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Module 02:Electrical Instruments
Reference Text books:1. Basic Electrical Engineering by D. C.
Kulshreshtha2. A Course in Electrical & Electronic
Measurements & Instrumentation by A. K. Sawhney
Tuesday, 16 August 2011 Measuring Instruments 2
Measuring InstrumentsClassification1. Absolute instruments:-
Gives the magnitude of the quantity in terms of the constants of the instrumentsExample :-A tangent galvanometer, measures current in terms of the tangent of the angle of deflection produced by the current, radius & no. of turns of the galvanometer
2. Secondary instruments:-These have to be calibrated by comparison with an absolute instrument
Classification of Secondary Instruments
1. Indicating instruments Ordinary voltmeters, ammeters & wattmeter's.
2. Recording instruments X-Y plotter e.g. ECG (Electro-Cardio-Gram).
3. Integrating instruments Ampere-hour meter, watt-hour (energy) meter
and odometer in a car (which measures the total distance covered)
Indicating Instruments
Principle of Operation
• Different effects like Magnetic effect, Thermal effect (thermocouple is used), Electrostatic effect, Induction Effect (disc or drum), Hall effect
Essentials of an Indicating InstrumentsIn order to ensure proper operation of indicating instruments. Three torque are needed
(i) Deflecting torque– It is produced by use of magnetic field, heating, chemical, electromagnetic or electrostatic effect of current and voltage to be measured.
(ii) Controlling torque (By Spring or gravity)- It is opposing the deflecting torque and increases with deflection. It is produced by either spring or gravity. for spring control Tc α θ for gravity control Tc α sinθ where θ- deflection
The controlling torque serves two functions : (i) the pointer stops moving beyond the final deflection, (ii) the pointer comes back to its zero position when the instrument is disconnected.
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 7
(i) Spring Control • Most commonly used.• One or two hairsprings made of phosphor bronze are used.• The outer end of this spring is fixed to the pointer and the
inner end is attached with the spindle. • When the pointer is at zero of the scale, the spring is normal. • As the pointer moves, the spring winds and produces an
opposing torque. • The balance-weight balances the moving system so that its
centre of gravity coincides with the axis of rotation, thereby reducing the friction between the pivot and bearings.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 8 Next
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 9
• Advantages :• Since
• These instruments have uniform scale.
• Disadvantages :• The stiffness of the spring is a function of temperature.• Hence, the readings given by the instruments are
temperature dependent. • Furthermore, with the usage the spring develops an inelastic
yield which affects the zero position of the moving system.
c d c dand ; at final position, I Hence, I
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(i) Spring Control
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 10
• Two springs A and B are wound in opposite directions.
• On deflection, one spring winds while the other unwinds.
• The controlling torque produced is due to the combined torsions of the two springs.
• To make the controlling torque directly proportional to the angle of deflection, the springs should have fairly large number of turns.
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Double Springs
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 11
Double Springs
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(ii) Gravity Control
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 13
• A small control weight is attached to the moving system.
• In addition, an adjustable balance weight is also attached to make the centre of gravity pass through the spindle.
• In zero position of the pointer, this control weight is vertical.
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(ii) Gravity Control
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 14
When deflected by an angle θ, the weight exerts a force,
The restraining or controlling torque is thus developed is given as
sinW
c sin sinW L WL
d c dSince , and
or sin
I
WL kI
sin
or sin
WLI
k
I
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 15
Disadvantage :
1. These do not have uniform scale. 2. These must be used in vertical position so that the control
may operate properly.
Advantages :
1. Less expensive.2. Unaffected by changes in temperature.3. Free from fatigue or deterioration with
time.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 16
Due to inertia of the system, the pointer moves ahead to position A, before coming to rest.
This way the pointer keeps oscillating about its final steady-state position with decreasing amplitude.
It settles at its final steady-state position when all its energy is dissipated in friction.
The situation described above is very annoying.
Moreover, for every change in the magnitude of the quantity being measured, one has to wait for some time.
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Damping Torque
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 17
Damping Torque
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 18
• The remedy lies in providing a suitable damping torque.
• If over-damped, the time-delay in taking the reading becomes unnecessarily long.
• If under damped, the oscillations of the pointer would not be killed completely.
• Thus, the damping torque should be just sufficient to kill the oscillation without increasing the delay-time.
• This condition is said to be critically damped or ‘dead beat’.
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Damping Torque
Methods for obtaining Damping Torques
1. Air Friction Damping Torques2. Fluid Friction Damping3. Eddy Current Damping (Most commonly
employed method)
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 20
MOVING COIL INSTRUEMNTS
• There are two types :(1) Permanent Magnet Type : It is the most accurate and useful for dc measurements. Popularly known as d’Arsonval Movement.(2) Dynamometer Type : It can be used for both dc and ac measurements.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 21
PMMC• It consists of an iron-core coil
mounted on bearings between permanent magnet
• Very fine insulated wire of many turns is used
• Coil is wound on an aluminium bobbin which is free to rotate by about 90◦
• An aluminium pointer attached to the coil can move on a calibrated scale.
