MEASURING INSTRUMENTS

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1 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 MEASURING INSTRUMENTS. Definition of instruents An instruent is a device in which we can deterine the agnitude or value of the quantity to be easured. The easuring quantity can be voltage, current, power and energy etc. Generally instruents are classified in to two categories. Instruent Absolute Instruent Secondary Instruent. Absolute instruent An absolute instruent deterines the agnitude of the quantity to be easured in ters of the instruent paraeter. This instruent is really used, because each tie the value of the easuring quantities varies. So we have to calculate the agnitude of the easuring quantity, analytically which is tie consuing. These types of instruents are suitable for laboratory use. Exaple: Tangent galvanoeter..3 Secondary instruent This instruent deterines the value of the quantity to be easured directly. Generally these instruents are calibrated by coparing with another standard secondary instruent. Exaples of such instruents are volteter, aeter and watteter etc. Practically secondary instruents are suitable for easureent. Secondary instruents Indicating instruents Recording Integrating Electroechanically Indicating instruents 9

2 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION Indicating instruent This instruent uses a dial and pointer to deterine the value of easuring quantity. The pointer indication gives the agnitude of easuring quantity..3. Recording instruent This type of instruents records the agnitude of the quantity to be easured continuously over a specified period of tie..3.3 Integrating instruent This type of instruent gives the total aount of the quantity to be easured over a specified period of tie..3.4 Electroechanical indicating instruent For satisfactory operation electroechanical indicating instruent, three forces are necessary. They are (a) Deflecting force (b) Controlling force (c)daping force.4 Deflecting force When there is no input signal to the instruent, the pointer will be at its zero position. To deflect the pointer fro its zero position, a force is necessary which is known as deflecting force. A syste which produces the deflecting force is known as a deflecting syste. Generally a deflecting syste converts an electrical signal to a echanical force. Fig.. Pointer scale 0

3 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION Magnitude effect When a current passes through the coil (Fig..), it produces a iaginary bar agnet. When a soft-iron piece is brought near this coil it is agnetized. Depending upon the current direction the poles are produced in such a way that there will be a force of attraction between the coil and the soft iron piece. This principle is used in oving iron attraction type instruent. Fig.. If two soft iron pieces are place near a current carrying coil there will be a force of repulsion between the two soft iron pieces. This principle is utilized in the oving iron repulsion type instruent..4. Force between a peranent agnet and a current carrying coil When a current carrying coil is placed under the influence of agnetic field produced by a peranent agnet and a force is produced between the. This principle is utilized in the oving coil type instruent. Fig Force between two current carrying coil When two current carrying coils are placed closer to each other there will be a force of repulsion between the. If one coil is ovable and other is fixed, the ovable coil will ove away fro the fixed one. This principle is utilized in electrodynaoeter type instruent.

4 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05.5 Controlling force Fig..4 To ake the easureent indicated by the pointer definite (constant) a force is necessary which will be acting in the opposite direction to the deflecting force. This force is known as controlling force. A syste which produces this force is known as a controlled syste. When the external signal to be easured by the instruent is reoved, the pointer should return back to the zero position. This is possibly due to the controlling force and the pointer will be indicating a steady value when the deflecting torque is equal to controlling torque. T d = T c (.).5. Spring control Two springs are attached on either end of spindle (Fig..5).The spindle is placed in jewelled bearing, so that the frictional force between the pivot and spindle will be iniu. Two springs are provided in opposite direction to copensate the teperature error. The spring is ade of phosphorous bronze. When a current is supply, the pointer deflects due to rotation of the spindle. While spindle is rotate, the spring attached with the spindle will oppose the oveents of the pointer. The torque produced by the spring is directly proportional to the pointer deflectionθ. T θ (.) C The deflecting torque produced T d proportional to I. WhenT C = Td, the pointer will coe to a steady position. Therefore θ I (.3)

