in a slot in a rubber block attached to the base.
Ohm's Law and the Ohm.--The various tests here described depend for their truth upon the definite relation existing between the electric current, its pressure, and the resistance which the circuit offers to its flow. This relation was fully investigated by Ohm in 1827. Using the same conductor, he proved not only that the current varies with the pressure, but that it varies in direct proportion.
Ohm's law has already been discussed in a previous chapter and the several ways of expressing it are repeated here for convenience:
| 1. | Amperes | = | voltsohms ; |
| 2. | Volts | = | amperes × ohms ; |
| 3. | Ohms | = | voltsamperes . |
Various values have been assigned, from time to time, to the ohm or unit of resistance, the unit in use at the present time being known as the International ohm. This was recommended at the meeting of the British Association in 1892, was adopted by the International Electrical Congress held in Chicago in 1893, and was legalized for use in the United States by act of Congress in 1894. The International ohm in graphically defined in fig. 548. The previous values given to the ohm which were more or less generally accepted are as follows:
Fig. 547.--Double contact key. It is of especial value in connection with a Wheatstone bridge. When used with the latter it forms a combination battery and galvanometer key. The battery is wired to the top leaves of the key and the galvanometer to the lower leaves. Hence, when operated, the battery circuit will be closed before the galvanometer circuit, as it is desirable to avoid undue disturbance of the needle.
The Siemens' Ohm.--A resistance due to a column of mercury 100 cm. long and 1 sq. mm. in cross section at 0° C.
B. A. (British Association) Ohm.--A resistance due to a column of mercury approximately 104.9 cm. long and 1 sq. mm. in cross section at 0° C.
Fig. 548.--The international ohm. It is defined as the resistance of 14.452 grammes of mercury in the form of a column of uniform cross section 106.3 centimeters in length, at a temperature of 0° C. This is approximately equivalent to a column 106.3 cm. long, having a uniform cross section of 1 sq. mm. In the figure the international ohm is defined graphically. The resistance of the external circuit and the standard one volt cell is assumed to be zero.
Legal Ohm.--A resistance due to a column of mercury 106 cm. long and 1 sq. mm. in cross section at 0° C. This unit was adopted by the Paris conference of 1884.
OHM TABLEA
| Date | International Ohm | Legal Ohm | B. A. Ohm | Siemens' Ohm | |
| International Ohm | 1893-4 | 1.0000 | 1.0028 | 1.0136 | 1.0630 |
| Legal Ohm | 1884 | .9972 | 1.0000 | 1.0107 | 1.0600 |
| B. A. Ohm | 1864 | .9866 | .9894 | 1.0000 | 1.0488 |
| Siemens' Ohm | .9407 | .9434 | .9535 | 1.0000 |
[A] NOTE.--In the above table to reduce, for instance, British Association ohms to International ohms, multiply by .9866, or divide by 1.0136; to reduce legal ohms to International ohms, multiply by .9972, or divide by 1.0028, etc.
Fig. 549.--Leeds and Northrup one ohm standard resistance (Reichsanstalt form); adjusted at 20° C. Low resistance standards may be properly divided into two classes: 1. those which are designed primarily as resistance standards, and 2. those designed as current carrying standards. Those of the first mentioned class are often used to measure currents up to their capacity. The above standard has both pressure and current terminals. The binding posts for the former are mounted on high posts so as to be easily accessible when the standard is immersed in oil. When used as a resistance standard of precision, it should not be subjected to a current of more than one ampere, and when used as a current carrying standard of lesser accuracy, a current of 2 or 3 amperes may be used.
Practical Standards of Resistance.--The column of mercury as shown in fig. 548, is the recognized standard for resistance, however, in practice, it is not convenient to compare resistances with such a piece of apparatus, and therefore secondary standards are made up and standardized with a great degree of precision. These secondary standards are made of wire. The material generally used being manganin or platinoid.
Fig. 550.--Direct deflection method of testing resistances; a useful and simple method which may be used in numerous tests. Galvanometer readings are taken through the known, and unknown resistances, and the current being proportional to the deflections, the value of the unknown resistance is easily calculated.
Resistance Measurement.--Resistance is that which offers opposition to the flow of electricity. Ohm's law shows that the strength of the current falls off in proportion as the resistance in the circuit increases. This gives a basis for measuring resistance.
There are various methods by which an unknown resistance may be measured, as by the:
Direct Deflection Method.--This method is based on the fact that the greater the current through a galvanometer the greater the deflection of the needle; it is a simple method and is capable of extended application.