• Two springs one at top and other at bottom were attached to the assembly and serves two purposes
• One is to provide path for current and other for providing controlling torque.
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 22
PMMC• Core is made of soft iron• Magnetic poles & iron core are
cylindrical in shape. This has two advantages
• Firstly, the length of the air gap is reduced (flux leakage=0)
• Secondly, the iron core helps in making the field radial in the air gap which ensures uniform magnetic field throughout the motion of the coil.
• This way the angle of deflection is proportional to the current in the coil and hence the scale is uniform
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 23
PMMC• When a current is passed through a
coil in a magnetic field, the coil experiences a torque proportional to the current.
• A coil spring provides the controlling torque.
• The deflection of a needle attached to the coil is proportional to the current.
• Such "meter movements" are at the heart of the moving coil meters such as voltmeters and ammeters.
• Now they were largely replaced with solid state meters.
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 24
How the Deflection Torque is Produced
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 25
• Consider a single turn PQ of the current carrying coil.
• The outward current in P set up a counterclockwise magnetic field.
• Thus, the field on the lower side is strengthened and on upper side weakened.
• The inward current in Q, on the other hand, strengthens the field on the upper side while weakens it on the lower side.
• The coil experience forces F-F.
• If d is the width of the coil
( / 2) ( / 2)F d F d Fd
PMMC
• Since the force F=NIBL , is directly proportional to the current I and to the flux density B in the air gap, the net deflecting torque=NIBA, Where A = area of the coil=Ld
• The controlling torque of the spiral springs (with c as spring constant)
• In the final steady position,
• The deflection is proportional to the current and hence the scale is uniformly divided
d kI
c c
orc d
kc kI I
c
PMMC
• The coil is suspended by a phosphor-bronze filament at the top
• A small mirror is attached to the suspension & a light beam is thrown on it
• Reflected light beam falls on calibrated scale
• When current passed through the coil , the coil deflect by an angle θ and the light beam rotates by 2θ and the beam moves on the scale.
Increasing sensitivity of PMMC
This way even a small deflection makes the light beam move over the scale by large distance providing high sensitivity to the instrument
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 28
Advantages :(i) High sensitivity.(ii) Uniform scale.(iii) Well shielded from any stray magnetic field.(iv) High torque/weight ratio.(v) Effective and reliable eddy-current damping.
Disadvantages :(i) Cannot be used for ac measurement.(ii) More expensive compared to moving-iron type.(iii) Ageing of control springs and of the permanent
magnets might cause errors.
PMMC
DYNAMOMETER TYPE INSTRUMENTSFor both ac & dc measurements
• These instruments are similar to the permanent magnet type instruments, except that the permanent magnet is replaced by a fixed coil.
• The coil is divided into two halves, connected in series with the moving coil.
• The two halves of the coil are placed close together and parallel to each other to provide uniform field within the range of the movement of moving coil.
DYNAMOMETER TYPE INSTRUMENTS
Dynamometer Type Instruments
• The deflecting torque depends on the fields of both fixed and moving coils
• Deflecting torque is proportional to square of the current.
• Moving coil is wound using a thin wire so that it deflects easily.
• Can be used as Voltmeter or Ammeter
• Best suits as a power meter
DYNAMOMETER TYPE-Ammeter & Voltmeter
Dynamometer Type WATTMETER
Dynamometer Type Wattmeter
Dynamometer Type InstrumentsAdvantages :(i) Can be used on both DC and AC systems(ii) No errors due to hysteresis or eddy currents(iii)Good accuracy(iv)Same calibration for DC and AC measurements and hence can be used as
Transfer Instruments ( used in situations where you can not measure directly. The measurement is transferred to another means of measurement)
Disadvantages :(i) Non-uniform scale
(ii) Torque/weight ratio is small(iii)Low sensitivity than PMMC(iv)More expensive than PMMC
MOVING-IRON INSTRUMENTSFor both ac & dc measurements
• Attraction (or Single-iron) Type Moving-Iron Instrument
MOVING-IRON INSTRUMENTSFor both ac & dc measurements
• Working of Moving-Iron Instrument
Repulsion (or Double-Iron) Type Moving-Iron Instrument
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 39
AMMETERS AND VOLTMETERS• Consider a d’Arsonval movement having current
sensitivity (CS) of 0.1 mA and internal resistance (Rm) of 500 Ω.
• The full-scale deflection current, Im, for this instrument is 0.1 mA.