5 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Fig..5 Since, θ and I are directly proportional to the scale of such instruent which uses spring controlled is unifor..6 Daping force The deflection torque and controlling torque produced by systes are electro echanical. Due to inertia produced by this syste, the pointer oscillates about it final steady position before coing to rest. The tie required to take the easureent is ore. To dap out the oscillation is quickly, a daping force is necessary. This force is produced by different systes. (a) Air friction daping (b) Fluid friction daping (c) Eddy current daping.6. Air friction daping The piston is echanically connected to a spindle through the connecting rod (Fig..6). The pointer is fixed to the spindle oves over a calibrated dial. When the pointer oscillates in clockwise direction, the piston goes inside and the cylinder gets copressed. The air pushes the piston upwards and the pointer tends to ove in anticlockwise direction. 3

6 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Fig..6 If the pointer oscillates in anticlockwise direction the piston oves away and the pressure of the air inside cylinder gets reduced. The external pressure is ore than that of the internal pressure. Therefore the piston oves down wards. The pointer tends to ove in clock wise direction..6. Eddy current daping Fig..6 Disc type An aluinu circular disc is fixed to the spindle (Fig..6). This disc is ade to ove in the agnetic field produced by a peranent agnet. 4

7 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 When the disc oscillates it cuts the agnetic flux produced by daping agnet. An ef is induced in the circular disc by faradays law. Eddy currents are established in the disc since it has several closed paths. By Lenz s law, the current carrying disc produced a force in a direction opposite to oscillating force. The daping force can be varied by varying the projection of the agnet over the circular disc. Fig..6 Rectangular type.7 Peranent Magnet Moving Coil (PMMC) instruent One of the ost accurate type of instruent used for D.C. easureents is PMMC instruent. Construction: A peranent agnet is used in this type instruent. Aluinu forer is provided in the cylindrical in between two poles of the peranent agnet (Fig..7). Coils are wound on the aluinu forer which is connected with the spindle. This spindle is supported with jeweled bearing. Two springs are attached on either end of the spindle. The terinals of the oving coils are connected to the spring. Therefore the current flows through spring, oving coil and spring. Daping: Eddy current daping is used. This is produced by aluinu forer. Control: Spring control is used. 5

8 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Fig..7 Principle of operation When D.C. supply is given to the oving coil, D.C. current flows through it. When the current carrying coil is kept in the agnetic field, it experiences a force. This force produces a torque and the forer rotates. The pointer is attached with the spindle. When the forer rotates, the pointer oves over the calibrated scale. When the polarity is reversed a torque is produced in the opposite direction. The echanical stopper does not allow the deflection in the opposite direction. Therefore the polarity should be aintained with PMMC instruent. If A.C. is supplied, a reversing torque is produced. This cannot produce a continuous deflection. Therefore this instruent cannot be used in A.C. Torque developed by PMMC Let T d =deflecting torque T C = controlling torque θ = angle of deflection K=spring constant b=width of the coil 6

9 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 l=height of the coil or length of coil N=No. of turns I=current B=Flux density A=area of the coil The force produced in the coil is given by F = BIL sinθ (.4) When θ = 90 For N turns, Torque produced Td T d = NBIL b = BINA F = NBIL (.5) F = r distance (.6) (.7) T d = BANI T d I (.8) (.9) Advantages Torque/weight is high Power consuption is less Scale is unifor Daping is very effective Since operating field is very strong, the effect of stray field is negligible Range of instruent can be extended Disadvantages Use only for D.C. Cost is high Error is produced due to ageing effect of PMMC Friction and teperature error are present 7

10 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION Extension of range of PMMC instruent Case-I: Shunt A low shunt resistance connected in parrel with the aeter to extent the range of current. Large current can be easured using low current rated aeter by using a shunt. Fig..8 Let R =Resistance of eter R sh =Resistance of shunt I = Current through eter I sh =current through shunt I= current to be easure V = V sh I R = I sh R sh (.0) I I sh R R sh = (.) Apply KCL at P Eq n (.) by I I I I + sh I I I + I = sh (.) = (.3) 8