The apparatus required consists of battery, galvanometer, known resistance, and double contact key. The connections are made as in fig. 550. The known resistance is put in circuit with the galvanometer and after noting the deflection, the key is moved so as to cut out the known resistance and throw into circuit the unknown resistance. The deflection of the galvanometer is again noted and compared with the first deflection.
Fig. 551.--Charge and discharge key, adapted to condenser testing where the condenser is to be alternately charged and discharged. The insulated handle enables the key to be used without insulating the body.
Fig. 552.--Pohl commutator. This is equivalent to a two pole double throw switch. The depressions in the base are filled with mercury into which the contacts dip in closing the circuit.
If the deflections be proportional to the current, the unknown resistance will be as many times the known resistance as the deflection with the known resistance is greater than the deflection with the unknown resistance.
Method of Substitution.--This is the simplest method of measuring resistance. The resistance to be measured is inserted in series with a galvanometer and some constant source of current, and the galvanometer deflection noted. A known adjustable resistance is then substituted for the unknown and adjusted till the same deflection is again obtained. The value of the adjustable resistance thus obtained is equal to that of the resistance being tested.
Fig. 553.--Substitution method of testing resistances. The connections and apparatus are the same as in fig. 550, except that a resistance box is used in place of the known resistance. In making the test, first note deflection with unknown resistance in circuit, then press key so that the current will pass through the resistance box, and adjust the resistance in the box so that the deflection of the galvanometer is about the same as with the unknown. Now switch from one circuit to the other, changing the resistance in the box until equal deflections are obtained. When this obtains, the resistance in the box is the same as the resistance being tested.
Ques. What kind of adjustable resistance is used in making the above test?
Ans. A resistance box.
Ques. Describe a resistance box.
Ans. It consists of a box containing numerous resistance coils with their ends connected to terminals and provided with plugs so that they may be thrown into or out of circuit at will, thus varying the resistance in the circuit.
Fig. 554.--Ordinary resistance box. It contains sets of standard resistances consisting of coils of insulated wire having low conductivity and small temperature coefficient. The ends of the coils are joined to the section of the bar between the plugs. The insertion of a plug cuts out a coil. In using, care should be taken to put the plugs in with a slight twist so that there shall be no resistance introduced by poor contact.
Fall of Potential Method.--This is a very simple method of measuring resistances, and one that is convenient for practical work in electrical stations because it requires only an ammeter, voltmeter, battery and switch--apparatus to be found in every station. The connections are made as shown in fig. 555.
In making the test the ammeter and voltmeter readings are taken at the same time, and the unknown resistance calculated from Ohm's law. Accordingly, since:
solving for the resistance,
Fig. 555.--Fall of potential method of testing resistances; a convenient method for testing at stations, requiring only the usual instruments to be found at a station. The resistance of the voltmeter must be very high, otherwise the test must be made as in fig. 556.
EXAMPLE.--If in fig. 555 the readings show 6 volts and 2 amperes how many ohms is the resistance being tested?
Substituting in formula (2)
Ques. Can this test be made with any kind of voltmeter?
Ans. Its resistance must be very high to avoid error. When a voltmeter having small resistance is used, it should be connected so as to measure the fall of pressure across both ammeter and unknown resistance as shown in fig. 556.
Fig. 556.--Fall of potential method of testing resistances; diagram showing connections for testing with low resistance voltmeter. The resistance measured with this connection will be the sum of the resistances of the coil and the ammeter. The resistance of the ammeter is usually known and can be subtracted from the sum to obtain the required resistance.
Differential Galvanometer Method.--This is what is known as a nil or zero method, that is, a method of making electrical measurements in which comparison is made between two quantities by reducing one to equality with the other, the absence of deflection from zero of the instrument scale showing that the equality has been obtained.
The test is made with a differential galvanometer, and resistance box connected as in fig. 557. The current then will divide so that part of it flows through the resistance being tested and around one set of coils of the galvanometer while the other part will flow through the resistance box and the other set of coils as indicated. When the resistance box has been so adjusted that its resistance is the same as the unknown resistance the current in the two branches will be equal, and the needle of the galvanometer will show no deflection.
Fig. 557.--Differential galvanometer method of testing resistances. In making the test, the resistance box is adjusted till the galvanometer needle shows no deflection. When this condition obtains, the resistance in circuit in the resistance box is equal to the unknown resistance, hence, a reading of the box gives the value of the unknown resistance.
Ques. What name is given to this method of testing?
Ans. It is called a zero method, distinguishing it from deflection methods.
Ques. For what kind of resistance is the method adapted?
