Measurement of Medium and High Resistance PDF

Measurement of Resistance 14.1 CLASSIFICATION OF RESISTANCES conditions in the circuit are not disturbed. However, The classification of resistances, from the point of in practice this is not possible and hence both the view of measurement, is as follows :...

Measurement of Resistance 14.1 CLASSIFICATION OF RESISTANCES conditions in the circuit are not disturbed. However, The classification of resistances, from the point of in practice this is not possible and hence both the view of measurement, is as follows : methods give inaccurate results. (i) Low resistances. All resistances of the order of Consider circuit of Fig. 14.1(a). In this circuit the 1 Q and under may be classified as low ammeter measures the true value of the current resistances. through the resistance but the voltmeter does not (ii) Medium resistances. This class includes resis­ measure the true voltage across the resistance. The tances from 1 Q upwards to about 0.1 MQ. voltmeter indicates the sum of the voltages across the (iii) High resistances. Resistances of the order of ammeter and the measured resistance. 0.1 MQ and upwards are classified as high resistances. The classification outlined above is not rigid, but forms a basis for techniques, followed or measure­ ment, which may be different for different classes. 14.2 MEASUREMENT OF MEDIUM RESISTANCES («) The different methods used for measurement of medium resistances are : Fig. 14.1 Measurement of resistance by ammeter-voltmeter method. (i) Ammeter-Voltmeter method. (ii) Substitution method. Let Ra be the resistance of the ammeter. (iii) Wheatstone bridge method..'. Voltage across the ammeter, Va = IRa (iv) Ohmmeter method. Now, measured value of resistance, _VR^a IR+1Ra (1A 14.2.1 Ammeter-Voltmeter Method R L\n 1 — P. -KI 1? K a...(14.2) I This method is very popular since the instruments required for this test are usually available in the True value of resistance, laboratory. The two types of connections employed for R=Rmt~Ra...(14.3) ammeter-voltmeter method are shown in Figs. 14.1(a) and (b). In both the cases, if readings of ammeter and = R,nl 1-i...(14.4) Rnt 1 > voltmeter are taken, then the measured value of resistance is given by : Thus the measured value of resistance is higher _ voltmeter reading _ V (14 1) than the true value. It is also clear from above that the m ammeter reading I true value is equal to the measured only if the ammeter resistance, Ra, is zero. The measured value of resistance R , would be equal to the true value, R, if the ammeter resistance is Relative error, e, = -^211—— = H4 5) zero and the voltmeter resistance is infinite, so that the r R R "v ' ’ (421)  422 Electrical and Electronic Measurements and Instrumentation It is clear from Eqn. 14.5 that the error in measure­ Fig. 14.1(b). If the two instruments are of 0.5% ments would be small if the value of resistance under accuracy and are read near full scale, the instrumental measurement is large as compared to the internal error in the result may be any thing from 0 to 1%. If resistance of the ammeter. Therefore the circuit of read near half scale, the percentage error may be twice Fig. 14.1(a) should be used when measuring high as great and for lower readings may mount resistance values. considerably higher. With less accurate instruments Consider the circuit of Fig. 14.1(b). In this circuit the possible error, of course is increased. It is difficult the voltmeter measures the true value of voltage but to obtain accuracy much better than 1% in a resistance the ammeter measures the sum of currents through value under usual conditions and the error sometimes the resistance and the voltmeter. may be considerably higher. However, the method is useful in some laboratory work in which high Let Rp be the resistance of the voltmeter. accuracy is not required. Current through the voltmeter, I = VI Iv The suitability of a particular method for Measured value of resistance, resistance measurement depends upon the relative r = V- V _ V R values of resistance under measurement and the m2 1 Ir + Iv~V/R + V/Rv~ 1+R/Rv resistance of the meters. The division point between the two methods is at True value of resistance, the resistance for which the relative errors given by R=^n2Rv =R f----- 1-------...