CHAPTER XXVII
TESTING AND TESTING APPARATUS
The practical electrician frequently has to make tests of various kinds which require the rapid and accurate measurement of voltage, current and resistance. It is therefore essential that he understand the methods employed in testing and the operation of the instruments used.
Most tests are made with a galvanometer, and the devices, such as resistances, switches, etc., which are used in connection with the galvanometer may be obtained put up in a neat and substantial box together with the galvanometer, the combination being called a "testing set." Numerous forms of testing set are illustrated in this chapter.
The construction, use, and operation of the various types of galvanometer have been explained in chapter twenty-six. Ammeters and voltmeters, which are simply special forms of galvanometer, and which are largely used are fully described in the preceding chapter.
Pressure Measurement.--An electromotive force has been defined as that which causes or tends to cause a current; it is analogous to water pressure; potential difference corresponds to difference of level. The _total_ electromotive force of a circuit is independent of resistance or current, and cannot be limited to mean the fall of pressure between any two points, as for instance the terminals of a battery.
If the pressure of a battery be two volts when measured on open circuit by a static voltmeter, there will still be two volts on closed circuit, but there will now be a loss of pressure through the internal resistance of the battery and the voltage across the terminals will be less than the _total_ voltage. The static voltmeter, never closing the circuit, actually measures the total voltage.
Ques. What error is introduced in measuring the pressure of a battery with an ordinary voltmeter?
Ans. Since the measurement is made on _closed circuit_ the reading does not give the total pressure of the battery.
The error is very slight because the resistance of the voltmeter is very high and the current so small that the loss of pressure in the battery can be neglected.
Ques. Define the International volt.
Ans. _It is the electromotive force that, steadily applied to a conductor whose resistance is one International ohm, will produce a current of one International ampere, and which is represented sufficiently well for practical use by 1,000/1,434 of the voltage between the poles of the Clark cell at a temperature of 15° C., when prepared as in fig. 540._
The relation between the units volt, ampere and ohm, are shown graphically in figs. 542 and 543.
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_.
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_.
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:
1. Weight voltameters;
2. Gas voltameters.
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.
Fig. 544 shows a weight voltameter and fig. 545 a gas voltameter.
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_.
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:
volts 1. Amperes = -------; ohms
2. Volts = amperes × ohms;
volts 3. Ohms = ---------. amperes
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:
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.
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 TABLE[A]
| | Inter-| | | | | Date |national| Legal|B. A. |Siemens'| | | Ohm| Ohm|Ohm | 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.
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.
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:
1. Direct deflection method;
2. Method of substitution;
3. Fall of potential method;
4. Differential galvanometer method;
5. Drop method;
6. Voltmeter method;
7. Wheatstone bridge method.
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.
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.
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.
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:
(1) amperes = volts / ohms
solving for the resistance,
(2) ohms = volts / amperes
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)
ohms = 6/2 = 3
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.
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_.
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.
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 resistance known resistance ------------------------------ = ------------------ drop across unknown resistance unknown resistance
from which
unknown known resistance × drop across unknown resistance resistance = --------------------------------------------------------- drop across known resistance
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.
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.
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.
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.
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.
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:
(1) A:C = B:D
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.
D = BC/A
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.
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.
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.
Ques. Why should the battery key be depressed before the galvanometer key?
Ans. To avoid the sudden swing of the galvanometer needle, which occurs on closing circuit in consequence of self-induction.
Ques. How is it known whether too much or too little resistance be unplugged?
Ans. The galvanometer needle will be deflected to one side for too much resistance, and to the opposite side for too little resistance.
Ques. What is the meaning of "Inf.," marked on the bridge?
Ans. It stands for "infinity," because the resistance coil at the point marked infinity is omitted so that adjacent sections of the arm are disconnected when the plug is taken out.
In fact, the air gap interposed by the removal of the plug by no means provides an infinitely great resistance, but is usually called such because it is vastly greater than any of the other resistances of the bridge.
The Decade Plan.--In this method of combining resistance coils, there are 9 or 10 one ohm coils for the units place, 9 or 10 ten ohm coils for the tens place, 9 or 10 one hundred ohm coils for the hundreds place and so on. Each series of coils of the same value is designated a _decade_. The connections are usually made as shown in figs. 570 and 571.
