OPERATING FORCES
Any indicating instrument requires three torques for its operation, namely deflecting force, controlling force and damping force.
(a) Deflecting force
l The systems that create a deflecting force are said to be deflecting systems or
moving systems and their task is to convert the electrical current or potential into a mechanical force.
This force causes the deflection of pointer. (b) Controlling force
l The systems that produce controlling force are said to be controlling systems.
These forces are incorporated in an indicating system, so that the deflection of pointer should be proportional to the signal’s magnitude.
l Controlling forces are opposite to the deflecting force and the instant when the
two forces becomes equal, the pointer comes to rest. Thus, due to the controlling force, the deflection of the pointer is definite for a magnitude of current.
l Due to the controlling force only, the moving system comes back to the zero
position when the force causing that movement is removed.
l The following methods produce a controlling force in an instrument
- Gravity control - Spring control (c) Damping force
l Damping forces are necessary for a system, so that the moving system comes to
its equilibrium state rapidly and without any oscillations.
l Due to the damping forces, the pointer quickly comes to its final steady position
without over shooting or without oscillating near its final value.
l The following methods produce damping forces in an instrument:
- Air friction damping - Eddy current damping - Fluid friction damping - electromagnetic damping MOVING ELEMENT SUPPORT
Power consumption of the instrument should be kept low, so that the introduction of the instrument into a circuit causes least change in the circuit condition. Therefore, in order to obtain a correct reading, frictional forces of the system should be kept minimum and hence, following types of supports may be used:
- Suspension - Taut suspension
- Pivot and jewel bearings
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PERMANENT MAGNET MOVING COIL (PMMC) INSTRUMENT
l PMMC instruments are used only to measure DC quantities and not AC quantities.
This is so, because permanent magnets are used for creating magnetic fields.
l Constructional diagram of a PMMC instrument is shown in the fig. 1.
l A PMMC type instrument consists of a moving coil, made up of enameled copper
wire, which is mounted on an aluminium drum. This drum is pivoted on the spindle of a jeweled bearing. The pointer of the scale is also connected to this spindle.
l The end of the moving coils are connected to springs which produce a controlling
force and also provide a way to lead current in and out of the coil.
l The moving coil is placed in the magnetic field which is produced by the two magnets. l The supply to be measured is provided to the ends of the moving coil.
l We know that when a current carrying conductor is placed in a magnetic field, a
force is induced in it. Therefore, when the current flows through the coil, a force is induced in it and since a spindle is attached to it, there is a movement in the spindle.
l The movement of the spindle moves the pointer. This movement is controlled by
the controlling springs and thereby we get the final reading.
l To avoid unwanted oscillations of the pointer, a damping torque is produced by
the eddy current method.
l Torque equation
Deflecting torque, Tdµ I And controlling torque, T =c Kcq At steady position of pointer, Tc = Td And thus, I µ q
- since the deflection is directly proportional to the current flowing through the instrument, we get a uniform scale for the instrument.
- D.C. voltage and D.C. current can be measured using PMMC instruments. MOVING IRON TYPE INSTRUMENT
Such instruments are of two types – attraction type and repulsion type. Attraction Type
l Constructional arrangement of attraction type moving iron type instrument is
shown in the fig. 2.
l Moving system of this instrument comprises a moving iron which is fixed at one
end and its other end is free to move. The pointer is also attached to this moving iron.
l There is a former which supports the coil and the coil is made up of enameled
copper wire.
l Controlling forces are provided by the gravity control method and damping forces
are provided by the air friction damping torque.
l Voltage or current to be measured is given as an input across the coil and when
current flows through the coil, a magnetic field is produced.
l Due to the magnetic field, the moving iron is attracted towards it and due to this
force of attraction, the pointer deflects. This deflection of pointer is controlled by the controlling forces and thus, the pointer comes to rest and we get a reading on the scale.
l Torque equation
Deflecting torque, 2 d T =KI
And controlling torque, Tc =K1sinq At steady position of pointer, Tc =Td
And thus, qµI2
l Since deflection of the pointer is directly proportional to the square of the current,
the scale of the attraction type moving iron type instrument is not uniform.
