COMPARISION METHODS OF MEASUREMENTS

Transcription

1 UNIT 3 COMPARISION METHODS OF MEASUREMENTS OBJECTIVES: We shall learn D.C & A.C potentiometers, D.C & A.C bridges, Transformer ratio bridges, Self-balancing bridges.. History: Bridges are among the most accurate types of measuring devices used in the measurement of impedance. In addition, bridges are also used to measure DC resistance, capacitance, and inductance. Certain types of bridges are more suitable for measuring a specific characteristic, such as capacitance or inductance. The bridge circuits shown are similar in that they usually contain two branches in the measuring circuit, two branches in the comparing circuit, a detector circuit, and a power circuit. The general principles of circuit operation for AC remain the same. DC and AC bridge circuits As we saw with DC measurement circuits, the circuit configuration known as a bridge can be a very useful way to measure unknown values of resistance. This is true with AC as well, and we can apply the very same principle to the accurate measurement of unknown impedances. To review, the bridge circuit works as a pair of two-component voltage dividers connected across the same source voltage, with a null-detector meter movement connected between them to indicate a condition of balance at zero volts: (Figure below)

2 A balanced bridge shows a null, or minimum reading, on the indicator. Any one of the four resistors in the above bridge can be the resistor of unknown value, and its value can be determined by a ratio of the other three, which are calibrated, or whose resistances are known to a precise degree. When the bridge is in a balanced condition (zero voltage as indicated by the null detector), the ratio works out to be this: One of the advantages of using a bridge circuit to measure resistance is that the voltage of the power source is irrelevant. Practically speaking, the higher the supply voltage, the easier it is to detect a condition of imbalance between the four resistors with the null detector, and thus the more sensitive it will be. A greater supply voltage leads to the possibility of increased measurement precision. However, there will be no fundamental error introduced as a result of a lesser or greater power supply voltage unlike other types of resistance measurement schemes. Impedance bridges work the same, only the balance equation is with complex quantities, as both magnitude and phase across the components of the two dividers must be equal in order for the null detector to indicate zero. The null detector, of course, must be a device capable of detecting very small AC voltages. An oscilloscope is often used for this, although very sensitive electromechanical meter movements and even headphones (small speakers) may be used if the source frequency is within audio range. One way to maximize the effectiveness of audio headphones as a null detector is to connect them to the signal source through an impedance-matching transformer. Headphone speakers are typically low-impedance units (8 Ω), requiring substantial current to drive, and so a step-down transformer helps match low-current signals to

3 the impedance of the headphone speakers. An audio output transformer works well for this purpose: (Figure below) Modern low-ohm headphones require an impedance matching transformer for use as a sensitive null detector. Using a pair of headphones that completely surround the ears (the closed-cup type), I've been able to detect currents of less than 0.1 µa with this simple detector circuit. Roughly equal performance was obtained using two different step-down transformers: a small power transformer (120/6 volt ratio), and an audio output transformer (1000:8 ohm impedance ratio). With the pushbutton switch in place to interrupt current, this circuit is usable for detecting signals from DC to over 2 MHz: even if the frequency is far above or below the audio range, a click will be heard from the headphones each time the switch is pressed and released. Connected to a resistive bridge, the whole circuit looks like Figure below. Bridge with sensitive AC null detector.

4 Listening to the headphones as one or more of the resistor arms of the bridge is adjusted, a condition of balance will be realized when the headphones fail to produce clicks (or tones, if the bridge's power source frequency is within audio range) as the switch is actuated. When describing general AC bridges, where impedances and not just resistances must be in proper ratio for balance, it is sometimes helpful to draw the respective bridge legs in the form of box-shaped components, each one with a certain impedance: (Figure below) Generalized AC impedance bridge: Z = nonspecific complex impedance. For this general form of AC bridge to balance, the impedance ratios of each branch must be equal: Again, it must be stressed that the impedance quantities in the above equation must be complex, accounting for both magnitude and phase angle. It is insufficient that the impedance magnitudes alone be balanced; without phase angles in balance as well, there will still be voltage across the terminals of the null detector and the bridge will not be balanced. Bridge circuits can be constructed to measure just about any device value desired, be it capacitance, inductance, resistance, or even Q. As always in bridge measurement circuits, the unknown quantity is always balanced against a known standard, obtained from a high-quality, calibrated component that can be adjusted in value until the null detector device indicates a condition of balance. Depending on how the bridge is set up, the unknown component's value may be determined directly from the setting of the calibrated standard, or derived from that standard through a mathematical formula.