It is apparent from the figure that any value in any one decade can be obtained by inserting between a bar and a block, only one plug; moreover if several decades be in series, any value up to the limit of the set can be read off directly from the position of the plugs without having to add up the unplugged resistance as in the ordinary arrangement.
Ques. What other advantages are gained with the decade arrangement?
Ans. The single plug used with each decade is never out of use, being either in the zero position or set on some value, and is therefore not easily lost by being laid aside. The use of only one plug in a decade makes it easy to ascertain that the plug is making good contact as only one block in a row is plugged at a time, the other blocks are not kept under a strain by having plugs forced tightly between them.
This strain on the blocks, which always exists in those sets in which a resistance is thrown in by removing a plug, tends to separate or loosen them and often to warp the hard rubber upon which they are mounted. Another advantage of the decade plan is that it permits obtaining a succession of values by means of sliding contacts or dial switches, a method which is becoming deservedly more appreciated.
Ques. What is the difference between "plug out" and "plug in" types of resistance box?
Ans. In the plug out type, resistance is put in the circuit by removing plugs, as in fig. 565; in the plug in type, resistance is put in the circuit by inserting plugs as in figs. 570 and 571.
Testing Sets.--For convenience in testing, a combination of the instruments used is put up in a neat and substantial case, and known as a testing set. There are innumerable forms of testing set, a few of which are shown in the accompanying illustrations. The usual combination is a Wheatstone bridge, galvanometer, battery and necessary keys and connections.
Ques. Describe the operation of the Queen Acme testing set figs. 576 and 577, in measuring resistance.
Ans. Connect the terminals of the resistance to be measured to the line posts C and D. Place the battery connections on the two upper tips 0 and 1, thus throwing one end of the battery into circuit, which is sufficient until an approximate balance is obtained. Employ the 100 ohm coil in each bridge arm, and place the commutator plugs in the position PQ, or in the position ST. Then remove plugs from the rheostat until the value of total resistance employed, or nearly as may be guessed is equal to that of the unknown resistance. Now press the battery key Ba, and holding it down momentarily, press the galvanometer key Ga. If the galvanometer needle swing to the right toward the symbol + the resistance employed in the rheostat is too high and must be reduced. If the needle swing to the left toward -, the resistance employed is too low and must be increased. By altering the resistance of the rheostat accordingly, a value will soon be found, which when varied slightly either way, will reverse the deflection of the galvanometer needle. Now remove the battery connection from tip 1, and place it on the tip 4, thus throwing the whole battery into circuit. Then press the keys again as before, first the battery key, then the galvanometer key. This will increase the deflection of the galvanometer needle for the same variation in the rheostat, thus enabling the making of a more accurate adjustment. The measurement thus made will be the best result that can be obtained with bridge arms of equal value, but by selecting more suitable values of the two arms from the following table of bridge ratios a much higher degree of accuracy may be obtained.
Table Showing the Best Values of Bridge Arms for Measuring any Desired Resistance
| | Position of| | Best Values of| Commutator| | | Plugs as| Value of Resistance being measured | | | shown in| | A = | B = | fig. 582| --------------------------------------+-------+-------+------------| Below 1.5 ohms | 1| 1,000| PQ| Between 1.5 and 11 ohms | 1| 100| PQ| " 11 and 78 ohms | 10| 100| PQ| " 78 and 1,100 ohms | 100| 1,000| PQ| " 1,100 and 6,100 ohms | 100| 100| PQ or ST| " 6,100 and 110,000 ohms | 1,000| 100| ST| " 110,000 and 1,110,000 ohms | 1,000| 10| ST| " 1,110,000 and 11,110,000 ohms | 1,000| 1| ST|
Ques. In testing with the Queen Acme set how should the plugs be placed in the commutator?
Ans. Always make the arm A the smaller except when the two arms are of equal value.
Ques. If the resistance being measured is higher than 6,100 ohms, or lower than 1,100 ohms, how should the commutator plugs be placed?
Ans. If higher than 6,100 ohms, they should be placed in the position ST; if lower than 1,100 ohms, in position PQ.
