AC DC METERS 1
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AC DC METERS
1
Sine waves
by far the most important form of alternating quantity
important properties are shown below
2
Average value of a sine wave
average value over one (or more) cycles is clearly zerohowever, it is often useful to know the average magnitude of the waveform independent of its polarity
we can think of this asthe average value over half a cycle…… or as the average valueof the rectified signal
p
p
p
pav
VV
V
VV
637.02
cos
θdsin1
0
0
3
r.m.s. values are useful because their relationship to average power is similar to the corresponding DC values
rmsrmsavIVP
RV
P rmsav
2
RIPrmsav
2
4
Form factorfor any waveform the form factor is defined as
for a sine wave this gives
value averagevalue r.m.s.factor Form
11.1 0.637
0.707factor Form
pVpV
5
Peak factorfor any waveform the peak factor is defined as
value r.m.s.value peak
factor Peak
414.1 0.707
factor Peak p
Vp
V
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. 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.
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CLASSIFICATION OF INSTRUMENTSElectrical measuring instruments may also be classified
according to the kind of quantity, kind of current, principle ofoperation of moving system.
CLASSIFICATION OF SECONDARY INSTRUMENTS
• Secondary instruments can be classified into threetypes;
i. Indicating instruments;
ii. Recording instruments;
iii. Integrating instruments.
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CLASSIFICATION OF SECONDARY INSTRUMENTS
- Indicating Instruments:
It indicate the magnitude of an electricalquantity at the time when it is being measured. Theindications are given by a pointer moving over a graduateddial.
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CLASSIFICATION OF SECONDARY INSTRUMENTS
- Recording Instruments:
The instruments which keep acontinuous record of the variations of the magnitude of anelectrical quantity to be observed over a defined period oftime.
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CLASSIFICATION OF SECONDARY INSTRUMENTS
- Integrating Instruments:
The instruments which measure the totalamount of either quantity of electricity or electrical energysupplied over a period of time. For example energy meters.
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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.
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Shunt resistance ammeter.
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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.
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Vsh=Vm
IshRsh=ImRm
Rsh=ImRm/Ish
Rsh=ImRm/(I-Im)
The voltage across the shunt and movement must be same.
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•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: Im=2mA, Rm= 100 Ω, I= 150mATo find: Rsh=?
Solution: m= I/Im= 150mA/ 2mA= 150/2 =75Rsh= 1/ m-1 x Rm
1/ 75-1 x 100
100/74Rsh= 1.35Ω
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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.
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Given: Ifsd = Im = 200 μA
= 200X 10-6 A
Rm = 100Ώ
V = 50V
solution:
RS1 = V/ Ifsd – Rm
•(50/ 200 X 10-6 ) – 100
•250000 – 100
•249900
•249X 103 Ώ
RS1 = 249 kΏ
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Why ammeter never connected across source of emf ? Justify.
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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
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MULTIRANGE AMMETER
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Aytron shunt type ammeter
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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& RmHence I2(R2+R3) = Im( R1+ Rm )---------------------(2)when switch is at 1A position
The resistor R3 is in parallel combination with R1+R2+R3Hence I3(R3) = Im (R1+ R2 + R3 )---------------------(3)
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Design a multi range DC ammeter using a basic movement with an internal resistance Rm =50Ω and full scale deflection current Im = LmA. The range required are 0-10 mA, 0-50 mA, 0-100 mA, 0-500mA.
Ans
Given= Rm =50ΩIm =10mA-…… ConsiderI1= 10mA, I2= 50mA, I3= 100mA, I4= 500mARsh1=? , Rsh2=? Rsh3=? Rsh4=?
m1= I1/ Im= 10 mA/ 1mA = 10
Rsh1= Rm/ m1-1= 50/ 10-1= 50/9= 5.55Ω
m2= I2/ Im= 50 mA/ 1mA = 50
Rsh2= Rm/ m2-1= 50/ 50-1= 50/49= 1.02Ω
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• m3= I3/ Im= 100 mA/ 1mA = 100
Rsh3= Rm/ m3-1
= 50/ 100-1
= 50/39= 0.505Ω
m4= I4/ Im= 500 mA/ 1mA
= 500
Rsh4= Rm/ m4-1
= 50/ 500-1
= 50/9= 0.100ΩRsh1 = 5.55ΩRsh2= 1.02ΩRsh3= 0.505ΩRsh4= 0.100Ω
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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: Rm= 50ΩIfsd= Im= 2mATo find: a) Rs1 b) Rs2
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For range (0-10V), V1=10V
Therefore,
Rs1= V1/ Ifsd – Rm
= 10/ 2x10-3 -50
•5000-50
•4950Ω
Rs1= 4.95kΩFor range (0-50V), V2=50VTherefore,
Rs2= V2/ Ifsd – Rm = 50/ 2x10-3 -5025000-5024950Ω
Rs2=24.95kΩ
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•Sensitivity is high as compared to normal shunt type
ammeter
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Basic DC voltmeter
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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 .
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
Rs
Im
RmMultiplier
V
+
_: Basic DC Voltmeter
m
m
s
m
mm
mms
msm
RI
VR
RI
V
I
RIVR
RRIV
)(
From the circuit of Figure
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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.
kuA
VR
I
VR m
m
s 5.19950050
10
Solution:
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Sensitivity and voltmeter range can be used to calculate the multiplier resistance, Rs of a DC voltmeter.
Rs=(S x Range) - RmFrom example 2.4:
Im= 50uA, Rm=500Ω, Range=10VSensitivity,
VkuAI
Sm
/2050
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So, Rs = (20kΩ/V x 10V) – 500 Ω= 199.5 kΩ
33
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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 shown in Figure 2.6.
Figure 2.6: Multirange voltmeter
R1 R2 R3 R4
+
_
V1V2
V3
V4
Rm
Im
PMMC instruments
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Basic d’Arsonval meter movement.
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Basic d’Arsonval meter movement with rectifier to change AC voltage to DC voltage.
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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.
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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.
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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.
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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.
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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 introduceerrors.
4. Friction due to jewel- pivot suspension.
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Applications:
Ammeter:Voltmeter:Ohm Meter:
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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
rangeS = RT / VWhere, RT – Total resistance…… RT = RS + RmV= Voltage range.
ORIt is also defined as the reciprocal of full scale deflection current of the basic movement.S = 1 / Ifsd
Ifsd = full scale deflection current.
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Rectifier type AC voltmeter
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•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; aresistance R2 is connected in parallel with the meter.Now during positive half cycle of input signal, diode D1 is forward biased with the polarities.
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•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.
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full wave rectifier type AC voltmeter.
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50
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diodes. Also the
variation
in impedance meter is compensated by negative
feedback.
The D.C. milliammeter is calibrated in terms.
The average
reading is
obtained by filtering the signal coming gives
from the rectifier.
Thus for meter
movement gives response to average value.
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
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Analog Multimeter.
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