Wheatstone bridge pdf download

This ensures greater evenness in the scale divi- sions throughout the range. Queen Instruments. The Queen Wirt voltmet- ers and ammeters can be used on circuits of either direct or alternating current.

They are electromagnetic, the principle being that in which an iron armature tends to move into the strongest part of a magnetic field. A tube of soft iron lies parallel with the axis of a coil of wire through which current passes.

Being mounted away from the true centre of the coil it moves towards that centre where the field is strongest. The electromagnetic principle does not allow of absolutely even scale divisions, but those in the middle of the scale are fairly uniform. Although for use on both circuits, the scales must be graduated for either one or the other.

For alternating current the divisions are most uniform. In the Queen portable form, an upper scale can be graduated for direct current and a lower scale for alternating current. Electro-Static Instruments. A type of instru- ment much used on circuits of extremely high e.

A movable plate of aluminum is suspended be- tween fixed plates of similar metal. The jnovable plate carries an index and is controlled either by gravity or springs, generally the former. The instrument in fact is a form of condenser. When a source of high e. As the attractive force depends upon the square of the e. Such instruments consume no current. The chief advantage of the electrostatic volt- meter is that it can be directly connected to a circuit of extremely high potential.

In the case of alternating current circuits with voltages up in the tens of thousands it becomes necessary with other types of voltmeters to reduce the voltage before applying it to the instrument.

This is done by means of a " potential transfor- mer," which is a small transformer especially con- structed to reduce the high voltage to a lower one suitable to the instrument in use. The voltmeter is thus not directly connected to the circuit but is inductively connected. Reading Instruments Parallax. One source of error in reading voltmeters and ammeters lies in. If the eye is not directly in front of the index a reading to one side or the other is liable to be.

Where an index stands as much as a quarter of an inch away from the scale, a large error in read- ing might result. This error is called parallax and is prevented in portable instruments for accurate testing by the following device: The index is made thin and flat, lying edgewise towards the eye.

A strip of mirror is placed be-. The reading is made when by looking down on index and mirror, the index hides its own reflection. Some switchboard instruments are made for edgewise reading, that is, the scale is at right angles to the base, Fig. The scale is curved and the index is bent so as to follow it.

In this type, the error of parallax is likely to be greater than with the ordinary type. Care of Instruments. Electrical measuring in- struments must be handled with at least ordinary care. Although made as air tight as possible, damp- ness and excessive heat should not be permitted to attack them. Violent swinging of a pointer through excessive current is liable to do more than bend the pointer.

Even if it does not permanently injure the in- strument it does it no good. This is more likely to happen in using a double scale instrument, or by reversing the connections.

When taking measurements the instrument should not be set down on a generator or its bed plate. Anda direct current voltmeter should not be tried on an alternating current circuit. They may be dissipated by touching the finger to the middle of the cover, but are best omitted.

In the case of two or more compound wound generators being connected together to run in multiple, a so-called equalizer is used. This is a bus-bar or cable connecting together a point on each dynamo between the series field winding and its brush connection. Otherwise current flowing in the equalizer bus would not be indicated. Ammeters for storage battery circuits are made with a central zero as the deflections of charge or discharge are in different directions.

This is of course only true of that class of in- strument in which the direction of deflection de- pends upon the direction of current flow, that is, polarized instruments. If a polarized instrument without a central zero be used for storage battery work, a reversing switch becomes necessary between the shunt and the ammeter.

This is but a makeshift and is by no means to be recommended. Any instrument built to be used only in a ver- tical position must not be used when laid hori- zontally and vice versa. Readings may be made, but they are liable to be inaccurate, owing to fric- tion or gravity. The Wheatstone Bridge. AB are two adjustable resistances. These form the proportional arms of the bridge. R is an adjustable resistance or rheostat, G a galvanometer, B the battery and KK keys closing the battery or galvanometer circuits respectively.

If the battery key be closed, current will divide between A and B and flow through R and x back to battery B. Even if the galvanometer key be closed, no current will flow into G. X be greater in resistance than R, part of the If current through B will travel through G and thence through R in accordance with the law of shunts.