When the plugs are placed in the ST position, the unknown resistance is found by dividing the value of the larger bridge arm by that of the smaller, and multiplying the total employed resistance in the rheostat by the quotient. When the plugs are placed in the PQ position, the employed resistance in the rheostat is divided by the quotient.
Direct Deflection Method with Queen Acme Set.--To measure for instance, insulation resistance by direct deflection connect a known high resistance, say 100,000 ohms between the line post C (fig. 577), and the positive battery post. Remove all plugs from the commutator, and place all plugs in the rheostat, as any employed resistance in the rheostat will be in circuit with the galvanometer and the battery. Place the battery connection so as to throw only one cell into circuit. Now press the keys and obtain a deflection of the galvanometer needle. For example: assume that the needle to be deflected about 8 divisions of the scale. Since this deflection is due to the current from one cell passing through a resistance of 100,000 ohms, then 100,000 × 8 = .8 megohms represents the resistance through which one cell will produce a deflection of one division on the scale. Hence, .8 megohms is the constant of the galvanometer.
Now, replace the known high resistance (100,000 ohms) by the unknown resistance (for instance such as a cable) the value of which is to be determined. Add enough cells to produce as large a deflection of the needle as possible. Assume that 75 cells give a deflection of 1.5 scale division. Then, the galvanometer constant multiplied by the number of cells and the product divided by the deflection will give the insulation resistance of the cable; or
0.8 megohm × 75 cells = 60.0; and
60.0 ÷ 1.5 = 40 megohms
as the resistance of the cable.
Fall of Potential Method with Queen Acme Set.--To compare electromotive forces by this method, place the battery connection (fig. 577), so as to throw into circuit all the cells, taking care not to reverse them by crossing the battery cords. Plug the commutator as shown in fig. 582, and remove 1,000 ohms from bridge arm B. Place all plugs in arm A. From the rheostat unplug 5,000 ohms. Then connect one of the cells being tested, with its positive terminal to the + battery post and its negative terminal to the line post C.
When the keys are pressed, the galvanometer needle will swing either to the right or to the left. If it swing toward +, reduce the resistance in the rheostat; if it swing toward -, add resistance to the rheostat. When a value is found wherein a variation of an ohm either way reverses the deflection, add to this value the resistance unplugged in arm B, and divide the sum by the resistance in arm B. The result gives the ratio between the voltages of the testing set battery and cell being tested respectively. The division is decimal and may be readily accomplished by merely pointing off as many places as there are ciphers in the resistance employed from arm B. This operation repeated with any number of different cells, will give their voltages in terms of the voltage of the testing set battery, and from these ratios their relative values may be readily obtained.
If the testing set battery be replaced by a standard cell, the first measurement gives at once the voltage of the cell tested.
If the voltage of the cell or battery being tested exceed that of the testing set battery, reverse the position of the two batteries, and the subsequent operations, as outlined above, will give the desired results.
How to check a Voltmeter with the Queen Acme Set.--In using a set as in fig. 576, first remove about 10,000 ohms from the rheostat, plug the commutator as shown in fig. 582, remove 100 ohms from the arm B, of the bridge, and connect a standard cell with the positive terminal to the + battery post and the negative terminal to the line post C. Then, connect the circuit to the battery posts of the testing set the positive lead to the + post and the negative lead to the - post. Now, press both keys and note the direction of the deflection of the galvanometer needle. If it move toward +, the rheostat resistance is too high; if toward -, too low.
Change the rheostat resistance accordingly until the balance attained is such that a very slight variation of the rheostat resistance one way or the other will reverse the galvanometer deflection. To find the pressure on the circuit, add 100 to rheostat resistance and point off two places. Multiply this value by the voltage and the product will be the desired voltage.
If the voltage of the standard cell be exactly one volt, the total employed resistance represents the voltage on the circuit.
For instance, in making a measurement on a 110 volt circuit, assume that the employing of 7,840 ohms rheostat resistance produces balance, and that increasing or decreasing this resistance by two ohms, reverses the galvanometer deflection. This indication that the setting 7,840 is uncertain, about 1/40 of 1 per cent. Since the rheostat coils are adjusted to an accuracy of only 1/5 of 1 per cent., that will be about the accuracy of the measurement.