5 A couple of simple bridge circuits are shown below, one for inductance (Figure below) and one for capacitance: (Figure below) Symmetrical bridge measures unknown inductor by comparison to a standard inductor. Symmetrical bridge measures unknown capacitor by comparison to a standard capacitor. Simple symmetrical bridges such as these are so named because they exhibit symmetry (mirror-image similarity) from left to right. The two bridge circuits shown above are balanced by adjusting the calibrated reactive component (L s or C s ). They are a bit simplified from their real-life counterparts, as practical symmetrical bridge circuits often have a calibrated, variable resistor in series or parallel with the reactive component to balance out stray resistance in the unknown component. But, in the hypothetical world of perfect components, these simple bridge circuits do just fine to illustrate the basic concept. An example of a little extra complexity added to compensate for real-world effects can be found in the so-called Wien Bridge, which uses a parallel capacitor-resistor standard

6 impedance to balance out an unknown series capacitor-resistor combination. (Figure below) All capacitors have some amount of internal resistance, be it literal or equivalent (in the form of dielectric heating losses) which tend to spoil their otherwise perfectly reactive natures. This internal resistance may be of interest to measure, and so the Wien Bridge attempts to do so by providing a balancing impedance that isn't pure either: Wein Bridge measures both capacitive C x and resistive R x components of real capacitor. Being that there are two standard components to be adjusted (a resistor and a capacitor) this bridge will take a little more time to balance than the others we've seen so far. The combined effect of R s and C s is to alter the magnitude and phase angle until the bridge achieves a condition of balance. Once that balance is achieved, the settings of R s and C s can be read from their calibrated knobs, the parallel impedance of the two determined mathematically, and the unknown capacitance and resistance determined mathematically from the balance equation (Z 1 /Z 2 = Z 3 /Z 4 ). It is assumed in the operation of the Wien Bridge that the standard capacitor has negligible internal resistance, or at least that resistance is already known so that it can be factored into the balance equation. Wien bridges are useful for determining the values of lossy capacitor designs like electrolytic, where the internal resistance is relatively high. They are also used as frequency meters, because the balance of the bridge is frequencydependent. When used in this fashion, the capacitors are made fixed (and usually of equal value) and the top two resistors are made variable and are adjusted by means of the same knob. An interesting variation on this theme is found in the next bridge circuit, used to precisely measure inductances.

7 Maxwell-Wein bridge measures an inductor in terms of a capacitor standard. This ingenious bridge circuit is known as the Maxwell-Wien bridge (sometimes known plainly as the Maxwell bridge), and is used to measure unknown inductances in terms of calibrated resistance and capacitance. (Figure above) Calibration-grade inductors are more difficult to manufacture than capacitors of similar precision, and so the use of a simple symmetrical inductance bridge is not always practical. Because the phase shifts of inductors and capacitors are exactly opposite each other, capacitive impedance can balance out inductive impedance if they are located in opposite legs of a bridge, as they are here. Another advantage of using a Maxwell bridge to measure inductance rather than a symmetrical inductance bridge is the elimination of measurement error due to mutual inductance between two inductors. Magnetic fields can be difficult to shield, and even a small amount of coupling between coils in a bridge can introduce substantial errors in certain conditions. With no second inductor to react with in the Maxwell bridge, this problem is eliminated. For easiest operation, the standard capacitor (C s ) and the resistor in parallel with it (R s ) are made variable, and both must be adjusted to achieve balance. However, the bridge can be made to work if the capacitor is fixed (non-variable) and more than one resistor made variable (at least the resistor in parallel with the capacitor, and one of the other two). However, in the latter configuration it takes more trial-and-error adjustment to achieve balance, as the different variable resistors interact in balancing magnitude and phase. Unlike the plain Wien bridge, the balance of the Maxwell-Wien bridge is independent of source frequency, and in some cases this bridge can be made to balance in the presence