(14.6) the two methods are equal. Rv~Rm2 The relative errors for the two cases are equal From Eqn. 14.6 it is clear that the true value of when : resistance is equal to the measured value only if the =— (See Eqns. 14.5 and 14.9) resistance of voltmeter, Rv, is infinite. However, if the resistance of voltmeter is very large as compared to R Rv the resistance under measurement: or when true value of resistance Or ^>>R„i2' and therefore Rm2! Rv is very small. R = 7rX -(14.10) For resistances greater than the value given by We have, R = Rm z_...(14.7) Eqn. 14.10 the method of Fig. 14.1(a) is used while for lower resistances method of 14.1(b) is used. Thus the measured value of resistance is smaller than the true value. Example 14,1 In the measurement of a resistance, R, by the Ammeter-voltmeter method, connections as in R — R R^ Relative error, e = ——-----= ——...(14.8) Figs. 14.1(a) and 14.1(b) are used. The resistance of ammeter r R RvR is 0.01 Q and that of voltmeter, 2000 Q. In case of (b) the The value of Rn;2 is approximately equal to R. current measured is 2 A and the voltage 180 V. Find the percentage error in calculating resistance Ras a quotient of er...(14.9) the readings and the true value ofR. Also find the reading of the voltmeter in case of (a) if the current indicated by the It is clear from Eqn. 14.9 that the error in ammeter is 2 A. measurement would be small if the value of resistance Solution. Case (b) See Fig. 14.1(b) under measurement is very small as compared to the Measured value of resistance resistance of the voltmeter. Hence the circuit of Fig. 14.1(b) should be used when measuring low Rm2 = V/ 1 = 180/2 =90 Q. resistance values. Current through the voltmeter The Ammeter-Voltmeter method, in the two forms lv = VI Rv = 180/2000 = 0.09 A. explained above, is a simple method but is, essentially Current through the resistance a comparatively rough method, the accuracy being IR = I-Iv =(2.0-0.09) A. limited by accuracy of ammeter and voltmeter used, even if corrections are made for the voltage drop True value of resistance across the ammeter for connections of Fig. 14.1(a) and R = — =---- —---- = 94.24 Q. for the shunting effect of voltmeter for connections of IR (2.0 -0.09) Measurement of Resistance 423 Percentage error Example 14,3 A resistance R is measured using the 90 794 24=_45% connections of Fig. 14.1(a). The current measured is 10 A = Rm2-LRx100 on range 10 A and the voltage measured is 125 V on 150 V R 94.24 range. The scales of the ammeter and voltmeter are uniform, Case (a) See Fig. 14.1(a) the total scale divisions of ammeter are 100 and that of Reading of voltmeter voltmeter are 150. The scales of these instruments are such V = Va+VR=I(Ra + R)= 2 (0.01+ 94.24) that 1/10 of a scale division can be distinguished. The = 188.50 V. constructional error of the ammeter is ± 0.3% and that of voltmeter ± 0.4%. The resistance of the ammeter is 0.25 Cl. Example 14.2 A resistance of approximate value of 80 Cl Calculate the value of R and the limits of possible error in is to be measured by voltmeter-ammeter method using al A the results. ammeter having a resistance of 2 Cl and a 50 V voltmeter having a resistance of 5000 Q. Solution. Reading error of ammeter (a) Suggest which one of the two methods should be = ±---- ----- x 100 = ±0.1% used ? 