Scale
Magnetic Coil
Pointer
Balanced
Weight Moving Iron Piece Control Weight Former Air Damping Chamber Air Damping Piston Arm
Fig. 2: Attraction type instrument
N S Aluminium Drum Coil Control Spring Jewelled Bearing Pointer Spindle In p u t S u p p ly Permanent Magnet Fig. 1: PMMC instrument
Repulsion Type
In repulsion type instrument, two vanes of soft iron are used inside the coil. One vane is fixed and the other one is free to move. When current flows through the coil, both vanes are magnetized and therefore, there is a force of repulsion between the two and this force acts as the driving force for the instrument. Two different designs of repulsion type moving iron type instruments are common – radial type and co-axial type. ELECTRODYNAMOMETER TYPE INSTRUMENT
l This type of instrument is capable of measuring AC voltage and AC current as
well as DC voltage and DC current.
l The fig. 3 shows the arrangement of electrodynamometer type instrument. l Magnetic field in this type of instrument is produced by a fixed coil which is
divided into two parts: F1 and F2.
l The pointer of the instrument is attached to the moving coil and this moving coil
is generally wounded on a non-metallic former.
l The moving coil is placed in series with the two fixed coils.
l Air friction damping system is used to provide damping force and controlling
torque is provided by the control springs.
l When measuring input is applied to the instrument, current starts flowing through
the fixed coil and moving coil.
l Current flowing through the fixed coil creates a magnetic field and the current
carrying moving coil is placed in that magnetic field. Therefore, the moving coil experiences a force which results in the movement of pointer over the scale.
l This force is controlled by the control springs and thus, the pointer comes to rest
and in this way, we get the reading.
l Torque Equation
Deflecting torque, Td µI2
And controlling torque, Tc =Kcq At steady position of pointer, Tc =Td And thus, qµI2
l Since, the deflection of the pointer is directly proportional to the square of the
current, the scale of the electrodynamometer type instrument is not uniform. INDUCTION TYPE INSTRUMENTS
l Induction type instrument works on the principle of induction and therefore, this
method is used in measuring AC voltage and AC current.
l The maximum length of scale is possible in induction type instrument as the angle
of deflection of this instrument may be 360 degrees.
l Ferraris type induction type instrument is shown in the fig. 4
l This type of instrument consists of two coils – one coil is highly resistive and the
other one is highly inductive.
l When we give signal to the instrument, current starts flowing through the system
and this current splits up, i.e. some portion of current flows through the resistive coil and the remaining current flows through the inductive coil.
l These two currents produce two flux and these two flux produce the deflecting
torque which rotates the laminated iron core which is mounted on the spindle.
l With the movement of the spindle, the pointer also deflects. This deflection of
pointer is controlled by controlling forces, which is produced from the control spring.
MEASUREMENT OF VOLTAGE
Voltmeter is an instrument used for measuring the voltage between any two points in an electrical circuit. There are two types of voltmeters: Analog and Digital. In an analog voltmeter, a pointer shows deflection across the scale, which indicates the voltage
Moving Coil F1 F2 Input A.C/D.C Pointer Scale Fixed coil
Fig. 3: Electrodynamometer instrument
Pointer Scale Laminated Magnetic System Spring Laminated Iron Core Aluminium Drum Supply R L
reading with respect to the applied current; whereas a digital voltmeter gives a numerical display of the voltage according to the applied current, with the help of an ADC (analog-to-digital convertor).