8 of mixed frequencies from the AC voltage source, the limiting factor being the inductor's stability over a wide frequency range. There are more variations beyond these designs, but a full discussion is not warranted here. General-purpose Impedance Bridge circuits are manufactured which can be switched into more than one configuration for maximum flexibility of use. A potential problem in sensitive AC bridge circuits is that of stray capacitance between either end of the null detector unit and ground (earth) potential. Because capacitances can conduct alternating current by charging and discharging, they form stray current paths to the AC voltage source which may affect bridge balance: (Figure below) Stray capacitance to ground may introduce errors into the bridge. While reed-type meters are imprecise, their operational principle is not. In lieu of mechanical resonance, we may substitute electrical resonance and design a frequency meter using an inductor and capacitor in the form of a tank circuit (parallel inductor and capacitor). One or both components are made adjustable, and a meter is placed in the circuit to indicate maximum amplitude of voltage across the two components. The adjustment knob(s) are calibrated to show resonant frequency for any given setting, and the frequency is read from them after the device has been adjusted for maximum indication on the meter. Essentially, this is a tunable filter circuit which is adjusted and then read in a manner similar to a bridge circuit (which must be balanced for a null condition and then read). The problem is worsened if the AC voltage source is firmly grounded at one end, the total stray impedance for leakage currents made far less and any leakage currents through these stray capacitances made greater as a result: (Figure below)

9 Stray capacitance errors are more severe if one side of the AC supply is grounded. One way of greatly reducing this effect is to keep the null detector at ground potential, so there will be no AC voltage between it and the ground, and thus no current through stray capacitances. However, directly connecting the null detector to ground is not an option, as it would create a direct current path for stray currents, which would be worse than any capacitive path. Instead, a special voltage divider circuit called a Wagner ground or Wagner earth may be used to maintain the null detector at ground potential without the need for a direct connection to the null detector. (Figure below) Wagner ground for AC supply minimizes the effects of stray capacitance to ground on the bridge.

10 The Wagner earth circuit is nothing more than a voltage divider, designed to have the voltage ratio and phase shift as each side of the bridge. Because the midpoint of the Wagner divider is directly grounded, any other divider circuit (including either side of the bridge) having the same voltage proportions and phases as the Wagner divider, and powered by the same AC voltage source, will be at ground potential as well. Thus, the Wagner earth divider forces the null detector to be at ground potential, without a direct connection between the detector and ground. There is often a provision made in the null detector connection to confirm proper setting of the Wagner earth divider circuit: a two-position switch, (Figure below) so that one end of the null detector may be connected to either the bridge or the Wagner earth. When the null detector registers zero signals in both switch positions, the bridge is not only guaranteed to be balanced, but the null detector is also guaranteed to be at zero potential with respect to ground, thus eliminating any errors due to leakage currents through stray detector-to-ground capacitances: Switch-up position allows adjustment of the Wagner ground. REVIEW: AC bridge circuits work on the same basic principle as DC bridge circuits: that a balanced ratio of impedances (rather than resistances) will result in a balanced condition as indicated by the null-detector device. Null detectors for AC bridges may be sensitive electromechanical meter movements, oscilloscopes (CRT's), headphones (amplified or unamplified), or any other device capable of registering very small AC voltage levels. Like DC null detectors, its only required point of calibration accuracy is at zero. AC bridge circuits can be of the symmetrical type where an unknown impedance is balanced by a standard impedance of similar type on the same side

11 (top or bottom) of the bridge. Or, they can be nonsymmetrical, using parallel impedances to balance series impedances, or even capacitances balancing out inductances. AC bridge circuits often have more than one adjustment, since both impedance magnitude and phase angle must be properly matched to balance. Some impedance bridge circuits are frequency-sensitive while others are not. The frequency-sensitive types may be used as frequency measurement devices if all component values are accurately known. A Wagner earth or Wagner ground is a voltage divider circuit added to AC bridges to help reduce errors due to stray capacitance coupling the null detector to ground. Questions For Practice Multiple Choice Type Questions: 1. A bridge used for measurement of dielectric loss and power factor is a) Maxwell s bridge b) Wien bridge c)schering bridge c) bridge d) Owen bridge 2. The bridge used for measuring inter- electrode capacitance is a) Schering b) De Sauty s c) Wine s d) Owen bridge 3. The bridge used for measuring dissipation factor of a capacitor is a) Campbell s b) Schering c)anderson s d) Oxen s 4. Most commonly used ac bridge circuit for the measurement of capacitance is a) Maxwell Wien bridge b) Kelvin s bridge c) De Sauty bridge d) Schering bridge 5. The bridge suitable for measurement of capacitance of capacitor at high voltage is a) Wien b) De Sauty bridge c) Schering bridge d) Anderson s 6. The ac bridge that can accurately determine the excitation frequency is a) Maxwell bridge b) Anderson s bridge c) Wien bridge d)schering bridge 7. Which of the following bridges is frequency sensitive? a) Wheat stone b) Maxwell c) Anderson d)wien Answer: 1. (c) 2. (a) 3. (b) 4 (d) 5(c) 6.(c) 7.(d) TRUE OR FALSE: 8. The potentiometer is usually calibrated by means of a standard cell 9. Potentiometer is one of the most useful instruments are accurate