10x100 (b) Supposing in the suggested method the following Reading error of voltmeter measurements are made : = ±---- - ---- X100 = ±0.087% I = 0.42 A and V= 35.5 V. 10x150 Total error of ammeter 81 = ±0.3 ±0.1 = ±0.4% What is the resulting error if the accuracy of the instruments is ± 0.5% at full scale and the errors are standard deviations. Total error of voltmeter Solution, (a) Value of resistance for which the 8 V = ±0.4 ± 0.067 = ±0.467% errors are equal for the two types of connections Now, resistance R = V /1 and therefore total systematic error in measurement R = JRaRv =V2x5000 = 100 Q = ± 8 V ± SA = ±0.467 ±0.4 = ±0.867% Since the resistance to be measured has a value less than 100 Cl, the method of Fig. 14.1 (b) should be Measured value of resistance used as it results in smaller error. Rm2 = 125/10 = 12.5 Q. Measured value of resistance True value of resistance Rm2 = V/ I = 35.5/0.42 = 84.52 Q i-A_ R = Rm, (See Eqn. 14.4) True value of resistance R..., 1 ( 0 25 A R=Rm2 = 12.5 1-— =12.25 Cl. I 12.5 J Therefore the value of R is specified as 84.52 --------- - --------- | = 86Q. 1-84.52/5000 J 12.25 Q ± 0.867% = 12.25 ± 0.11 Q. (b) Error in ammeter reading 14.2.2 Substitution Method = (0.5/100)x 1 = 0.005 A The connection diagram for this method is shown Percentage error at 0.42 A reading in Fig. 14.2. R is the unknown resistance while S is a = (0.005/ 0.42 )x 100= 1.19% standard variable resistance. 'A' is an ammeter and 'r' Error in voltmeter reading is a regulating resistance. There is a switch for putting R and S into the circuit alternately. = 0.5 x (50/100)= 0.25 V The switch is put at position' I' and resistance R is.’. Percentage error at 35.5 V reading connected in the circuit. The regulating resistance r is = (0.25 / 35.5) x 100 =0.704% adjusted till the ammeter pointer is at a chosen scale Since the errors correspond to standard mark. Now, the switch is thrown to position '2' deviations, error due to ammeter and voltmeter putting the standard variable resistance S in the = 7(1.19)2+(0.704)2 = ± 1.38% circuit. The value of S is varied till the same deflection as was obtained with R in the circuit is obtained. The Absolute error due to ammeter and voltmeter settings of the dials of S are read. Since the substitution = (1.38/100)x86«± 1.2 Q. of one resistance for another has left the current :. The resistance is specified as 86 ± 1.2 Q. unaltered, and provided that the emf of battery and  424 Electrical and Electronic Measurements and Instrumentation the position of r are unaltered, the two resistances Hence, unknown resistance must be equal. Thus the value of unknown resistance R = (S+G)-1-G R is equal to the dial settings of resistance S. 02 = (0.5 x 106 +10 x 103)x (41 / 51) -10 x 103 = 0.4xl06Q =0.4 MQ. 14.2.3 Wheatstone Bridge A very important device used in the measurement of medium resistances is the Wheatstone bridge. A Wheatstone bridge has been in use longer than almost Fig. 14.2 Substitution method. any electrical measuring instrument. It is still an accurate and reliable instrument and is extensively This is a more accurate method than the used in industry. The Wheatstone bridge is an Ammeter-Voltmeter method, as it is not subject to the instrument for making comparison measurements and errors encountered in the latter method. However, the operates upon a null indication principle. This means accuracy of this method is greatly affected if there is the indication is independent of the calibration of the any change in the battery emf during the time the null indicating instrument or any of its characteristics. readings on the two settings are taken. Thus in order For this reason, very high degrees of accuracy can be to avoid errors on this account, a battery of ample achieved using Wheatstone bridge. Accuracy of 0.1% capacity should be used so that its emf remains is quite common with a Wheatstone bridge as constant. opposed to accuracies of 3% to 5% with ordinary The accuracy of the measurement naturally ohmmeter for measurement of medium resistances. depends upon the constancy of the battery emf and of Figure 14.3 shows the basic circuit of a Wheatstone the resistance of the circuit excluding R and S, upon bridge. It has four resistive arms, consisting of the sensitivity of the instrument, and upon the resistances P, Q, R and S together with a source of emf accuracy with which standard resistance S is