If the pressure of the standard cell be 1.018 volts, then 7,840 + 100 = 7,940. Pointing off two places, gives 79.40, which multiplied by 1.018 gives 80.82 for the voltage on the circuit.
To Measure Internal Resistance of Cell with Queen Acme Set.--First compare its voltage on open circuit with the pressure of the testing set battery. Then, shunt the cell with a known resistance, about 100 ohms, and again measure its terminal voltage. The difference between the two values thus obtained, divided by the value of the shunt resistance, will give the value of the current. To find the internal resistance, multiply the value of the shunt resistance by the ratio between the first and second measured values.
For instance, assume that the open circuit voltage of the cell being tested as compared with the voltage of the testing set battery is .212 of the latter, and that when it is shunted with a resistance of 1,000 ohms, its terminal voltage is .179. Then, the total resistance is to the 1,000 ohms shunt resistance as .212 is to .179 or (.212/.179) × 1,000 = 1,184, from which deducting the 1,000 ohms shunt resistance, gives 184 ohms as the internal resistance of the cell.
Ammeter Test with Queen Acme Set.--Connect a low resistance in series with the ammeter and run leads from it to the testing set, the positive lead to the + battery post and the negative lead to the line post C (fig. 577). Insert a standard cell between the battery posts, with positive terminal to + battery post, and negative terminal to - battery post. Plug commutator as shown in fig. 582. Remove 10,000 ohms from rheostat, and 100 ohms from bridge arm B. Determine a balance in the usual way by changing the value of the resistance in the rheostat. This operation will balance the difference of pressure at the terminals of the shunt resistance against the standard cell, and its value is equal to
(1.40 × 100) / (R + 100) = 140 / (R + 100)
To determine the current flowing, divide the value of the difference of pressure thus obtained by the value of the shunt resistance.
Loop Test.--This is a method of locating a fault in a telegraph or telephone circuit when there is a good wire running parallel with the defective one. In the process, the good and bad wires are joined at their distant ends and one terminal of the battery is connected to a Wheatstone bridge, while the other terminal is grounded. There are different ways of making loop tests as by:
1. The Murray loop;
2. The Varley loop;
3. Special loop.
The Murray Loop.--In this test only one of the two regular bridge arms is used, the other being replaced by the rheostat giving an arm of large adjustment.
The connections are shown in fig. 595. In making the test, close key and note the deflection of the needle due to pressure of chemical action at fault, if any. This is called the _false zero_.
Now apply the positive or negative pole of the battery by depressing the battery key, and balance to the false zero previously obtained by varying the resistance in arms A or B. Then by Wheatstone bridge formula: RX=AY, and L=X+Y; Y=L-X, whence
X = A/(R+A)
Y = L(R/(B+A))
Ques. How may the distance from 2 to the fault be determined in knots or miles.
Ans. Divide Y by resistance per knot or mile.
The Varley Loop.--This is a method of locating a cross or ground in a telephone or telegraph line or other cable by using a Wheatstone bridge in a loop formed of a good wire and the faulty wire joined at their distance ends. One terminal of the battery is grounded and the other connected to a point on the bridge at the junction of the ratio arms. The rheostat arm then includes the resistance of the rheostat plus the resistance of the fault, while the unknown arm includes the resistance of the good wire plus the resistance of the bad wire beyond the fault. When the bridge is balanced, the unknown resistances may be readily determined by a simple equation.
In making the Varley loop test, the resistance of looped cable or conductors is measured, and then connected as in fig. 598. Close the battery key and adjust R for balance.
When earth current is present, the best results are obtained when the fault is cleared by the negative pole, and just before it begins to polarize. If X be the resistance from 2 to the fault, then X = (L - R) / 2
also, X divided by the resistance of the cable or conductor per knot or mile gives the distance of fault in knot or miles.
When the resistance of the good wire used to form a loop with the defective wire, together with that portion of the defective wire from the joint to the fault is less than the resistance of the defective wire from the testing station to the fault, the resistance R must be inserted between point 1 and the good conductor, the defective wire being connected directly to point. The formula in this case is X = (L + R) / 2
Special Loop.--This method may be used to advantage where the length of the cable or faulty wire only is known and where there are two other wires which may be used to complete the loop. It is not necessary that the resistance of the faulty wire and the length and resistance of the other wires be known. Figs. 601 to 604 show the connections and method of testing.
