Sine waves by far the most important form of alternating quantity important properties are shown below

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Miles Cross
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1 AC DC METERS 1

2 Sine waves by far the most important form of alternating quantity important properties are shown below 2

3 Average value of a sine wave average value over one (or more) cycles is clearly zero however, it is often useful to know the average magnitude of the waveform independent of its polarity we can think of this as the average value over half a cycle or as the average value 1 of the rectified signal Vav Vpsin dθ 0 Vp cos 0 2V p Vp 3

4 r.m.s. values are useful because their relationship to average power is similar to the corresponding DC values P V av rms I rms P av V 2 rms R P av I rms 2 R 4

5 Form factor for any waveform the form factor is defined as for a sine wave this gives Form factor r.m.s. value average value Form 0.707V factor p 0.637V p

6 Peak factor for any waveform the peak factor is defined as Peak factor peak value r.m.s. value Peak factor V p V p

7 . classification of analog meters:4m The main types of instrument used as ammeters and voltmeters are as follows: Permanent magnet moving coil instrument (PMMC) Electro dynamometer type instruments. Moving Iron type instruments Attraction type moving iron instruments. Repulsion type moving iron instruments Thermocouple instruments. Electrostatic instruments. Induction instruments. Hot wire Instruments. 7

8 CLASSIFICATION OF INSTRUMENTS Electrical measuring instruments may also be classified according to the kind of quantity, kind of current, principle of operation of moving system. CLASSIFICATION OF SECONDARY INSTRUMENTS Secondary instruments can be classified into three types; i. Indicating instruments; ii. Recording instruments; iii. Integrating instruments. 8

9 CLASSIFICATION OF SECONDARY INSTRUMENTS - Indicating Instruments: It indicate the magnitude of an electrical quantity at the time when it is being measured. The indications are given by a pointer moving over a graduated dial. 9

10 CLASSIFICATION OF SECONDARY INSTRUMENTS - Recording Instruments: The instruments which keep a continuous record of the variations of the magnitude of an electrical quantity to be observed over a defined period of time. 10

11 CLASSIFICATION OF SECONDARY INSTRUMENTS - Integrating Instruments: The instruments which measure the total amount of either quantity of electricity or electrical energy supplied over a period of time. For example energy meters. 11

12 Analog meters are characterized by the fact that they use a pointer and scale to indicate their value. One of the common types of meters uses the d Arsonval type of meter movement. Analog meters use a moving coil placed between the poles of a magnet. 12

13 Shunt resistance ammeter. 13

14 The basic movement of dc ammeter circuit consists of D Arsonval galvanometer. When large current is to be measured then some extra modification is required. For measurement of large current by using same movement a shunt resistor is connected as shown in circuit. The value of shunt resistor is very small so that most of the current pass through it and only small current allow to pass through the coil. The coil winding of basic movement is small and light therefore it carries very small current. 14

15 The voltage across the shunt and movement must be same. V sh =V m IshRsh=ImRm R sh =I m R m /I sh R sh =I m R m /(I-I m ) 15

16 A 2mA meter with an internal resistance of 100Ω is to be converted to 0-150mA ammeter. Calculate the value of shunt resistance required. Given: I m =2mA, R m = 100 Ω, I= 150mA To find: R sh =? Solution: m= I/I m = 150mA/ 2mA= 150/2 =75 R sh = 1/ m-1 x R m 1/ 75-1 x /74 R sh = 1.35Ω 16

17 Calculate the value of multiplier resistance on the 50V range of a dc voltmeter that uses a 200μA meter movement with an internal resistance of 100Ώ. 17

18 Given: I fsd = I m = 200 μa = 200X 10-6 A R m = 100Ώ V = 50V solution: R S1 = V/ I fsd R m (50/ 200 X 10-6 ) X 10 3 Ώ R S1 = 249 kώ 18

19 Why ammeter never connected across source of emf? Justify. 19

20 1.While connecting an ammeter across the emf source always a series resistance should be used. 2. This is necessary to limit the current passing through the meter movement maybe damaged. This is because the meter is having a small internal resistance. So it maydraw very high current from the emf source. 3. The polarity of the meter should be first observed and then it should be connected 20