known. (a battery) and a null detector, usually a galvanometer This method is not widely used for simple G or other sensitive current meter. The current resistance measurements and is used in a modified through the galvanometer depends on the potential form for the measurement of high resistances. The difference between points c and d. The bridge is said to substitution principle, however, is very important and be balanced when there is no current through the finds many applications in bridge methods and in galvanometer or when the potential difference across high frequency a.c. measurements. the galvanometer is zero. This occurs when the Example 14.4 In a measurement of resistance by voltage from point ‘V to point ‘d equals the voltage substitution method a standard 0.5 MD resistor is used. The from point ‘d! to point ‘If; or, by referring to the other galvanometer has a resistance oflOkD and gives deflections battery terminal, when the voltage from point'd' to as follows : point'd equals the voltage from point 'V to point'd. (z) With standard resistor, 41 divisions, For bridge balance, we can write, (zz) With unknown resistance, 51 divisions. fP=I2R...(14.11) Find the unknown resistance. Solution. The deflection of the galvanometer is directly proportional to the current passing through the circuit and hence is inversely proportional to the total resistance of the circuit. Let S, R and G be respectively the resistances of standard resistor, unknown resistor and the galvanometer. Also let 0] be the deflection with standard resistor in circuit and 02 with unknown resistor in circuit. £1 - R + G 02 “ S+G Fig. 14.3 Wheatstone bridge. Measurement of Resistance 425 For the galvanometer current to be zero, the 14.2.4 Sensitivity of Wheatstone Bridge following conditions also exist: It is frequently desirable to know the galvano­ meter response to be expected in a bridge which is...(14.12) 1 3 P+Q slightly unbalanced so that a current flows in the galvanometer branch of the bridge network. This may and / -j =_L_...(14.13) be used for : 2 4 R+S (z) selecting a galvanometer with which a given where E - emf of the battery. unbalance may be observed in a specified Combining Eqns. 14.11, 14.12 and 14.13 and bridge arrangement, simplifying, we obtain : (zz) determining the minimum unbalance which can be observed with a given galvanometer in the specified bridge arrangement, and (z'zz) determining the deflection to be expected for from which QR = PS...(14.15) a given unbalance. Equation 14.15 is the well known expression for The sensitivity to unbalance can be computed by the balance of Wheatstone bridge. If three of the solving the bridge circuit for a small unbalance. The resistances are known, the fourth may be determined solution is approached by converting the Wheatstone from Eqn. 14.15 and we obtain : bridge of Fig. 14.3 to its "Thevenin Equivalent" circuit. P R = S±...(14.16) Assume that the bridge is balanced when the branch resistances are P, Q R, S so that P / Q = R / S. Suppose where R is the unknown resistance, S is called the the resistance R is changed to R +\R creating an 'standard arm' of the bridge and P and Q are called the unbalance. This will to cause an emf e to appear across 'ratio arms'. the galvanometer branch. With galvanometer branch In the industrial and laboratory form of the open, the voltage drop between points a and b is : bridge, the resistors which make up P, Q and S are p =1p= _ mounted together in a box, the appropriate values ab 1 P+Q being selected by dial switches. Battery and galvano­ E(R + AR) Similarly, Efld=/2(R + AR) = meter switches are also included together with a R+AR+S galvanometer and a dry battery in the portable sets. P Therefore voltage difference between points d and and Q normally consist of four resistors each, the b is : values being 10, 100, 1000 and 10,000 Q respectively S consists of a 4 dial or 5 dial decade arrangement of resistors. Figure 14.4 shows the commercial form of ab R+AR+S P+Q Wheatstone bridge....