12 Measurement of voltage, current and resistance 10. For audio frequency measurement electronic oscillator and amplifier are used 11. If an inductance is connected in one arm of the bridge and resistance in the Remaining three arms, the bridge can be balanced. 12. Maxwell bridge can be employed for measuring the power factor Answer: 8. True 9.True 10.True 11.False 12.false Fill in the blanks: 13. Shunt type ohm meter are suitable for measurement of resistance 14. An ohmmeter is a/an instrument 15. A megger has a source of high emf in the form of a hand driven cranked A megger, when not in operation, indicate a resistance of a For determination of surface resistively the instrument usually used is Answer: 13. Low 14.moving coil 15.Generator megger OBJECTIVES: We shall learn Multiple earth and earth loops Electrostatic and electromagnetic interference Grounding techniques

13 Self-balancing bridges paring circuit contains branches as provisions for changing the ranches with respect to each enables various measuring ranges d. Comparison of Figures 1 and 2 her or both branches of the cuit do not necessarily contain e. Branch B of the Hay bridge, and RB in series connection, king contrast with the parallel CB and RB of the Maxwell suring circuit in Figure 2 also branches. The resistance, r inductance to be measured is branch X of the bridge-measuring bscript X is also used in Figure 1 he circuit parameters involved in e values of various electronic S contains the variable control the bridge into a balanced otentiometer is used for this ost bridge equipment, because it range of smoothly variable es within the measuring circuit. Figure 1: Basic bridge circuits. d arm of the bridge is the detector etector circuit may use a for sensitive measurements that ccuracy. In the case of bridges e power source, the must be adapted for use in an AC y practical bridge circuits using the bridge, an electron-ray e is used to indicate the balanced pening and closing the shadow be. Headsets are also used for ce detection, but this method ccuracy obtainable with the s are used in bridge circuits to plication of operating power to

14 d to complete the detector circuit. e two switching functions are o a single key, called a bridge key, erating power is applied to the o the detector circuit. This uces the effects of inductance and uring the process of. Figure 2: Typical bridge circuit configuration. t unfavorable condition for surement occurs when the pacitance, or inductance to be ompletely unknown. In these vanometer cannot be protected by dge arms for approximate duce the possibility of damage to eter, you should use an adjustable cross the meter terminals. As the ght closer to the balanced resistance of the shunt can be en the bridge is in balance, the an be removed to obtain ector sensitivity. Bridges designed specifically for capacitance measurements provide a DC source of potential for electrolytic capacitors. The electrolytic capacitors often require the application of DC polarizing voltages in order for them to exhibit the same capacitance values and dissipation factors that would be obtained in actual circuit operation. The DC power supply and meter circuits used for this purpose are connected so that there is no interference with the normal operation of the capacitance-measuring bridge circuit. The dissipation factor of the capacitor may be obtained while the capacitor is polarized. In Figure 2, the signal voltage in the A and B branches of the bridge will be divided in proportion to the resistance ratios of its component members, R A and R B, for the range of values selected. The same signal voltage is impressed across the branches S and X of the bridge. The variable control, R S, is rotated to change the current flowing through the S and X branches of the bridge. When the voltage drop across branch S is equal to the voltage drop across branch A, the voltage drop across branch X is equal to the voltage drop across branch B. At this time the potentials across the detector circuit are the same, resulting in no current flow through the detector circuit and an indication of zero-current flow. The bridge is balanced at these settings of its operating controls, and they cannot be placed at any other setting and still maintain this balanced condition.