EXAMPLE.--All the wires in a cable 10,852 ft. long were found to be grounded so that none of them could be used as good wires. Two wires were selected out of another cable going to the same place by a different route and securely joined to one of the grounded wires at the distant end. This grounded wire and one of the good ones were connected as shown in figs. 601 and 602 and the reading A was found to be 307. Connections were then made as shown in figs. 603 and 604 and A was found to be 610. What is the value of d?
According to formula
d = AL/A = (307 × 10,853)/610 = 5,461 ft.
The Potentiometer.--For the rapid and accurate measurement of voltage, current, and resistance, the potentiometer can be recommended. Those in charge of electric light and power companies, and also those who purchase large amounts of electrical energy are realizing, more and more, the necessity of having satisfactory primary standards with which to check their volt-, ampere-, and watt-meters.
When it is realized that an error of one per cent. in a commercial instrument means an error of one dollar one way or the other in every one hundred dollars charged, the need of such standardization apparatus becomes at once apparent.
The potentiometer, it should be noted, relies for its accuracy, only upon the constancy and accuracy of resistances and upon standard cells.
With the materials now available, and the skill which has been acquired in their manufacture, both the resistances and the standard cells are obtainable which are remarkably constant, and both can be readily checked for accuracy.
Location of Opens.--These measurements are based on the fact that the capacity of wires in a cable is ordinarily a measurable quantity, which, in wire of uniform diameter, is proportionate to length. In making these tests, a fault finder is used together with a buzzer, dry cells to operate it, small induction coil, and telephone receiver. These instruments are to be found in any telephone exchange. It is best to locate the buzzer at some distance from the fault finder in order that it cannot be heard by the operator.
Before attempting locations for opens it is well to make the following measurements:
1. The insulation of the broken wire and the insulation of the good wire with which it is to be compared.
This may be done as shown in fig. 606. It is best that the insulation resistance be fairly good, but experiments indicate that good results can be obtained by the methods which follow, even when the insulation is as low as 100,000 ohms, and fair results when as low as 50,000 to 100,000 ohms.
2. The resistance between the two sections of the broken wire should be measured.
This may be done by joining the broken wire and a good wire at the distant end of the cable and measuring the resistance of the loop. To ensure close locations, this resistance should be over 100,000 ohms. Fair locations can be made when the resistance is much lower and it is worth while to attempt it even if the resistance be as low as 10,000 ohms. The difficulty of determining the balance point increases as the resistance decreases.
Ques. Describe the method of locating an open with a fault finder.
Ans. (_Case I_) The broken wire will be one of a pair. Select another pair in the cable that will have the same capacity per mile and join together the mate of the broken wire and one wire of the other pair. Make the connections as shown in fig. 607, then depress the battery key and move the contact to the point of minimum sound in the telephone. The distance to the break is equal to LA ÷ (1,000 - A), where L is the length of the good wire.
EXAMPLE: A cable 1.45 miles long contained a broken wire. It was found that the insulation resistance of the end of this wire was over 10 megohms, as was that of the good pair selected to test against it. The resistance between the two pieces of the good wire was also over 10 megohms. Connections were made as in fig. 607, and it was found that the balance point was 476. Accordingly from the table
A / (1,000 - A) = 0.9084
and
d = 1.45 × .9084 = 1.317 + miles.
Location of Opens.--(_Case II_) Open wire in telegraph or other cables in which the wires are not grouped in pairs. The connections are made as in fig. 608, and the measurement and calculation exactly as in the preceding case.
The accuracy of the location of both of the above methods depends on the good and broken pair, or the good and broken wires having equal and uniform capacity per unit length. It is not always possible to select wires that are alike in this respect. In such cases, as for instance, where there is no good wire in the cable containing the broken wire, and a good wire has to be selected from another cable, the method of _Case III_ may be used.
Location of Opens.--_Case III_, in which the broken wire and good wire are not in the same cable. Connect the good wire and broken wire in the same way as shown in fig. 607, and set the pointer for a balance. Call the reading A. Then connect the good wire and the broken wire at the distant end and set the pointer for a new balance. Call this A'. The connections for this reading are shown in fig. 609. The distance to the break will be
d = (A A' L) / (1,000(A - A') + A A')
where L is the total length of the broken wire.