11 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 I I R R = + (.4) sh R I = I + (.5) Rsh R + is called ultiplication factor Rsh Shunt resistance is ade of anganin. This has least theroelectric ef. The change is resistance, due to change in teperature is negligible. Case (II): Multiplier A large resistance is connected in series with volteter is called ultiplier (Fig..9). A large voltage can be easured using a volteter of sall rating with a ultiplier. Fig..9 Let I = I se R V V = se R Rse V se R = se V R =resistance of eter R se =resistance of ultiplier V =Voltage across eter V se = Voltage across series resistance V= voltage to be easured (.6) (.7) (.8) 9

12 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Apply KVL, V = V + Vse (.9) Eq n (.9) V V V V + se R = + se (.0) V R = R V = V + se (.) R R + se Multiplication factor R.8 Moving Iron (MI) instruents One of the ost accurate instruent used for both AC and DC easureent is oving iron instruent. There are two types of oving iron instruent. Attraction type Repulsion type.8. Attraction type M.I. instruent Construction: The oving iron fixed to the spindle is kept near the hollow fixed coil (Fig..0). The pointer and balance weight are attached to the spindle, which is supported with jeweled bearing. Here air friction daping is used. Principle of operation The current to be easured is passed through the fixed coil. As the current is flow through the fixed coil, a agnetic field is produced. By agnetic induction the oving iron gets agnetized. The north pole of oving coil is attracted by the south pole of fixed coil. Thus the deflecting force is produced due to force of attraction. Since the oving iron is attached with the spindle, the spindle rotates and the pointer oves over the calibrated scale. But the force of attraction depends on the current flowing through the coil. Torque developed by M.I Let θ be the deflection corresponding to a current of i ap Let the current increases by di, the corresponding deflection is θ + 0

13 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Fig..0 There is change in inductance since the position of oving iron change w.r.t the fixed electroagnets. Let the new inductance value be L+dL. The current change by di is dt seconds. Let the ef induced in the coil be e volt. d di dl e = ( Li) = L + i (.) dt dt dt Multiplying by idt in equation (.) di dl e idt = L idt + i idt (.3) dt dt e idt = Lidi + i dl (.4) Eq n (.4) gives the energy is used in to two fors. Part of energy is stored in the inductance. Reaining energy is converted in to echanical energy which produces deflection. Fig..

14 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Change in energy stored=final energy-initial energy stored = ( L + dl)( i + di) = = {( L + dl)( i Li {( L + dl)( i + di + idi) Li = { Li + Lidi + i + idi) Li } } dl + ididl Li } = { Lidi + i dl } = Lidi + i dl Mechanical work to ove the pointer by d θ = T d By law of conservation of energy, Electrical energy supplied=increase in stored energy+ echanical work done. (.5) (.6) Input energy= Energy stored + Mechanical energy Lidi + i dl = Lidi + i dl + Td i dl = Td T d = i dl At steady state condition T d = TC i dl Kθ = θ = i K dl (.7) (.8) (.9) (.30) (.3) θ i (.3) When the instruents easure AC, θ i rs Scale of the instruent is non unifor.

15 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Advantages MI can be used in AC and DC It is cheap Supply is given to a fixed coil, not in oving coil. Siple construction Less friction error. Disadvantages It suffers fro eddy current and hysteresis error Scale is not unifor It consued ore power Calibration is different for AC and DC operation.8. Repulsion type oving iron instruent Construction: The repulsion type instruent has a hollow fixed iron attached to it (Fig..). The oving iron is connected to the spindle. The pointer is also attached to the spindle in supported with jeweled bearing. Principle of operation: When the current flows through the coil, a agnetic field is produced by it. So both fixed iron and oving iron are agnetized with the sae polarity, since they are kept in the sae agnetic field. Siilar poles of fixed and oving iron get repelled. Thus the deflecting torque is produced due to agnetic repulsion. Since oving iron is attached to spindle, the spindle will ove. So that pointer oves over the calibrated scale. Daping: Air friction daping is used to reduce the oscillation. Control: Spring control is used. 3