• When full-scale current flows, the voltage across its terminals is given as
• So, it can serve either as an ammeter of range 0 - 0.1 mA, or as a voltmeter of range 0 - 50 mV.
• We need to extend the range of the meter, by providing a suitable additional circuitry.
m m m (0.1 mA) (500 ) 50 mVV I R
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 40
Ammeters• Connected in series in circuits.• Low impedance (resistance) so as not to affect
the circuit.• Constructed by adding a low resistance (or shunt
or bypass resistor) in parallel with the meter.
MAmmeter
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 41
Ammeters
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 42
The ratio Ifsd/Im = N is called the range-multiplier.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 43
Since the voltage across the parallel elements must be the same,
m m fsd m sh( )I R I I R
m msh
fsd m( )
I RR
I I
m m m m
fsd m fsd m
or ( ) ( / 1) ( 1)sh
I R R RR
I I I I N
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Click
Ammeter ExampleAn ammeter uses a meter with an internal resistance of 600 and a rating of 1 mA fsd. How can it be used to measure 20 A fs?
Maximum current through meter is 0.001 A.
Therefore, the shunt resistor must take 19.999 A
RM
R
M
Because both M and R are in parallel, the same V must be dropped across both
V = Im Rm = 0.001 A x 600 Ω = 0.6 V
Thus R must be V / IR = 0.6 V / 19.99 A = 0.03 (in parallel.)
iR
im
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 45
A multi-range ammeter.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 46
Universal shunt for multi-range milliammeter
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 47
Example 3An ammeter uses a meter with an internal resistance of 600 and a rating of 1 mA fsd. How can it be used to measure 20 A fs?
Solution : Maximum current through meter is Im = 0.001 A.
Therefore, the shunt resistor must take Ish = 19.999 A
Because both M and Rsh are in parallel, the same V must be dropped across bothV = Im Rm = 0.001 A x 600 Ω = 0.6 V
Thus, Rsh must be V / IR = 0.6 V / 19.999 A = 0.0300015..
Rm
Rsh
M
Ish
Im
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Click
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 48
Ammeter Sensitivity• Measured in ohms/amp; should be as low /A (small V drop) as possible.• Sensitive ammeters need large indicator changes for small current.• Example : (1) A 0.01 /A meter with 5 A fsd,
Rm = /A x A = 0.01 x 5 = 0.05 Vmax across the Meter will be
5 A x 0.05 = 0.25 V for fs.
(2) A 0.1 /A meter with 5 A fsd, will drop 2.5 V (i.e., it is 10 times less sensitive), which may bias the results.
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Click
Click
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 49
Ammeter loading• Significant where ammeters are used in circuits with
components of resistance comparable to that of the meter.
What is the current in the circuit ?
+
-
1.0 V
1.0
AIs it i = 1 V / 1 Ω = 1 A ?
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 50
• Now, suppose that the meter has a resistance of 1
• How much will be current in the circuit ?
• Obviously, the current in the circuit will be halved !When working with low value resistors, be sure to use very low impedance ammeters.
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Click
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 51
Voltmeters• Connections to circuits and components in parallel.
• High impedance (resistance) so as not to affect circuit.
• Constructed by adding a high resistance (R) in series with an electrically sensitive meter (M).
M
Voltmeter
R
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 52
Extending the Range of Voltmeters
Suppose that we want to extend the voltage range of this basic meter to 0-10 V.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 53
The total resistance RT must be such that
m T Tm
10 Vor 100 kΩ
0.1 mA
VV I R R
I
s T m 100 k 0.5 kR R R 99.5 kΩ
Now, suppose that the range of a basic meter is to be extended to Vfsd volts. Then, we should have
fsdfsd m m s s m
m
( ) or V
V I R R R RI
The series resistor Rs is also called a range-multiplier, as it multiplies the voltage range.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 54
Example 4A meter is rated at 1 mA fsd and has an internal resistance of 2000 Ω. How can it be used to measure 100 V fsd ?
Maximum voltage that can be put across galvanometer is Vm = I Rm = 0.001 x 2000 = 2.0 V
Thus, Vs = VT - Vm = 100 V - 2 V = 98 V
This voltage must be dropped across Rs. Therefore,
Rs = Vs/I = 98 V / 0.001 A = 98 kΩ
Vs = 98 VVm = 2 V RT = Rs + Rm
MRm Rs1 mA Click
Click
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Solution :Click
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 55
Voltage Scaling or Multiplying Factor
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It is defined as the number of times the voltage range is increased. Thus,
fsd fsd
m m m
V Vn
V I R
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 56
Example 5• A 50-μA meter movement with an internal
resistance of 1 kΩ is to be used as a dc voltmeter of range 50 V. Calculate
(a) the multiplier resistance needed, and
(b) the voltage multiplying factor.