Ans. Since it is a nil or zero method, it is better adapted to the measurement of non-inductive than of inductive resistances.
Ques. What precaution should be taken with inductive resistances?
Ans. The current must be allowed to flow until it becomes steady to overcome the influence of self-induction.
Ques. What may be said with respect to the differential galvanometer method?
Ans. With an accurate instrument it is very reliable.
Fig. 558.--Drop method of testing resistances. The apparatus is connected as shown and readings taken with voltmeter across known and unknown resistance. The unknown resistance is then easily calculated.
Drop Method.--This is a convenient method, and one which may be used for measuring either high or low resistances with precision. It is used for many practical measurements, and requires only a voltmeter, battery, known resistance and a two way switch.
The instruments are connected as in fig. 558, and in making the test, the voltmeter is switched into circuit across the known resistance and then across the unknown resistance, readings being taken in each case. The value of the unknown resistance, is then easily calculated from the following proportion:
| drop across known resistancedrop across unknown resistance | = | known resistanceunknown resistance |
from which
| unknown resistance | = | known resistance × drop across unknown resistancedrop across known resistance |
Fig. 559.--Leeds and Northrup portable galvanometer (pointer type A). The sensitiveness of this instrument is such that it may be substituted in numerous cases for the non-portable reflecting type of galvanometer; as for instance, in the checking of ammeters and voltmeters to an accuracy of .2% by the potentiometer method, and on almost all Wheatstone bridge measurements to commercial accuracies. A current of 2 micro-amperes will cause the pointer to move 1 mm. over the scale, that is, it has a sensibility of 500,000 ohms. The method of suspending the moving system is such as to practically eliminate initial friction which is of value in all zero deflecting methods. The suspensions and moving system are guarded by springs, which together with the solid construction of the case render the instrument capable of withstanding rough usage. Overall dimensions are 5-1/4" x 2-5/8" x 3-1/2"; weight about 3 pounds.
Ques. What may be substituted for the voltmeter?
Ans. A high resistance galvanometer, whose deflections are proportional to the current, the value of the deflections being substituted in the formula.
Ques. What precaution should be taken in making the test?
Ans. The current used should not be strong enough to appreciably heat the resistance, and if the current be not very steady, several readings should be taken of each measurement and the average values used in the formula.
Ques. How are the most accurate results obtained?
Ans. By selecting the known resistance as near as possible to the supposed value of the unknown resistance.
Fig. 560.--Voltmeter method of testing resistances. Knowing the resistance of the voltmeter, turn switch to the left and from reading calculate resistance corresponding to one division of the scale. Turn switch to right and multiply reading by resistance required for deflection of one division. This gives resistance of voltmeter and unknown resistance; subtracting from this the resistance of voltmeter gives value of the unknown resistance.
Voltmeter Method.--This is a direct deflection method and consists in determining first the resistance that will deflect the needle through one division of the scale on a given battery current, then with this as a basis for comparison the voltmeter is connected across the unknown resistance whose value is easily calculated from the reading.
In making the test, the instruments are connected as in fig. 560. The current from battery is first passed through the galvanometer by turning switch as shown.
Fig. 561.--Megohm box or set of standard high resistances. The box contains five resistances of 200,000 ohms each. The six pillars are petticoat insulated, the resistances being placed between each pair of pillars. There is a double contact post on top of each pillar so that these can be connected together with copper links.
Assuming that the resistance of the instrument is 8,000 ohms and that the current deflects the needle through 10 divisions of the scale, then for a deflection of one division the resistance is
8,000 × 10 = 80,000 ohms.
Accordingly, if, when the switch is moved to the right, connecting the voltmeter across the unknown resistance, the needle be moved through 6 divisions of the scale, the combined resistance of the voltmeter and unknown resistance is
80,000 ÷ 6 = 13,333-1/3 ohms,
and subtracting the resistance of the voltmeter, the value of the unknown resistance is
13,333-1/3 - 8,000 = 5,333-1/3 ohms.
Ques. For what kinds of test is the voltmeter method best adapted?
Ans. For measuring high resistances, as the insulation of wires, etc.
Ques. What may be said with respect to the current used?
Ans. Its voltage should be as high as possible within the limits of the voltmeter scale.
Fig. 563.--Standard resistance box: 100,000 ohms, in four units of 10,000, 20,000, 30,000, and 40,000 ohms. An "infinity" plug separates each coil from the ones adjacent. Segments are elevated from the hard rubber top by special washers in order to increase insulation. Binding posts are so arranged as not to be in the way when plugs are used.