21 MULTIRANGE AMMETER 21

22 Aytron shunt type ammeter 22

23 When switch is at 100mA range position, the series combination of R1,R2,R3 is in parallel with meter resistance Rm. Hence I1(R1+R2+R3) = Im Rm (1) When switch is at 500mA range position, The resistor R2 and R3 are in parallel with R1& Rm Hence I2(R2+R3) = Im( R1+ Rm ) (2) when switch is at 1A position The resistor R3 is in parallel combination with R1+R2+R3 Hence I3(R3) = Im (R1+ R2 + R3 ) (3) 23

24 Design a multi range DC ammeter using a basic movement with an internal resistance R m =50Ω and full scale deflection current I m = LmA. The range required are 0-10 ma, 0-50 ma, ma, 0-500mA. Ans Given= R m =50Ω I m = 10mA - Consider I 1 = 10mA, I 2 = 50mA, I 3 = 100mA, I 4 = 500mA R sh1 =?, R sh2 =? R sh3 =? R sh4 =? m 1 = I 1 / I m = 10 ma/ 1mA = 10 R sh1 = R m / m 1-1= 50/ 10-1= 50/9= 5.55Ω m 2 = I 2 / I m = 50 ma/ 1mA = 50 R sh2 = R m / m 2-1= 50/ 50-1= 50/49= 1.02Ω 24

25 m 3 = I 3 / I m = 100 ma/ 1mA = 100 R sh3 = R m / m 3-1 = 50/ = 50/39= 0.505Ω m 4 = I 4 / I m = 500 ma/ 1mA = 500 R sh4 = R m / m 4-1 = 50/ = 50/9= 0.100Ω R sh1 = 5.55Ω R sh2 = 1.02Ω R sh3 = 0.505Ω R sh4 = 0.100Ω 25

26 A basic D Arsonval movement withan internal resistance of 50Ω and a full scale deflection current of 2mA is to be used as multirangevoltmeter. Design a series of string of multipliers to obtain the voltage ranges of 0-10V, 0-50V. Given: R m = 50Ω I fsd = I m = 2mA To find: a) R s1 b) R s2 26

27 For range (0-10V), V 1 =10V Therefore, R s1 = V 1 / I fsd R m = 10/ 2x Ω R s1 = 4.95kΩ For range (0-50V), V 2 =50V Therefore, R s2 = V 2 / I fsd R m = 50/ 2x Ω R s2 =24.95kΩ 27

28 Sensitivity is high as compared to normal shunt type ammeter 28

29 Basic DC voltmeter 29

30 2.4: A DC VOLTMETER A basic D Arsonval movement can be converted into a DC voltmeter by adding a series resistor (multiplier) as shown in Figure. V + Rs Multiplier Im Rm _ : Basic DC Voltmeter Im =full scale deflection current of the movement (Ifsd) Rm=internal resistance of the movement Rs =multiplier resistance V =full range voltage of the instrument 30

31 From the circuit of Figure V I ( R R ) m s m R s V I I m m R m V I m R m V R s I m R m 31

32 A basic D Arsonval movement with a full-scale deflection of 50 ua and internal resistance of 500Ω is used as a DC voltmeter. Determine the value of the multiplier resistance needed to measure a voltage range of 0-10V. Solution: R V I R 10V uA s m 5 m k 32

33 Sensitivity and voltmeter range can be used to calculate the multiplier resistance, Rs of a DC voltmeter. Rs=(S x Range) - Rm From example 2.4: Im= 50uA, Rm=500Ω, Range=10V Sensitivity, S 1 I m 1 50uA 20k / V So, Rs = (20kΩ/V x 10V) 500 Ω = kω 33

34 2.5: MULTI-RANGE VOLTMETER A DC voltmeter can be converted into a multirange voltmeter by connecting a number of resistors (multipliers) in series with the meter movement. A practical multi-range DC voltmeter is R1 R2 R3 R4 shown in Figure 2.6. V1 V2 V3 Rm Im + V4 _ Figure 2.6: Multirange voltmeter 34