(14.17) P _ R Battery © Galvanometer terminals P+Q-R+S terminals © ©GO Terminals © % R + AR P e= E for connecting R + AR + S ~P+S unknown © X2 ESAR resistance (R + S)2 + AR(R + S) Ratio selector ESAR ~ (R + S)2...(14.18) as AR(R + S)«(R + S)2 x 1000 x 100 x 10 x1 Let Sv be the voltage sensitivity of galvanometer. Lock for Lock for battery ° galvanometer0 Ohmat20°C Therefore, deflection of galvanometer is ESAR e = sve = sv...(14.19) Fig. 14.4 Commercial form of Wheatstone bridge. (R+S)2  426 Electrical and Electronic Measurements and Instrumentation R + AR R The bridge sensitivity SB is defined as the deflection of the galvanometer per unit fractional R + AR + R R+R change in unknown resistance. 'R + AR 1 Bridge sensitivity 2R + AR 2...(14.20) B AR/R as AR « R....(14.25) _ SVESR...(14.21) The resistance of the Thevenin equivalent circuit “(R + S)2 is found by looking back into terminals c and d From Eqn. 14.21, it is clear that the sensitivity of (Fig. 14.3) and replacing the battery by its internal the bridge is dependent upon bridge voltage, bridge resistance. In most cases, however, the extremely low parameters and the voltage sensitivity of the galvano­ resistance of the battery can be neglected and this meter. Rearranging the terms in the expression for simplifies the solution as we can assume that sensitivity, terminals a and b are shorted. The Thevenin equivalent S - S»E - S» E resistance can be calculated by referring to Fig. 14.5. B (R + S)2/SR ^+2 + 4 5 1\...(14.22) P +2 +Q Q P From Eqn. 14.22, it is apparent that maximum sensitivity occurs where R / S = 1. As the ratio becomes either larger or smaller, the sensitivity decreases. Since Fig. 14.5 Finding resistance of bridge looking into the accuracy of measurement is dependent upon terminals d and b. sensitivity a limit can be seen to the usefulness for a given bridge, battery and galvanometer combination. Thevenin equivalent resistance of bridge RS PQ For a bridge with equal arms, R = S - P = Q, R + S+ P+Q...(14.26) S E Bridge sensitivity...(14.23) Considering AR « R As explained above the sensitivity is maximum For a bridge with equal arms, when the ratio is unity. The sensitivity with ratio p=Q = S = Rf P / Q = R/ S =1000 would be about 1/250 of that for R0 = R...(14.27) unity ratio. The sensitivity with PIQ = R/S = 1000 The Thevenin equivalent of the bridge circuit would similarly be about 1/250 of that for unity ratio. therefore reduces to a Thevenin generator with an emf Thus the sensitivity decreases considerably if the £0 and an internal resistance Rq. This circuit is shown ratio P/ Q - R/ S is greater or smaller than unity. This in Fig- 14.6. reduction in sensitivity is accompanied by a reduction in accuracy with which a bridge can be balanced. Galvanometer current. The current through the galvanometer can be found out by finding the Thevenin equivalent circuit. The Thevenin or open circuit voltage appearing between terminals b and d with galvanometer circuit open circuited is, aa ac £Un = E. -En = UR 2v + AR)-LP ' 1 Fig. 14.6 Thevenin equivalent circuit of _ £(R + AR) EP Wheatstone bridge. ~ R + AR + S P+Q The current in the galvanometer circuit R + AR P...(14.24)...(14.28) R + AR + S P+Q For a bridge with equal arms, R = S = P = Q. where G = resistance of the galvanometer circuit. Measurement of Resistance 427 For a bridge with equal arms, reversal. The results are obtained by averaging the I _ E(AR/4R) two readings. This way the effect of thermo-electric...(14.29) emfs is eliminated with the added advantage of s (R + G) doubling the sensitivity of the bridge. The deflection of the galvanometer for a small 3. Temperature effects. The errors caused by change in resistance in the unknown arm is, change of resistance due to change of temperature SVESAR produces serious errors in measurements especially in 0= (R + S)2 the case of resistances made up of materials having a Sj large value of resistance temperature coefficient. For But Sv = example in the case of copper, which has a resistance temperature coefficient of 0.004/qC, a change in where S = current sensitivity of the galvanometer. temperature of 1°C will cause an error of 0.4% or 1 part SESAR in 250. 