16 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Fig...9 Dynaoeter (or) Electroagnetic oving coil instruent (EMMC) Fig..3 4

17 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 This instruent can be used for the easureent of voltage, current and power. The difference between the PMMC and dynaoeter type instruent is that the peranent agnet is replaced by an electroagnet. Construction: A fixed coil is divided in to two equal half. The oving coil is placed between the two half of the fixed coil. Both the fixed and oving coils are air cored. So that the hysteresis effect will be zero. The pointer is attached with the spindle. In a non etallic forer the oving coil is wounded. Control: Spring control is used. Daping: Air friction daping is used. Principle of operation: When the current flows through the fixed coil, it produced a agnetic field, whose flux density is proportional to the current through the fixed coil. The oving coil is kept in between the fixed coil. When the current passes through the oving coil, a agnetic field is produced by this coil. The agnetic poles are produced in such a way that the torque produced on the oving coil deflects the pointer over the calibrated scale. This instruent works on AC and DC. When AC voltage is applied, alternating current flows through the fixed coil and oving coil. When the current in the fixed coil reverses, the current in the oving coil also reverses. Torque reains in the sae direction. Since the current i and i reverse siultaneously. This is because the fixed and oving coils are either connected in series or parallel. Torque developed by EMMC Fig..4 5

18 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Let L =Self inductance of fixed coil L = Self inductance of oving coil M=utual inductance between fixed coil and oving coil i = current through fixed coil i =current through oving coil Total inductance of syste, L total = L + L M + But we know that in case of M.I d( L) T d = i d T d = i ( L + L + M ) The value of L and L are independent of θ but M varies with θ dm T d = i dm T d = i If the coils are not connected in series i i T d = i i T C = T d θ = i dm i dm K (.33) (.34) (.35) (.36) (.37) (.38) (.39) (.40) Hence the deflection of pointer is proportional to the current passing through fixed coil and oving coil. 6

19 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION Extension of EMMC instruent Case-I Aeter connection Fixed coil and oving coil are connected in parallel for aeter connection. The coils are designed such that the resistance of each branch is sae. Therefore = I I = I Fig..5 To extend the range of current a shunt ay be connected in parallel with the eter. The value R sh is designed such that equal current flows through oving coil and fixed coil. T d = I I dm dm Or T d = I T C = Kθ θ = dm K I (.4) (.4) (.43) (.44) θ I (Scale is not unifor) (.45) Case-II Volteter connection Fixed coil and oving coil are connected in series for volteter connection. A ultiplier ay be connected in series to extent the range of volteter. 7

20 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 V V I =, I = Z Z Fig..6 (.46) V V dm T d = (.47) Z Z K V K V dm T d = (.48) Z Z KV T d = Z Z T d V dm (.49) (.50) θ V (Scale in not unifor) (.5) Case-III As watteter When the two coils are connected to parallel, the instruent can be used as a watteter. Fixed coil is connected in series with the load. Moving coil is connected in parallel with the load. The oving coil is known as voltage coil or pressure coil and fixed coil is known as current coil. Fig..7 8

21 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 Assue that the supply voltage is sinusoidal. If the ipedance of the coil is neglected in coparison with the resistance R. The current, v wt I sin = R (.5) Let the phase difference between the currents I and I is φ I = I sin( wt φ) T d = I I T d = I dm V sin( wt φ) sin wt R dm dm Td = ( IV sin wt sin( wt φ)) R Td = IV sin wt.sin( wt φ) R The average deflecting torque dm d θ (.53) (.54) (.55) (.56) (.57) Π ( Td ) avg = Td d( wt) (.58) Π Π 0 dm ( Td ) avg = IV wt wt d( wt) Π sin.sin( φ ) (.59) R 0 = V I dm ( T Π wt R d dwt d ) avg {cosφ cos( φ)} θ (.60) ( T Π Π V I dm = Π cosφ. dwt cos(wt φ) dwt 4 R 0 0 d ) avg. Π [ cosφ[ ] 0 ] VI dm ( Td ) avg = wt 4ΠR VI dm ( Td ) avg = φ 4ΠR [ cos (Π 0) ] VI dm ( Td ) avg = cosφ R (.6) (.6) (.63) (.64) dm ( Td ) avg = Vrs Irs cosφ (.65) R 9