EXAMPLE: A pair of wires containing one broken wire was connected with a good pair in a different cable as shown in fig. 607. The reading A was found to be 180. The good and bad wires were then joined at the distant end as in fig. 609, and the reading A was found to be 88. The total length of the bad wire MN was 1.44 miles. Required, the distance to the break. Substituting the values in the formula:
d = 180 × 88 × 1.44 / 1,000(180 - 88) + 180 × 88 = .211 + mile.
To Pick Out Faulty Wires in a Cable.--Short circuit the coils E and R with switches U and V. Set the pointer at 1,000. Connect the post Gr. to ground or the cable sheath and apply the wires one after another to the binding post 2. The galvanometer will deflect for a faulty wire.
Ques. What is a potentiometer?
Ans. An arrangement of carefully standardized resistances for measuring voltages in comparison with a standard cell. It is used for accurate measurement of voltages, currents, and resistances.
In place of a series of standardized resistances, a slide wire may be used as in fig. 614.
Ques. Describe one form of potentiometer.
Ans. As shown in fig. 614, it consists of a fine German silver wire about 3 feet long stretched between the binding posts A, B, which are attached to a wooden base carrying a scale divided into 1,000 equal parts. There are three circuits, the terminal A being included in each, one including the battery, and the other two the galvanometer. A three point switch connects the galvanometer in series with the standard cell SC, or the cell to be tested C, the circuits being completed by leads terminating in the sliding contacts M and S.
Ques. Describe the method of measuring the voltage of a cell with a potentiometer.
Ans. Fig. 614 shows a method of comparing a pressure with that of a standard cell and is applicable whether the pressure of the cell to be tested be greater or less than that of the standard cell. In making the test the switch F is first closed, then the other switch is moved to D, and M adjusted till galvanometer shows no deflection; similarly, the switch is moved to G, and S adjusted till galvanometer shows no deflection. Then, C:SC = AS:AM. from which C = SC × AS ÷ AM.
EXAMPLE.--Let 1.016 volts be the known voltage of the standard cell SC, and the scale reading of AS be 657, and of AM, 225 as in the figure, then
C = (1.016 × 657) / 225 = 2.966 volts
The arrangement may, however, be made direct reading, that is, the slide wire may have a scale of volts instead of lengths or resistances, as follows: Suppose the standard cell to have a pressure of 1.434 volts, the sliding contact M is placed at the reading 1.434, and the adjustable resistance varied till the galvanometer shows no current. This means that the pressure between A and M is 1.434, and consequently the pressures all along the slide can be read off the scale _in volts_. Hence, when S has been adjusted to balance, the pressure of C is read off the scale in volts.
How to Use a Potentiometer.--All connections must be made as indicated by the stamping on the instrument. Particular attention must be given to the polarity of the standard cell, of the battery, and of the voltage, the corresponding + and - signs being marked. If used with a wall galvanometer having a telescope and scale, it will be found convenient to place the potentiometer so that the telescope is directly over the glass index of the extended wire, thus permitting the observer to read the galvanometer deflections and potentiometer settings without changing his position.
Potentiometer Current.--A medium sized storage cell will be found desirable, producing a steady current. Errors in measurements are frequently made by using an unsteady current.
Setting for Standard Cell.--Set the standard cell to correspond with the certified pressure of the standard cell as given in its certificate. In using the potentiometer shown in fig. 610, place the plug in hole 1, and see that it is always in this position when checking against the standard cell. Place the double throw switch at STD. CELL.
Adjust the regulating rheostat until the galvanometer shows no deflection. In making the first adjustment use the key marked R_{1}; when a balance is almost attained, use key R_{2}, and for the final adjustment use key marked R_{0}. This cuts out the resistance in series with the galvanometer and gives the maximum sensibility.
Measurement of Unknown Pressure.--The potentiometer (fig. 610), as ordinarily used, gives direct readings for voltages up to and including 1.6 volts. For pressures higher than 1.6 volts, a volt box or multiplier should be used. After obtaining the standard cell balance, as previously described, place the double throw switch in the position marked E.M.F. The balance for the unknown E.M.F. is obtained by manipulating the tenths switch and rotating the contact on the extended potentiometer wire. The final position of the two contacts in conjunction with the position of the plug at the left of the instrument indicates the voltage under test.