15 The ability of the bridge circuit to detect a balanced condition is not impaired by the length or the leads connecting the bridge to the electronic part to be measured. However, the accuracy of the measurement is not always acceptable, because the connecting leads exhibit capacitive and inductive characteristics, which must be subtracted from the total measurement. Hence, the most serious errors affecting accuracy of a measurement are because of the connecting leads. Figure 3: Resistance-ratio bridge residual elements. Figure 4: Wagner ground. Stray wiring capacitance and inductance, called residuals, that exist between the branches of the bridge also cause errors. The resistance-ratio bridge, for example, is redrawn in Figure 3 to show the interfering residuals that must be eliminated or taken into consideration. Fortunately, these residuals can be reduced to negligible proportions by shielding and grounding. A method of shielding and grounding a bridge circuit to reduce the effects of interfering residuals is through the use of a Wagner ground, as shown in Figure 4. Observe that with switch S in position Y, the balanced condition can be obtained by adjusting Z 1 and Z 2. With switch S in position X, the normal method of balancing the bridge applies. You should be able to reach a point where there is no deflection of the meter movement for either switch position (X or Y) by alternately adjusting Z 1 and Z 2 when the switch is at position Y and by adjusting R S when the switch is at position X. Under these conditions, point 1 is at ground potential; and the residuals at points 2, 3, and 4 are effectively eliminated from the bridge. The main disadvantage of the Wagner ground is that two balances must be made for each measurement. One is to balance the bridge, and the other is to balance the Wagner ground. Both adjustments are interacting because R A and R B are common to both switch positions X and Y. Many bridge instruments provide terminals for external excitation potentials; however, do not use a voltage in excess of that needed to obtain reliable indicator deflection because the resistivity of electronic parts varies with heat, which is a

16 function of the power applied. Capacitance, inductance, and resistance bridges. You can measure capacitance, inductance, and resistance for precise accuracy by using ac bridges. These bridges are composed of capacitors, inductors, and resistors in a wide variety of combinations. These bridges are operated on the principle of a dc bridge called a Wheatstone bridge. Figure 5: Wheatstone bridge. The Wheatstone bridge is widely used for precision measurements of resistance. The circuit diagram for a Wheatstone bridge is shown in Figure 5. Resistors R 1, R 2, and R 3 are precision, variable resistors. The value of R x is an unknown value of resistance that must be determined. After the bridge has been properly balanced (galvanometer G reads zero), the unknown resistance may be determined by means of a simple formula. The galvanometer (an instrument that measures small amounts of current) is inserted across terminals b and d to indicate the condition of balance. When the bridge is properly balanced, no difference in potential exists across terminals b and d; when switch S 2 is closed, the galvanometer reading is zero. The operation of the bridge is explained in a few logical steps. When the battery switch S 1 is closed, electrons flow from the negative terminal of the battery to point a. Here the current divides as it would in any parallel circuit. Part of it passes through R 1 and R 2 ; the remainder passes through R 3 and R x. The two currents, I 1 and I 2, unite at point c and return to the positive terminal of the battery. The value of I 1 depends on the sum of

17 resistance R 1 and R 2, and the value of I 2 depends on the sum of resistances R 3 and R x. In each case, according to Ohm's law, the current is inversely proportional to the resistance. R 1, R 2, and R 3 are adjusted so that when S 1 is closed, no current flows through G. When the galvanometer shows no deflection, there is no difference of potential between points b and d. All of I 1 follows the a b c path and all I 2 follows the a d c path. This means that a voltage drop E 1 (across R 1 between points a and b) is the same as voltage drop E 3 (across R 3 between points a and d). Similarly, the voltage drops across R 2 and R x (E 2 and E x ) are also equal. Expressed algebraically, and With this information, we can figure the value of the unknown resistor R x. Divide the voltage drops across R 1 and R 3 by their respective voltage drops across R 2 and R x as follows: We can simplify this equation: then we multiply both sides of the expression by R x to separate it: For example, in Figure 5, we know that R 1 is 60 ohms, R 2 is 100 ohms, and R 3 is 200 ohms. To find the value of R x, we can use our formula as follows: Use of ac Bridges. A wide variety of ac bridge circuits (such as the Wheatstone) may be used for the precision measurement of ac resistance, capacitance, and inductance. Let's look at ac bridges in terms of functions they perform.

18 Resistance bridge. An ac signal generator, as shown in Figure 6, is used as the source of voltage. Current from the generator passes through resistors R 1 and R 2, which are known as the ratio arms, and through R s and R x. Again, R x is known as resistance. R s has a standard value and replaces R 3 in Figure 6. When the voltage drops across R 2 and R s are equal, the voltage drops across R 2 and R x are also equal; no difference of potential exists across the meter and no current flows through it. As we discovered with the Wheatstone bridge, when no voltage appears across the meter, the following ratio is true: Figure 6: Resistance bridge (ac). For example, if in Figure 6 we know that R 1 is 20 ohms, R 2 is 40 ohms, and R s is 60 ohms, we can find the value of R x using our formula as follows: With the ac signal applied to the bridge, R 1 and R 2 are varied until a zero reading is seen on the meter. Zero deflection indicates that the bridge is balanced. (NOTE: In actual practice, the variables are adjusted for a minimum reading since the phase difference between the two legs will not allow a zero reading.)