Fig. 562.--Standard high resistance box: 100,000 ohms. It is mounted in a brass box with a hard rubber top. Connections should be made to terminals marked 3 and 4. When the flexible cord is on plug 1, the box is short circuited, but when on plug 2, the resistance of 100,000 ohms is in series. The box is especially suited to rapid cable testing.
Ques. In testing cable insulation what is desirable with respect to voltmeter and current?
Ans. A low reading voltmeter should be used in connection with a large battery.
Fig. 564.--Diagram showing principle of Wheatstone's bridge. A, B, C, and D, are the four members which constitute the bridge. The current from the battery divides at P, part traversing DC, and part traversing BA. The galvanometer connected to M and N will indicate when the currents are equal in the two branches by giving no deflection. This is then a zero or nil method of testing. The resistances and keys required in testing are shown in fig. 565. In the actual instrument, the members A, B, C, and D are known by the names given in the figure.
Wheatstone Bridge Method.--For accurate measurements of resistance this method is almost universally used. The so-called "Wheatstone" bridge was invented by Christie, and improperly credited to Wheatstone, who simply applied Christie's invention to the measurement of resistances.
Fig. 565.--Diagram showing arms of Wheatstone bridge, resistances and method of connecting galvanometer, battery and unknown resistance.
The bridge consists of a system of conductors as shown in fig. 564. The circuit of a constant battery is made to branch at P into two parts, which re-unite at Q, so that part of the current flows through the point M, the other part through the point N. The four conductors A, B, C, D, are spoken of as the arms of the balance or bridge. It is by the proportion existing between the resistances of these arms that the resistance of one of them can be calculated when the resistances of the other three are known. When the current which starts from the battery arrives at P, the pressure will have fallen to a certain value. The pressure in the upper branch falls again to M, and continues to fall to Q. The pressure of the lower branch falls to N, and again falls till it reaches the value at Q. Now if N be the same proportionate distance along the resistances between P and Q, as M is along the resistances of the upper line between P and Q, the pressure will have fallen at N to the same value as it has fallen to at M; or, in other words, if the ratio of the resistance C to the resistance D be equal to the ratio between the resistance A and the resistance B, then M and N will be at equal pressures. To find out if this condition obtain, a sensitive galvanometer is placed in a branch wire between M and N which will show no deflection when M and N are at equal pressure or when the four resistances of the arms "balance" one another by being in proportion, thus:
If, then, the value of A, B, and C be known, D can be calculated. The proportion (1) is reduced to the following equation before substituting.
For instance, if A and C be, as in fig. 565, 10 ohms and 100 ohms respectively, and B be 15 ohms, D will be (15 × 100) ÷ 10 = 150 ohms.
Fig. 566.--Diagram showing usual arrangement of resistances in arms of Wheatstone's bridge. In practice the bridge is seldom or never made in the lozenge shape of the diagrams, figs. 564 and 565, these being given merely for clearness. The resistance box of fig. 554 is, in itself, a complete "bridge," the appropriate connections being made by screws at various points. The letters in the above diagram correspond with those in figs. 564 and 565, and the three figures should be carefully compared.
As constructed, Wheatstone bridges are provided with some resistance coils in the arms A and C, as well as with a complete set in the arm B. The advantage of this arrangement is that by adjusting A and C, the proportionality between B and D can be determined, and can, in certain cases, be measured to fractions of an ohm. In fig. 565 resistances of 10, 100, and 1,000 ohms are included in the arms A and C.
Fig. 567.--Standard resistance box and Wheatstone bridge. This pattern is a modification of the Anthony form of bridge. All the resistances are wound upon metal spools. The bridge ratio coils are 1, 10, 100, 1,000, 10,000. The rheostat coils are arranged in five rows, of ten coils each. The ordinary decade plan (explained in fig. 570) is followed. The coils may be joined in series in multiple, or in any combination of series and multiple. The coils may thus be checked against each other in many combinations. For instance, all the ten ohm coils taken in parallel may be compared with any one ohm coil. The precision of adjustment is said to be 1/20th of 1% for the coils of the tenth ohm series, and 1/50th of 1% for the coils of the rheostat. The ratio coils are certified to be like each other to within 1/100th of 1%. The box is supplied with battery and galvanometer keys of substantial construction.
Ques. Describe the method of testing with the bridge.
Ans. Fig. 567 illustrates the general arrangement of resistances to be found in an ordinary bridge. The connections are made as shown. In testing, first depress the battery key, then tap the galvanometer key. This should be repeated adjusting the resistances till no deflection is obtained. The resistance then in the arm B × (C ÷ A) will give the value of the unknown resistance.