22 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05 ( T ) KVI cosφ d avg (.66) T C θ (.67) θ KVI cosφ θ VI cosφ (.68) (.69) Advantages It can be used for volteter, aeter and watteter Hysteresis error is nill Eddy current error is nill Daping is effective It can be easure correctively and accurately the rs value of the voltage Disadvantages Scale is not unifor Power consuption is high(because of high resistance ) Cost is ore Error is produced due to frequency, teperature and stray field. Torque/weight is low.(because field strength is very low) Errors in PMMC The peranent agnet produced error due to ageing effect. By heat treatent, this error can be eliinated. The spring produces error due to ageing effect. By heat treating the spring the error can be eliinated. When the teperature changes, the resistance of the coil vary and the spring also produces error in deflection. This error can be iniized by using a spring whose teperature co-efficient is very low..0 Difference between attraction and repulsion type instruent An attraction type instruent will usually have a lower inductance, copare to repulsion type instruent. But in other hand, repulsion type instruents are ore suitable for econoical production in anufacture and nearly unifor scale is ore easily obtained. They are therefore uch ore coon than attraction type. 30

23 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 05. Characteristics of eter.. Full scale deflection current( I FSD ) The current required to bring the pointer to full-scale or extree right side of the instruent is called full scale deflection current. It ust be as sall as possible. Typical value is between µ A to 30A... Resistance of the coil( R ) This is ohic resistance of the oving coil. It is due to ρ, L and A. For an aeter this should be as sall as possible...3 Sensitivity of the eter(s) Z S = ( Ω / volt), S = IFSD V It is also called ohs/volt rating of the instruent. Larger the sensitivity of an instruent, ore accurate is the instruent. It is easured in Ω/volt. When the sensitivity is high, the ipedance of eter is high. Hence it draws less current and loading affect is negligible. It is also defend as one over full scale deflection current.. Error in M.I instruent.. Teperature error Due to teperature variation, the resistance of the coil varies. This affects the deflection of the instruent. The coil should be ade of anganin, so that the resistance is alost constant... Hysteresis error Due to hysteresis affect the reading of the instruent will not be correct. When the current is decreasing, the flux produced will not decrease suddenly. Due to this the eter reads a higher value of current. Siilarly when the current increases the eter reads a lower value of current. This produces error in deflection. This error can be eliinated using sall iron parts with narrow hysteresis loop so that the deagnetization takes place very quickly...3 Eddy current error The eddy currents induced in the oving iron affect the deflection. This error can be reduced by increasing the resistance of the iron. 3

24 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION Stray field error Since the operating field is weak, the effect of stray field is ore. Due to this, error is produced in deflection. This can be eliinated by shielding the parts of the instruent...5 Frequency error When the frequency changes the reactance of the coil changes. Z = ( R + RS ) + X L (.70) I = V Z = V ( R + RS ) + X L (.7) Fig..8 Deflection of oving iron volteter depends upon the current through the coil. Therefore, deflection for a given voltage will be less at higher frequency than at low frequency. A capacitor is connected in parallel with ultiplier resistance. The net reactance, ( X X ) is very sall, when copared to the series resistance. Thus the circuit ipedance is ade independent of frequency. This is because of the circuit is alost resistive. C = 0.4 ( L R S ).3 Electrostatic instruent L C (.7) In ulti cellular construction several vans and quadrants are provided. The voltage is to be easured is applied between the vanes and quadrant. The force of attraction between the vanes 3

Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 12 Solutions

Concept Check (top) Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 12 Solutions Student Book page 583 Concept Check (botto) The north-seeking needle of a copass is attracted to what is called