The galvanometer needle is thus deflected. But by adjusting R to agree with x the two paths R and X being equal no current flows through G. A and through x by way of the galvanometer, and the needle is deflected, but in the opposite direc- tion to the former case. The Wheatstone bridge is based on the fact that no current flows between points of equal potential. Consider the two sides of the bridge A R and B X as two wires of equal resistance per unit length in multiple between the battery terminals.

The drop of e. If the galvanometer be connected to a point in each wire equally distant from either end, say the middle of each, no current will flow in the gal- vanometer. The effect is the same as if both terminals of the galvanometer were placed on the same spot in a single wire carrying current.

The galvanometer in the latter case will be in shunt with the piece of wire included between its contacts. As the points are at a different poten- tial, the galvanometer will show the potential in. The same applies to the double wires.

When the bridge galvanometer is connected as in the figurebut assuming A R B and x as equal, the galvanometer is connected between two points of the same potential. If X be increased in resistance over that of R it would be the same as increasing the length of the wire X.

In the latter case the galvanometer contact could be shifted along the x wire until it again stood at the middle, when the galvanometer would remain undeflected. In the bridge the resistance R would be ad- justed vintil it was equal to x, A being in the same. Of course B could be changed but R is the adjustable resistance. If yl is to 5 as -R is to x, then x will be the same as B multiplied by R and divided by A. This is just simple proportion in arithmetic as the following example shows. In simple proportion, to get the fourth term or answer, the second and third are multiplied together and divided by the first.

The Post-Office Bridge. Thre connection for re- sistance tests of the form of bridge known as the English Post-Office Bridge is in Fig. A tripod form of Thompson galvanometer is. And any form of galvanometer would be connected up in the same way. The shunt is not shown, it would be connected across the galvanometer terminals. The resist- ance to be measured is connected at x. The key on the left of the bridge is the battery key and should always be depressed first.

The right hand key is the galvanometer key and is to be only tapped until a close balance is obtained. Otherwise were the bridge rheostat not adjusted to the measurement being made, the deflection would be violent.

Much damage to a galvanometer is done by neglecting this rule. In a reflecting galvanometer where the mirror is suspended by a silk fibre, the latter may be broken. Replacing it is a work requiring expert knowledge and vast patience. Testing with the Bridge. For illustration of the use of the bridge the one shown in the last figure will be selected. Suppose it is desired to measure the resistance of a coil of wire.

The two ends are bared of in- sulation, scraped clean and inserted in the binding posts asshown at x. The other connections of the figure are already made as described. For the first test, however, it will be well to use only one cell of battery. All plugs are in the holes in the rows of resist- ance coil connections. Remove from both A and B the plugs from the 10 ohm coils. Remove a 10 ohm coil plug from the rheostat part. Depress the battery key and tap the galvano- meter key.

The deflection is noted both as to amount and direction. Suppose it is 60 to the left. Remove another plug say from ohm coil and tap key again. Deflection in same direction only Remove 20 ohm plug, deflection 5 to right. This indicates that too much resistance has been unplugged. Replace 20 ohm plug and remove 10 ohm plug, deflection is now 1 but to left.

Indicates that still too little resistance is out. Remove 1 ohm plug; no deflection perceptible. Then read resistance unplugged. When a resistance equal to that being measured is unplugged, no deflection takes place. It may be stated here that in these examples no actual statement of deflection due to resistance is meant.

The values given are only illustrative. It will be seen that the deflection is to one side when too much resistance is unplugged and to the other side when too little resistance is unplugged. Of course reversing the battery connections will reverse the value of these signs. In the bridge of the instruments being described in this section, there are three coils in each arm, reading from left to right in A and in B.

At present only equal ones are used in each arm. For measuring low resistances the 10 ohm coils in each arm are unplugged. For high resistances, ohm coils in each arm are used. For very high resistances ohms in each arm. The rule is to use the nearest bridge coils to the resistance being measured. As the total resistance of the rheostat is in this case only 11, ohms, evident that by the it is. Proportional Arms of Bridge. This is where the proportional arms of the bridge come in to use.

By unplugging a higher coil in the B side, the value of each coil in the rheostat is multiplied by the number of times the unplugged coil in A divides into that of B. As a memory aid A divides, B multiplies. This gives new values to the rheostat coils and vastly extends the range of measurement.