0 =------ -l------------- j...(14.30) (Ro + GXR + S)2 4. Contact resistance. Serious errors may be caused by contact resistances of switches and binding For a bridge with equal arms, posts. A dial may have a contact resistance of about SEAR 0.003 Q and thus a 4 dial resistance box has a contact 0 = —l----- -----...(14.31) 4R(R + G) resistance of about 0.01 Q. This value is quite high Also bridge sensitivity, especially when low resistance measurements are being done. Another aspect of the contact resistance is 0 S. ESR...(14.32) that error caused by it is difficult to account for since AR/R (Rq + GXR + S)2 its magnitude i.e., magnitude of contact resistance is For a bridge with equal arms, uncertain. Bridge sensitivity, In precision resistance measurements, the most accurate comparisons are made on an equal ratio S --§£...(14.33) bridge with a fixed standard resistance nominally B 4(R+G) equal to resistance under test. Then with equal leads, equal currents and equal heating of the ratio arms, the 14.2.5 Precision Measurement of Medium possible errors are minimized. The problem is then Resistances with Wheatstone Bridge reduced to that of determining the exact ratio of the It is sometimes necessary to measure resistances unknown resistance, R^ to the standard resistance S or to a precision of 1 part in 10,000 or even greater by the difference between them. The different methods comparing them with standard resistances. In such used for this purpose are : cases more than ordinary precautions are necessary in (/) Change in ratio arms. Small known changes are order to secure the required accuracy. The following made in the ratio arms and the exact balance is factors should be taken into consideration. obtained. 1. Resistance of connecting leads. A lead of (n) Using a high resistance shunt. In this case the 22 SWG wire having a length of 25 cm has a resistance bridge is balanced by means of an adjustable high of about 0.012 Q and this represents more than 1 part resistance put in parallel with one of the bridge arms. in 1000 for a 10 Q resistance or more than one part in A decade resistance box is used for this purpose. 10,000 for a 100 Q resistance. Suppose the test resistance, R, is slightly lower in 2. Thermo-electric effects. Thermoelectric emfs value than the standard resistance, S and let the are often present in the measuring circuit and they balance be obtained with a resistance xS, put in must be taken into account since they affect the parallel with S. galvanometer deflection in the same way as an emf The resistance of this arm is then occurring because of unbalance. The effect of thermoelectric emfs and other parasite emfs on the xS2/(S + xS), i.e., S/(1 + 1/ x). measurement may be eliminated by reversing the :. Value of unknown resistance battery connections to the bridge through a quick acting switch and adjusting the balance until no R=£._L_. change in galvanometer deflection can be observed on Q 1+1/x  428 Electrical and Electronic Measurements and Instrumentation Since x is very large and therefore 1/x is very Now, for first balance, small and hence we can write, p R + Lr + S+(L-L)r R + S+Lr... p — +1 — (0 R = ~-S(l-l/x)...(14.34) Q S + (L-Z1)r S + (L-/1)r also, for second balance, For an equal arm bridge, P = Q and therefore, P S + Lr+ R + (L-L)r S+R+Lr.... R = S(l-l/x)...(14.35) — +1 =-------------------- — =---------------...(u) Q R + (L-l2)r R + (L-l2)r The fractional difference, 1/x between S and R can be known. Since this method determines the fractional From (i) and (ii), we have, difference and x has a large value, the high resistance S + (L-Z1)r = R + (L-l2)r put in parallel with S need not be particularly accurate. Hence S-R^-lJr...