19 Capacitance bridge. Because current varies inversely with resistance and directly with capacitance, an inverse proportion exists between the four arms of the bridge in Figure 7; the right side of our expression is inverted from the resistance bridge expression as follows: or Figure 7: Capacitance bridge. Classifications of Resistances 1. Low resistances : <= 1 Ω 2. Medium resistances = (1 Ω, 100 K Ω) 3. High resistances: >= 100 K Ω Measurement of Low Resistance 1. Ammeter-voltmeter method 2. Potentio-meter method 3. Kelvin double bridge method 4. Ohm meter method Ammeter-voltmeter Method

20 FIGURE 10-1 Ammeter-voltmeter method of measuring low resistance This is most simple and quick method of measurement of resistance. It yields a moderately accurate value over a very wide range of resistances. The attainable accuracy-depends primarily on the accuracy and ranges of the instruments employed for measurement of current and voltage. If the available instruments are obtained and proper allowance is made for the effect of the instruments accuracy within 0.1 or 0.2 % is achieved. Current through ammeter = current through unknown resistance+current through voltmeter or I = I x + I v...(10-1)

21 or I x = I I v...(10-2) True value of unknown resistance, X = V V V V T = = =...(10-3) I I I = V x v I V I I Rv IR v Where V is the voltmeter reading, R v is the resistance of the voltmeter and I is the current indicated by the ammeter. If current is connected so that it indicates only the current flowing through the unknown resistance, the voltmeter measures voltage drop across the ammeter and unknown resistance X. In this case true value of unknown resistance is given by the expression. V X T = I R A...(10-4) Where R A is the resistance of the ammeter. Potentiometer Method FIGURE 10-2 Potentiometer method of measuring low resistance In this method unknown resistance X, an ammeter A, a rheostat R to limit the current and a standard resistance S are connected, all in series with a low-voltage, high current supply voltage. X Potentiometer reading across X = S Potentiometer reading across S = V...(10-5) V s

22 Since accuracy of this method depends on there being no change in current between the two readings, it is necessary that the source of supply of current through the circuit be extremely stable. The difficulty of ensuring that this condition is satisfied is the main disadvantage of this method. However error due to possible variation of the supply current is minimized by making several measurements alternately and taking their mean values as the voltage drops across the two resistances. Kelvin Double Bridge Method A sensitive galvanometer G is connected across the dividing points of PQ and pq. The ratio P is kept the same as Q p, these ratios being varied until the galvanometer reads zero. q In balance position of bridge, the currents in the bridge are shown in Fig Applying Kirchoff's second law to meshes AHFKBA and FEDCKF or and or we get I 1 P I 2 p IX = 0 IX = I 1 P I 2 P...(10-6) I 1 Q I 2 q IS = 0 IS = I 1 Q I 2 q...(10-7) Dividing Eq. (10-6) by Eq. (10-7) we get P I 1 p I 2 X I = 1 P I 2 p = P P p = since = q S I 1 Q I 2 q q Q P Q Q I 1 I 2 Q

23 or X = S IP...(10-8) Q FIGURE 10-3 Kelvin double bridge Measurement of Medium Resistances 1. Ammeter-voltmeter method 2. Substitution method 3. Wheatstone bridge method 4. Carey-Foster method Substitution Method FIGURE 10-4 Substitution method of measurement of resistance [2] X is unknown resistance and R is a variable known resistance which can be changed in small steps, say 0.1 Ω. The accuracy of the measurement obviously depends upon the consistency of the supply voltage, of the resistance of the circuit of the circuit

24 excluding X and R, and upon the sensitivity of the ammeter, as well as upon the accuracy with which the resistance R is known. Wheatstone Bridge Method FIGURE 10-5 Wheatstone bridge I 1 P = I 2 R...(10-9) I 1 Q = I 2 S...(10-10) Dividing Eq. (10-9) by Eq. (10-10) we get P R = Q S or R = P S...(10-11) Q It should be noted that this relationship between resistances will also hold good if the battery and galvanometer are interchanged. Advantages : 1. The method is a null one, therefore, errors due to inaccuracies in indicating- instrument calibration are completely avoided as the galvanometer is merely used to indicate zero current