For example, let A be 10 and B , then B is. The 1 ohm coil then becomes equivalent to a 10 ohm coil and the ohm a 10, ohm coil, and so on. And let A be 10 and B and the rheostat is multiplied by , the ohm coil is thus equal 1. This last setting of the arms will give a value to the rheostat of 11, X or 1,, ohms. If then the bridge arms were so set and a balance obtained at ohms, the actual resistance would be x or 16, In some bridges there are 1 ohm coils, then the.

The dividing method or higher coil in A is on the same plan. Unplug 10 ohms in B and in A, then the readings will be divided by 10, which is the number of times 10 goes into And the 1 ohm coil becomes ohm, the 10 ohm coil now being. Take the first example, the coil of wire. Set the bridge arms A , B 10, making a division by necessary of the rheostat readings. As the first test showed ohms, unplug one hundred. As the bridge now stands this only equals ohms.

It may be necessary to increase the bat- tery. Having depressed the battery key, depress the galvanometer key and there will probably be a deflection one way or the other. Suppose it is to the - side. Let it take 18 ohms more to get a balance or zero on the scale. Then the rheostat will read 12, which di- vided by gives It is a good plan to make a number of tests of coils of known resistance, or to check up tests by trying various combinations of tke arms.

It must be remembered that as the resistance of copper increases from heat, readings will vary from time to time owing to the current flowing in the wire being tested. The relation between heat and resistance will be found elsewhere in these pages.

In testing coils, electro magnets, etc. Where leads are necessary from the bridge to the apparatus being tested, the leads also should be tested as their added resistance would give a false value to the test.

A stating of the foregoing rules as formulas will be as follows: Let R be the resistance unplugged in rheostat, A that in arm A of bridge, B that in arm B of bridge, x the unknown resistance. A form of portable Wheatstone Bridge is shown in Fig. It is furnished with a small battery in the case, and a set of working shunts. The galvanometer is of the D'Arsonval type with a sensibility of one scale division for one volt through over two megohms.

It is not disturbed by the proximity of other electrical machinery or magnetic fields. Full directions are furnished with each instru- ment. The general rules of its use are those for all forms of Wheatstone Bridges. In testing a resistance with this instrument it is connected to binding posts C D, Fig.

The flexible battery cords are connected by their cup connectors to two adjacent studs on the battery. This cuts in one cell; if more are desired the cups are connected to include them in circuit. The commutator plugs connect A x and B R as shown. Plugs G a and B a are inserted. Plug all holes in the bridge arms but those corre- sponding to ohms in each arm. Then unplug rheostat until enough resistance is. When no idea is had of the latter, the galvanometer key must be tapped carefully that no undue deflection injures gal- vanometer.

Depress battery key and tap galvanometer key. The latter runs from 1 ohm to a total of 21, ohms. The working range of this set is from. And if a more sensitive gal- vanometer be connected where the shunt is, read- ings to a maximum of 21 megohms is claimed for this set.

But for such high resistance work as the latter, the direct deflection method will be found prefer- able. The Queen Portable Testing Set. The Queen Acme portable testing set, Fig. There are three rows of brass blocks and plugs controlling resistance coils.

The middle row is the Bridge, the top and bot- tom rows, the rheostat. In the centre of the Bridge is a split block com- mutator R X which can be connected to the Bridge arms by plugs. If the plugs are inserted in this commutator in the direction of arrow L as shown, the resistance in the rheostat is divided by the quotient obtained in dividing the higher Bridge arm by the lower. If plugs are in direction of arrow H, multiply rheostat by quotient.

The range of the Bridge arms is 1 to ohms, and the rheostat 11, ohms. This gives a range of testing from. For re- sistances above one megohro, however, more bat- tery is required than will be found in the case.

For this Bridge, the formula for the commutator setting in direction of arrow L is. The general directions for this set are similar to the regular Wheatstone Bridge tests. It is very simple and easily handled. Other adoptions of the set will be found in later pages of this book. Table III. It is used in conjunc- tion with the directions regarding the commutator before given. Showing setting of Bridge arms to measure re- sistances as in first column. Ohms Ohms. A B Below 1.