35 PMMC instruments 35

36 Basic d Arsonval meter movement. 36

37 Basic d Arsonval meter movement with rectifier to change AC voltage to DC voltage. 37

38 Construction: A coil of thin wire is mounted on an aluminum frame (spindle) positioned between the poles of a U shaped permanent magnet which is made up of magnetic alloys like alnico. The coil is pivoted on the jewelled bearing and thus the coil is free to rotate. The current is fed to the coil through spiral springs which are two in numbers. The coil which carries a current, which is to be measured, moves in a strong magnetic field produced by a permanent magnet and a pointer is attached to the spindle which shows the measured value. 38

39 Principle of Operation When a current carrying conductor is placed in a magnetic field, it experiences a force and tends to move in the direction as per Fleming s left hand rule. 39

40 Advantages of PMMC meter: It has uniform scale. Power consumption is low It can be obtained in wide ranges. High sensitivity & accuracy It is unaffected by external magnetic field. Additional damping device not required. Hysteresis problem is not there. 40

41 Torques which deflect the pointer from its zero position is known as deflecting torque. The deflecting of pointer is directly proportional to quantity to be measured. The deflection torque produced due to current flowing through coil. Let length of coil be L meter and width of coil be d meter. Assume, I is the current flowing through coil having N turn. B is consider as flux density produce in air gap. Therefore the force exerted by coil is Where, A = l x d = Area of coil former. F= BiL The deflecting torque is given by Td = Force x distance Td = F x S = B x l x I x N x d (1) Td = B x A x I x N (2) Where, A = l x d = Area of coil former. 41

42 Disadvantages of PMMC meter: 1.It is suitable for d.c. measurement only. 2.Comparatively highcost than moving iron type instrument. 3. Ageing of permanentmagnet & spring introduce errors. 4. Friction due to jewel- pivot suspension. 42

43 Applications: Ammeter: Voltmeter: Ohm Meter: 43

44 Sensitivity AND Loading effect of voltmeter. The sensitivity of voltmeter means the response given by a voltmeter to input signal. It is the ratio of total resistance (RT) to the voltage range S = RT / V Where, RT Total resistance RT = RS + Rm V= Voltage range. OR It is also defined as the reciprocal of full scale deflection current of the basic movement. S = 1 / I fsd I fsd = full scale deflection current. 44

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46 Rectifier type AC voltmeter 46

47 Basic rectifier type AC voltmeter is a general rectifier type of voltmeter. In this case for the rectification action two diodes namely D1 and D2 are used. An a.c input signal to be measured is applied. If a current passing through the diode is small then there is a non- linearity problem. But for higher current the diode shows linearity. So to increase the current passing through diode; a resistance R2 is connected in parallel with the meter. Now during positive half cycle of input signal, diode D1 is forward biased with the polarities. 47

48 While the diode D2 is reversed biased. So during this cycle the current passes the deflection.rough diode D1 and the meter. Thus the meter shows During the negative half cycle diode D1 is reversed biased and diode D2 is forward biased. So the current flows in opposite direction. In this case the meter is bypassed. Because of the diode action an a.c input signal is converted into pulsating dc. Thus the meter shows average value of an input signal. 48

49 full wave rectifier type AC voltmeter. 49

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52 Here high stabilized amplifier is used to provide the amplification. The one terminal of stabilized amplifier is connected to the attenuator network which consists of five resistors. The other terminal is connected with feedback path. Capacitor is used to block d.c entering into stabilized non linearity problem created by diodes. Also the in impedance meter is compensated by negative variation feedback. The D.C. milliammeter is calibrated in terms. The average obtained by filtering the signal coming gives reading is from the rectifier. Thus for meter movement gives response to average value. 52

53 Analog Multimeter. 53

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Half-wave Rectifier AC Meters

Note-4 1 Half-wave Rectifier AC Meters Disadvantages: 1. In negative half-cycle, reverse current flows through the circuit reduces average value of current meter reads lower than actual. 2. High peak inverse