25 2. The balance is quite independent of the source e.m.f., so the inaccuracies in the measured values due to fluctuation of the e.m.f. of the source are completely avoided. Range : from 1.0 up to 100,000 ohms, with a possible extension to this range at reduced sensitivity. Accuracy : The accuracy obtainable depends almost solely on the quality of the resistors. The accuracy obtainable with a good commercial bridge is of the order a few parts in 10,000. The portable form of Wheatstone bridge set, known as the Post Office box, contains three adjustable resistances and two switches in one box as shown in Fig FIGURE 10-6 Post office box Measurement of High Resistances The measurement of high resistance is involved in determination of : 1) insulation resistances of cables and of components and built-up electrical equipment of all types, 2) resistance of high resistance circuit elements, 3) volume resistivity of a material, and

26 4) Surface resistivity. Direct Deflection Method FIGURE 10-7 Direct defflection method In this method of measuring insulation resistance a very sensitive and high resistance (1,000 ohms or more) moving coil galvanometer is connected in series with the resistance to be measured, and to a battery supply. The deflection of galvanometer gives a measure of the insulation resistance. This is very simple but rough method of measuring insulation resistance. 128

27 Megger Method The insulation resistance of a cable may also be measured by a self - contained insulation tester, known as megger. FIGURE 10-8 Measurement of insulation resistance of cable by Megger method Loss of Charge Method FIGURE 10-9 Loss of charge method for measurement of high resistance 129

28 In this method the capacitor is first charged by means of a battery to some suitable voltage by putting switch S on stud 1 and then allowed to discharge through the resistances R and R 1 by throwing switch S to stud 2. The time taken t for the potential difference to fall from V 1 to V 2 during discharge is observed by a stop watch. i = q = C v...(10-12) t t or i = potential drop across resis tan ce R' = R' v v = C R' t v...(10-13) R' v t = v CR'...(10-14) V 2 v = v + + V 1 0 or [log e v] V 2 t V 1 t CR' = t CR' 0 or [log e v] V 2 = t V 1 CR' 0 t t or log e V 2 V 1 = t CR' or V 2 V 1 = e t CR ' or V 2 = V 1 e t CR '...(10-15) From Eq. (10-15) the value of R' can be determined. The test is then repeated with unknown resistance R disconnected, the capacitor being discharged through R 1 only. Thus the value of leakage resistance R 1 can also be determined. Knowing the value od R' and R 1 the value of unknown resistance can be determined from the relation : 1 = 1 1 R R' R 1...(10-16) The value of R 1 can be obtained directly from the expression : t V 2 = V 1 e RC...(10-17) 130

29 where V 1 is the voltage at the start instant of discharging and V 2 is the voltage across the object under test after time t seconds. Measurement of Insulation Resistance When the Power is On FIGURE Measurement of insulation resistance of two-wire live mains 1 V 1 = I R 1 R v since R 1 and R v in parallel across +ve main and earth R or V 1 = I 1 R v 1...(10-18a) R 1 + R v and V V 1 = I 1 R 2...(10-18b) Dividing Eq. (10-18b) by Eq. (10-18a) we have or or V V 1 = V 1 R 2 R 1 R v R 1 + R v V V 1 = R 2 (R 1 + R v ) V 1 R 1 R v V = R 1 R v + R 2 (R 1 + R v ) = R 1 R 2 + R v (R 1 + R 2 )...(10-19) V 1 R 1 R v R 1 R v Similarly if in second case the current flowing from +ve main to -ve main is I 2 then we have R 2 R v V2 = R2 + R v I 2...(10-20a) and V V 2 = I 2 R 1...(10-20b) Dividing Eq. (10-20b) by Eq. (10-20a) we have V V 2 R 1 (R 2 + R v ) = V 2 R 2 R v 131