Whitney Testing Set. This portable set, Fig. One plug only is used in each row of the rheostat inserting the plug cuts in a resistance equal to the number marked on the block.

The battery and galvanometer keys can be con- trolled by one button, the battery contacts being made first. Or they can be depressed separately, as desired. The inside connections are shown in Fig. To Use Bridge. Connect the terminals of the unknown resistance to the lower right hand bind- ing posts.

Assuming that nothing is known of the magni- tude of the resistance to be measured, insert the " plug in the bridge arm lettered " multiplied by in the gap numbered " " and the plug in the bridge arm " divide by " in the gap numbered " This act has inserted ohms in the rheostat arm of the bridge. Depress the combination key momentarily. If the galvanometer needle deflects towards " - " the rheostat resistance is too small and more should be added by moviig the plugs along.

Proceed in this manner until some combination of coil values is found where the galvanometer. The value of the unknown resistance is then indicatedby the position of the rheostat plugs.

If the resistance is lower than 1 ohm insert the plug in the left hand ratio arm into " 10 " and the right hand ratio arm plug into " " or " For resistances higher than 11, ohms the plug in the lefthand bridge arm must be inserted in a higher number than the plug in the right hand bridge arm. When using the set for the Varley loop as a " Wheatstone bridge see that the plug in the " loop bar is marked "V.

The upper right hand binding posts are for extra battery. If an external galvanometer is to be used, it is. The plug is shifted from the right hand hole in block marked galv. This cuts out the galvanometer in the set and cuts in the external galvanometer. The Slide Wire Bridge. A simple form of Wheat- stone bridge is in Fig. A piece of resistance wire about No. D Their distance apart is a little over one metre. Under this wire lies a scale graduated into equal divisions with a zero at each end.

Brass or copper strips of too small a resistance to be considered lie on the base connecting the binding posts as shown. The resistance to be measured is connected at x. A battery and galvanometer being connected as shown, the slider C is moved along the wire DE until the galvanometer needle stands at zero.

When the balance is obtained, the resistance of X willequal the result obtained by multiplying A by the length of wire between C E and dividing it by the length between D E. The length of the wire can be read either in millimetres or divisions of one thousand.

B the length between C E. The Steams Bridge. An ingenious application of the Wheatstone bridge to the measurement of the resistance of bare wire in continuous lengths isfound in the Stearns bridge.

One each of the x terminals of a bridge is con- nected to a contact device consisting of a metal roller and a form of knife edge. The bare wire is wound from one drum on to a second drum passing in its passage through both of the contact devices. The bridge is adjusted to zero by making the rheostat equal the resistance of a length of wire between the contacts. The distance between these contacts being un- changeable, the resistance of the wire included between them should also remain unchanged.

The Sage Ohmmeter. The Sage ohmmeter, Fig. The adjustable rheostat takes the form of a fine wire, under which are marked resistances in vari- ous colors. A stylus 5connected to the telephone T as is. PlugP cuts in various resistance coils in the Bridge arm, the plug holes being colored to correspond with the markings on the scale.

In operation the resistance to be measured is connected to posts A and D. The telephone is held to the ear and the battery key on the tele- phone is closed. The stylus is tapped at various points on the rheostat wire until no sound is heard. The numbers are to be read in that color. Spending to the plug socket in use. If the plug isin a red hole, read the red figures, and so on. The plug must always be in one of the sockets when testing. The Evershed Testing Set. This simple testing outfit, Fig.

To test an insulation or other resist- ance, all that isis to connect the resist- required ance to the binding posts, turn the generator handle and read the resistance off the dial. No calculations whatever are necessary.

The connections of the Evershed set are given in Fig. Current from the generator D flows to the ohm- meter f- where it divides.

The other path of the current is through the current coil C and the fault x. If X has no appreciable resistance the current in. C will be dependent only on the resistance of C and the e. In this case the current coil will deflect the necdh to zero, which is where the influence of each coil is equal. The resistance of x is in series with the current. And coil P turns the needle in proportion as its influence becomes strengthened by reason of the weakening of C.

Increase of voltage from the generator does not both coils. The different instruments range from ohms to 5 megohms in one instrument and 25, ohms to 50 megohms in another. Sets for intermediate readings can also be had. The generators furnished range from volts to volts in output.