As directed above, use key R_{1} for rough adjustment, R_{2} for intermediate adjustment, and key R_{0} for final adjustment.
Plug at 1 gives readings for voltage directly from settings of tenths switch and extended wire contact.
Plug at .1 shunts the potentiometer circuit so that the voltage measured is .1 of the reading taken directly from the scale. Hence, the readings taken from the setting of the tenths switch and the slide wire contact must be divided by 10.
To Balance Galvanometer for Unknown Voltage.--Place plug in hole 1 (fig. 610) for voltages up to 1.6, and in hole .1 for voltages up to .16. Rotate the tenths switch until a condition of balance is obtained exactly or approximately. To secure an exact balance, rotate the contact on the extended wire. The unknown voltage can now be read directly from the position of the tenths switch and the extended wire contact if plug be at 1, or by dividing by 10 if plug be at .1.
EXAMPLE.--A balance was obtained with the tenths switch at 1.3, the extended wire contact at 176 and the plug at 1. The voltage under test, therefore, is 1.3176. If the plug at .1 had been used, the same reading would have indicated .13176.
To ascertain if the current in the potentiometer circuit has altered during a measurement, it is only necessary to plug in at 1, place the double throw switch on STD. CELL and close the galvanometer key. No deflection indicates that the current has not changed. If the galvanometer deflect, the regulating rheostat must again be adjusted until the galvanometer shows no deflection.
To Measure Voltages from 1.6 to 16.--Pressures up to 16 volts may be measured by using a greater voltage across the BA posts (fig. 615). For this purpose a battery of about 20 volts should be used. Insert the large plug at .1 and throw the switch to STD. CELL, then balance the galvanometer by means of the regulating rheostat. When the rheostat has been set to secure a balance, insert the large plug at 1, set the switch on E.M.F. and read the voltage in the usual manner. Multiply the reading by 10.
Care of Potentiometer.--The slide wire, although protected to a great extent by the hood, in time accumulates dust and dirt with a thin film of oxide. This will tend to increase the resistance in this part of the circuit owing to poor contact. This wire should, therefore, be cleaned occasionally.
To do this, unscrew the stop against which the hood strikes when turned to read zero; then remove the hood and rub the entire slide wire vigorously with a soft cloth dipped in vaseline. _Do not use emery or sand paper as this will destroy the uniformity of the slide wire._ Clean also the steel contact which rubs on the wire, as this becomes glazed after much use. When the potentiometer is not in use, the hood should be screwed all the way down, and the lid put in place to exclude dust.
If it be used in a chemical factory, laboratory, or any place where acid fumes are prevalent, this latter precaution is important, because the fumes may attack the slide wire.
It is also well to keep the contact surfaces of the switch studs clean and bright by wiping them occasionally with a soft cloth dipped in vaseline.
Location of Faults where the Loop is Composed of Cables of Different Cross Sections.--Faults in loops of this character may be located with the same degree of accuracy as those in loops of a uniform cross section, provided the length and cross section of each length of cable are known. An example will illustrate the method:
In the diagram, fig. 617, assume the length of the cable AE to be 550 yards of 25,000 cir. mil., EF, 500 yards of 40,000 cir. mil., and FC, 1,050 yards of 30,000 cir. mil. These lengths must be reduced by calculation to equivalent lengths of one size, and for this purpose it is best to select the largest size. The results of this calculation are as follows:
550 yds. of 25,000 cir. mil. = 880 yds. of 40,000 cir. mil.
500 " " 40,000 " " = 500 " " 40,000 " "
1,050 " " 30,000 " " = 1,400 " " 40,000 " "
This makes the total resistance of the loop equivalent to 2,780 yards of 40,000 cir. mil. If the contact show a balance for a reading of 372.5, this indicates that the fault is at a distance of 372.5/1,000 of 2,780 = 1,035.5 equivalent yards. Of this, 880 are in the stretch A E. Consequently the fault is:
1,035.5 - 880 = 155.5 yards from E.