30 or V = R 2 R v + R 1 (R 2 + R v ) = R 1 R 2 + R v (R 1 + R 2...(10-21) V 2 R 2 R v R 2 R v Dividing Eq. (10-19) by Eq. (10-21) we have V 2 = R 2 V 1 R 1 or R = R V (10-22) V 1 Substituting R = R V V 1 in Eq. (10-19) we have V 2 V 2 R 1 R 1 V V + R R + R v V1 = V 1 R 1 R v V V 1 V 2 or R 1 = R v...(10-23) V 2 Similarly V V 1 V 2 R 2 = R v...(10-24) V 1 The combined insulation resistance of the system can be determined by assuming that two mains are bunged together so that the resultant value is the combined resistance of R 1 and R 2 in parallel. R Therefore, Insulation resistance of the system = 1 R 2...(10-25) R 1 + R 2 For measurement of insulation of 3 wire live mains use of electrostatic voltmeter is made and connection of middle wire to earth is temporarily removed. FIGURE Measurement of insulation resistance of 3-wire live mains. [ 132

31 V R = r (10-26)

32 V 2 Measurement of Resistance of Earth Connections FIGURE Testing of earth electrode resistance

33 FIGURE Circuit carrying direct current and alternating current R = Voltage drop between E and B = V...(10-27) e Current through earth path I

34 Questions for Practice: Multiple Choice Type Questions: 1. Ac bridges a) Have leakage error and eddy current errors only b) Have residual errors, frequency errors and wave form errors only c) Both A and B d) Are free from errors 2. Open circuit fault in cable can be located by a) Blaviers test b) capacity test c) varley loop test d) murrray loop test 3. Ballistic galvanometer can be calibrated by means of a a) Hibbert magnetic standard b) capacitor c) standard solenoid d)any of the above 4. Magnetic measurements are inaccurate because a) Magnetic flux cannot be measured directly merely by inserting an instrument in the magnetic circuit b) Magnetic flux dose not confine itself to a definite path c) Magnetic materials are not homogeneous d) all the above 5. Magnetic materials by a) Self inductance bridge b) camp bells mutual inductance bridge c) ac potentio meter d) oscillographic method 6. Campbell s bridge method is used to measure a) Copper loss b) iron loss c) both A and B d) none of the these Answer: 1. (c) 2. (b) 3.(d) 4. (d) 5. (e) 6. (b)

35 TRUE OR FALSE 7. Maxwell Wien bridge is very convenient and useful bridge for the Determination of inductance having Q- factor very low (Q<1) 8. Hay s bridge is quite suitable for measurement of low Q- factor of the inductors 9. Anderson bridge can be used for precise measurement of inductance over a Wide range 10. The low value of insulation resistance between two cores of an under Ground cables, with far ends isolated from the load, indicate open- circuit fault Answer: 7. False 8.False 9.True 10.False Fill in The Blanks: 11. The simple dc potentiometer consists of a German silver or wire 12. The cell used in a potentiometer is a The most commonly used null detector in bridge measurement is vibration galvanometer 14. De sauty bridge used for the measurements of and Answer: 11. Manganin 12.lead accumulator 13.AC 14. Capacitance; dissipation factor Part A( 2 Marks) Question Bank 1. What is meant by transformer ratio bridge (2) 2. What are the features of ratio transformer? List its applications. (2) 3. What is meant by electromagnetic interference? (2) 4. List the sources of electromagnetic interference. (2) 5. What are the ways of minimizing the electromagnetic interference? (2)

36 6. Define electromagnetic compatibility.(emc) (2) 7. What are the main causes of group loop currents? (2) 8. What are the limitations of single point grounding method? (2) 9. What is the necessity of grounding and state is advantages. (2) 10. What is meant by ground loop? How it is created? (2) 11. What are the sources of errors in bridge measurement? (2) 12. Define standardization. (2) 13. Give the relationship between the bridge balance equation of DC bridge and AC bridge (2) 14. What does a bridge circuit consists of? (2) PART B( 12 marks) 1. (i) Explain in detail about the laboratory type DC potentiometer. (8) (ii) Give the applications of AC potentiometers. (4) 2. (i) Describe about the multiple earth and earth loops. (8) (ii) Explain the different techniques of grounding. (4) 3. Explain voltage sensitive self balancing bridge, and derive the bridge Sensitivity of voltage sensitive bridge with fundamentals. (12) 4. (i) With fundamentals distinguish between DC and AC potentiometers, and give any two specific applications for each. (6) (ii) Discuss the advantages and limitations of electromagnetic interference in measurements. (6) 5. (i) Explain Kelvin s double bridge method for the measurement of low resistance. (6) (ii) Explain how inductance in measured by using Maxwell s bridge. (6) 6. (i) Explain the working principle of Anderson s bridge and also derive its balance equations. (6)

37 (ii) Explain the working principle of Schering bridge and also derive its balance equations. (6)