The cur- rent flow in all parts of a circuit is equal, but the e. When the battery current flows through A E, the ammeter placed Sit G F shows the same ov reading, the current at G, F, or in fact in any part of the circuit is the same.

If the wire A E is of uniform resistance, the e. If V be connected as at first to A and the con- nection at E be drawn along the wire towards A, the e. If the voltmeter be connected across any two points and a greater current flow be permitted by means of an adjustable resistance R, the e. As long as the resistance oi A E remains un- changed, a greater current flow requires a greater e. Applications of Ohms Law. For example, let AE measure 2 ohms and V indicate 4 volts, then the current will be 4.

Of 2 amperes. If any two readings be known, the third can be computed by Ohms law. From the e. And from the current and the resistance find the e. The applications of Ohms law and the fall of potential will be found in the potentiometer, the shunt ammeter and in various tests to be described later.

Testing Resistance. Let an unknown resistance be placed in series with a battery of constant e. Note the deflection and re- place the unknown resistance by an adjustable re- sistance. Adjust the latter until the second de- flection is equal to the first and the two resistances are equal. If the adjustable resistancebe of known value thismethod can be pursued, but a more practical method is to first ascertain the constant of the galvanometer.

The " Direct Deflection " Method. This is the simplest method of testing resistances or insula- tions and is capable of extended application. It is based upon the fact that the greater the current flow through the galvanometer the wider the angle of deflection. A known resistance R, Fig. After noting the deflection, the key is depressed and the unknown resistance x thrown in circuit. The second deflection is then noted and compared with the first. For example, let R equal one hundred ohms and the deflection through it be ten degrees.

The second deflection through x is twenty degrees. As a formula, let x equal the unknown resistance, R the known resistance, D the deflec- tion through R and d the deflection through x. In case the galvanometer resistance is to be allowed for it is to be added to R but deducted from X. Calling it r, the formula stands. Galvanometer Figure of Merit or Constant. It is customary in many uses of the galvanometer to determine the figure of merit or constant of the galvanometer.

This is the resistance through which the gal- vanometer will give a deflection of one scale de- gree for one volt of e. If , ohms could be inserted in series with the galvanometer and one volt e. And if 50, ohms with one and one-half volts gave a deflection of three degrees, the constant would be as lollows: The e.

Re- ducing it by one-third gives two degrees of deflec- tion. And it is evident that if two degrees are obtained through a certain resistance, one degree would be obtained through twice the resistance. One degree of deflection only requires one-half the current to produce it that two degrees' does, therefore the constant for the galvanometer is 50,x2 or , ohms.

To make a formula out of this let D be the deflection through the resistance, R be the resistance-, V the e. The terms constant, figure of merit and sensi- bility areused ta mean the same. Sensibility or constant are the most generally adopted, however. With Shunts.

If a shunt is used in obtaining the constant the deflection and resistance must be multiplied by the value of the shunt which will be known as n, as before. In the above example let the shunt be with a multiplying power of In some cases the full battery perhaps cells is used to get a constant by shunting the galvano- meter.

The constant is then not for one cell but for the whole battery. Its value will be the product of the deflection, the known resistance and the shunt. And it is evident that the constant for one cell.

Second Example. In testing an unknown resistance with the same shunt and battery the deflection is Then the constant is X.

Summary of Rule. When using the same shunt battery and galvanometer the value of an unknown resistance will be determined by dividing the con- stantby the deflection obtained through this un- known resistance.

If a different shunt 5 is used the formula will be. Deflection Constant. It is often convenient to use the deflection obtained through a known re- sistance as the constant. The degrees of deflection obtained in a test will then be calculated in terms of the resistance used when getting the constant.

For example, let the deflection through one megohm be 85 degrees. In testing an unknown resistance under the same conditions of battery, shunt, etc. Direct Deflection with Queen Set. The Queen Acme set, T may be used for tests of this , nature; a special set is, however, constructed hav- ing a resistance in series with the galvanometer. The latter can also be shunted by manipulating the Bridge. Remove all plugs from the commutator between the Bridge arms and plug in all coils.