(14.36) (iii) Carey foster slide wire bridge. A slide wire bridge is used for the purpose of determining the Thus the difference between S and R is obtained difference between the standard and the unknown from the resistance per unit length of the slide-wire resistances. The details are explained below. together with the difference (\-l2) between the two slide-wire lengths at balance. 14.2.6 Carey-Foster Slide-wire Bridge The slide-wire is calibrated i.e., r is obtained by The connections of this bridge are shown in shunting either S or R by a known resistance and again Fig. 14.7, a slide-wire of length L being included bet­ determining the difference in length (Z* -1'2). ween R and S as shown. This bridge is specially suited for the comparison of two nearly equal resistances. Suppose that S is known and that S' is its value when shunted by a known resistance ; then Resistances P and Q are first adjusted so that the ratio PIQ is approximately equal to the ratio R/ S. S-R = (Z1-Z2)r and S' - R =(l\-l'2)r Exact balance is obtained by adjustment of the sliding S-R _ S'-R contact on the slide-wire. Let f be the distance of the sliding contact form the left-hand end of the slide wire. The resistances R and S are then interchanged from which R = -^1——^1—^2...(14.37) and balance again obtained. Let the distance no-w be l2. (z;-z'-z1 + z2) Equation 14.37 shows that this method gives a direct comparison between S and R in terms of lengths only, the resistances of P and Q contact resistances, and the resistances of connecting leads being eliminated. As it is important that the two resistors R and S shall not be handled or disturbed during the measurement, a special switch is used to affect the interchanging of these two resistors during the test. 14.2.7 Kelvin-Varley Slide A Kelvin-Varley slide is used for voltage division. This method is very precise and finds extensive applications. A Kelvin-Varley slide is shown in Fig. 14.7 Carey-Foster Slide wire bridge. Fig. 14.8. It consists of several decades of resistors which are interconnected. The voltage division is Then for the first balance carried out successively. Each voltage division decade P _ R + fr is made up of eleven equal resistors with successive Q~ S + (L-f)r division decades having a total resistance equal to twice the value of a unit resistor in the previous where r is the resistance per unit length of the decade. For example, in the Kelvin Varley Slide shown slide-wire. in Fig. 14.8, there are four decade dividers. This „ -... P S+Lr For the second balance, — =------- -— decade is constructed using 11 resistance coils having Q R + (L-l2) a resistance of 10 kfl each. The second decade divider Measurement of Resistance 429 has 11 resistors of 2 kQ) each. * Similarly, the 3rd switch contact resistance due to current sharing within decade has 11 resistors of 400 Q each and the fourth the device. The disadvantages of the Kelvin-Varley and final decade has 10 resistors of 80 Q each. Slide are its calibration and the errors on account of temperature. The errors on account of temperature are Decade 1 Decade 2 Decade 3 Decade 4 o-------- a o —0 --------- --- 0 dut to the fact that the resistors carry different Kn/10 ^1/10 ^2/10 ^3/10 1 accounts and the changes in the value of r ohm resistance is different on account of different self­ ^in/10 ^1/10 ^2/10 V3/IO 1 heating conditions. The temperature effects can be reduced to negligible proportions by using resistors Vin/10 ^1/10 Vz/10 ^3/10 1 made of materials having a low resistance “0^3 temperature co-efficient. The error may be reduced to ^in/10 ^1/10 ^2/10 V3/10 u as low a value as ± 0.1 ppm. The principle of Kelvin-Varley Slides is used with advantage in ^in/10 ^1/10 ~7 potentio- meters and universal shunts. ^2/10 V3/10 1 —0 6 Figure 14.9 shows the use of Kelvin-Varley slide Kn/10 -O । ^1/10 V2/IO ^3/10 1 in a Wheatstone bridge. The device is used to replace vin —05 v n * the simple slide wire with the advantage that it gives ^1/10 VinA0 V2/IO v3/10 1 greater accuracy. ~°4 J—°3 —0 4 For the case shown in Fig. 14.9 ^1/10 Vin/W Kz/10 V3/10 I J-02 R _ 7554 —03 -