Solution : Here, Im = 50 μA, and Rm = 1 kΩ. (a) The series resistance needed is given as
fsds m
m
50 V1000
50 μA
VR R
I 999 kΩ
(b) fsd fsd6 3
m m m
50
50 10 1 10
V Vn
V I R
1000
Click
Click
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 57
Meter Sensitivity (Ohms-per-Volt Rating)
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• Measured in Ω/V.
• Higher the sensitivity, more accurate is the measurement.
• If current sensitivity (CS) of a meter is known, its Ω/V rating can easily be determined.
• Consider a basic meter with CS of 100 μA.
• If used as a voltmeter of range 1 V,
RT = 1 V / 100 μA = 10 kΩ
• Thus, the meter sensitivity is simply 10 kΩ/V.
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 58
In general,
ysensitivitcurrent
1ratingvolt -per-ohms
• Note that if the same meter was used for 2 V range, the required RT would be 20 kΩ.
• Its ohms/volt rating is 20 kΩ / 2 V = 10 kΩ/V. • The ohms-per-volt rating does not depend on the range of the voltmeter.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 59
• Also, note that the range of a voltmeter (or an ammeter) is changed by switching in another resistor in the circuit. • Therefore, for a given range the internal resistance of the voltmeter remains the same irrespective of the deflection of the pointer.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 60
Voltmeter Loading
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• A voltmeter, when connected, acts as a shunt for that portion of the circuit.
• This reduces the resistance of that portion.
• Hence, the meter gives a lower reading.
• This effect is called the loading effect of the meter.
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 61
Example 6• It is desired to measure the voltage across the 50-kΩ
resistor in the circuit.
• Two voltmeters are available for this measurement. Voltmeter-A has a sensitivity of 1000 Ω/V and voltmeter-B has a sensitivity of 20 000 Ω/V.
• Both meters are used on their 50-V range.
• Calculate
(a) the reading of each meter, and
(b) the error in each reading, expressed as a percentage of the true value.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 62
Solution : The true value of the voltage across A-B,
V50kΩ50kΩ100
kΩ50V150t
V
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 63
(a) Voltmeter-A
The internal resistance,1 Sensitivity Range (1000 / V) (50V) 50kΩiR
When connected, the equivalent parallel resistance across A-B is 50 kΩ || 50 kΩ = 25 kΩ. Hence, reading of voltmeter,
V30
kΩ25kΩ100
kΩ25V1501V
Voltmeter-B
2 Sensitivity Range (20000 / V) (50V) 1000kΩiR
A-B Eq (50k ) || (1000k ) 47.6 kR
2
47.6 kΩ150 V
100 kΩ 47.6 kΩV
48.36 V
Click
Click
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Click
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 64
(b) Error in reading of Voltmeter-A,
%40
%10050
3050%100Error %
t
1t
V
VV
Error in reading of Voltmeter-B,
%3.28
%10050
36.4850%100Error %
t
2t
V
VV
Note the voltmeter with higher sensitivity gives more accurate results, since it produces less loading effect on the circuit.
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Click
Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 65
RESISTANCE MEASUREMENT• The instrument is called ohmmeter.
• Three types :
1. Shunt-Type Ohmmeter : For low value resistors.
2. Series-Type Ohmmeter : For medium-value resistors.
3. Meggar-Type Ohmmeter : For high-value resistances, such as the insulation of a cable.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 66
Shunt-Type Ohmmeter
When Rx = 0, no current in meter.
When Rx = , entire current flows through the meter.
Proper selection of R1 gives full-scale deflection on open circuit.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 67
Series-Type Ohmmeter
RT is pre-set resistor.
R0 is zero-adjust resistor. It compensate for the decrease in battery voltage E with ageing.
Rs limits the current to fsd.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 68
• When X-Y shorted, the current is maximum (fsd).
• When X-Y open, the current is zero.• Thus the scale is inverted.• Different ranges are obtained by switching in
different Rs
Caution• Never connect to an energized circuit. • Make sure that there is no parallel branch
across the resistance you are measuring.
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Wednesday, April 19, 2023 Ch. 18 Electrical Measuring Instruments 69
The current and resistance scales.
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Wheatstone Bridge• A clever method to accurately measure a
resistance• R1 and R3 are known• R2 is a variable resistor
• Rx is an unknown resistor
• R2 is varied until no current flows through the galvanometer G
• Let I1, I2, I3 and Ix be the currents through the four resistors.
• I1 = I2 and I3 = Ix
• No current through G: no voltage difference across it• I1R1 = I3R3 and I2R2 = IxRx Rx = R3R2/R1
Single-Phase Induction Type Wattmeter/Energy Meter