Connect in one battery by means of the flexible cords. The slab, galvanometer and battery will thus be in series when B a and G a are depressed. If any plugs have been left out in the rheostat, the resistance of the coils they control will also be in- cluded in the circuit. When B a and G a are depressed a deflection of the galvanometer will ensue.

If this deflection is. Ifmore than 1 degree, remove plugs from rheo- s1:atand add resistance thereby interpolated tc resistance of slab. The constant will be the figure so obtained. And if less than one degree, a lower resistance than , ohms must be used, but it is not likely that this will be the case. The constant having been obtained, detach slab and connect resistance or insulation to be meas- ured in its place. If the deflection is too small add more cells.

A larger battery can be added by connecting it to the battery posts, detaching the flexible cords and cups from the battery in the case. To determine the resistance now being measured, divide the constant by the deflections obtained and multiply the result by the number of cells used. The deflection has been increased 10 times, which would show that the resistance was only one- tenth of the constant or 10, ohms. But as five times the e. Another method is to use the deflection obtained through , ohms as the constant.

The answer willbe in terms of , ohms. For example, let 8 be the deflection constant through , ohms with one cell, and 4 be that through the unknown resistance with five cells.

In such tests the resistance of the galvanometer may be neglected. In this circuit the resistance to be measured is unknown, R1, R2 and R3 are resistors of a known resistance and, furthermore, the resistance of R3 is adjustable. A sensitive galvanometer "G" is connected between their junctions as shown.

The circuit is provided with two switches S1 and S2. When S1 and S2 are closed and no current flows through the galvanometer, the bridge is called Balanced.

Making one of the resistors, say R3, a decay box with known resistance values and adjust until the galvanometer reads zero. It is possible only when the potential difference between the terminals of galvanometer is zero. If we identify the currents in the four branches, Fig 3.

Therefore the nodes B and D must have the same potential. The potential difference between the nodes A and B is The potential difference between the nodes B and C is With some algebraic manipulations we get the balanced condition If the bridge is unbalanced R3 is varied until there is no current through the galvanometer, which then reads zero. Detecting zero current with a galvanometer can be done to extremely high accuracy. Therefore, if R1, R2 and R3 are known with a high precision, then R4 can be measured with high precision also.

Very small changes in R4 disrupt the balance and are easily detected. In general, these generators will be of different electromotive forces and for the problem has a manageable complexity we have considered that the 4 resistors are of the same value, R, so that the CWB would be balanced without the presence of these 4 generators. In addition, we have assumed that the resistance of the galvanometer is negligible compared to the other present.

We solve this circuit by the method of meshes, to which we have represented the three mesh currents clockwise. Generalized CWB with four electric generators and with its loop currents. With two generators we can do it as long as we place them properly. We will solve analytically the second case, with only two generators and and in the circuit, as shown in Figure 5.

Generalized CWB with only two electric generators and with its loop currents. The currents are Being and then The current passing through the galvanometer is Noticing that the current is effectively zero when the electromotive forces are equal and positioned in the same sense.

Here we have considered an electric assembly in general is neither serial nor parallel, so its resolution involves some complexity. The Bakerian Lecture: Experimental Determination of the Laws of Magneto- electric Induction in different masses of the same metal, and its intensity in different metals. Philosophical Transactions of the Royal Society of London, vol. The Genesis of the Wheatstone.

Wheatstone bridge is used to measure the resistance with the help of a comparison method. The Wheatstone bridge work on the principle of null deflection.

Thus option 3 is correct. It used to measure the electrical resistance It works on the principle of null deflection. Meter bridge works on the principle of the wheat stone bridge It is used to measure the internal resistance of the battery.

Answer Detailed Solution Below Option 4 : It is used to measure the internal resistance of the battery. Therefore, option 1 is correct. Wheat stone bridge works on the principle of null deflection i.

Thus option 2 is correct. Meter bridge works on the principle of the wheat stone bridge. It is not used to measure the internal resistance of the battery. Thus option 4 is incorrect. Answer Detailed Solution Below Option 1 : 6 ohm. A battery with key and galvanometer is connected along its two diagonals respectively. The Wheatstone bridge works on the principle of null deflection, i. Means the middle wire can be said open circuit.