Analog Voltmeter : The fig. 5 shows the D’arsonval type moving coil galvanometer. The device consists of a pointer, a full deflection scale, magnets and a coil. The pointer is attached with the coil, which is suspended in a magnetic field, as shown in the figure 5. Under no biasing condition, the pointer is at the zero position, i.e. at the center of the scale, which also helps to notify if the voltage changes its polarity. Now, in order to measure the voltage, the galvanometer is connected in circuit with a series resistor as shown in fig. 6; the resistor is connected in series to ensure that the angular rotations of the indicator are directly proportional to the applied voltage. Normally, this device is used in case of direct current; however, we can also have an AC source by using a rectifier in the circuit. The output of this voltmeter is expressed in ‘ohms per volt’.
Digital Voltmeter : A Digital voltmeter uses the analog-to-digital convertor for displaying the voltage on the numerical display. The accuracy of a Digital voltmeter is higher than that of an analog voltmeter. The main parts of Digital voltmeter are an amplifier and a numeric display as shown in fig. 7. Just like the analog voltmeter, a digital voltmeter is also connected in series with the circuit, but the value of series resistance is fixed by the manufacturer (generally about 10 mega ohms).
MEASUREMENT OF CURRENT
Current is measured with the help of an instrument known as ‘Ammeter’. It consists of a deflection scale and a pointer. An ammeter is always connected in parallel with the circuit as shown in fig. 8, and the simplest method for determining circuit current is: Thermocouple or Resistive Heating : This technique is based on the Seebeck effect. In this method, a thermocouple made up of two dissimilar metals, is connected in parallel with an ammeter, as shown in the fig. 9. The hot junction is welded to a heater wire or conductor, while the cold junction is connected to the ammeter. Now, when current passes through the heater wire, the temperature of the junction gets raised, which leads to an increase in the thermoelectric EMF and sends more current to the ammeter. Since the deflection on the scale depends upon the heating effect and the length of the conductor, we can say that the amount of heat produced is directly proportional to the square of the current and resistance.
Q µ I2R
MEASUREMENT OF POWER
Power is generally measured through Wattmeters of which there are two types – electrodynamometer type and the induction type.
Electrodynamometer Type Wattmeter
l Electrodynamometer type wattmeter consists of two coils as shown in the fig. 10. l Fixed coil is split up into two identical coils and are made up of thick copper
wires.This fixed coils are connected in series with the load and so they carry the current in the circuit, thus, they form the current coil of the circuit.
l Moving coil is mounted on the spindle and is placed in between the two fixed
coil.The moving coil is connected across the voltage and therefore it forms the pressure coil of the wattmeter.
l Spring control method is used for producing controlling torque and damping
torque is produced by air friction damping system.
l The moving coil act as a current carrying conductor placed in a magnetic field
and thus force induced in it and since pointer is connected to this moving coil, it deflects on the scale.
l This deflection is controlled by the controlling spring and at last pointer comes to
rest showing a reading.
0 5 10 15 20 Magnets Pointer Deflection Scale Coil
Fig. 5: Analog Voltmeter Voltmeter Voltage to be
measured
Resistor
Fig. 6: Voltmeter connection in circuit
110
Display
Function keys
I/O port
Fig. 7: Digital Voltmeter
A R
Fig. 8: Circuit arrangement for Current measurement using ammeter
Cold junction Hot junction Conductor R Ammeter Thermocouple A B Ammeter connection
Induction Type Wattmeter
l Induction type wattmeter consists of two electromagnets – the upper one is
known as shunt electromagnet and the lower one is known as series electromagnet as shown in the fig. 11.
l The coil of shunt electromagnet is made up of a thin enameled copper wire and
this electromagnet also possesses some self short-circuiting bands. The shunt electromagnet acts as a pressure coil.
l The coil of series electromagnet is made of thick wire and the number of turns in
this coil is less compared to that of the shunt electromagnet. The series electromagnet acts as a current coil.
l An aluminium disc mounted on a spindle is in between the two electromagnets. l The spindle is supported by a jeweled bearing.
l Eddy current damping system is used for producing a damping force and the
controlling force is provided by the spring control method.
l When we apply voltage across the pressure coil, then a current starts flowing in
the coil, which further produces flux, which is also of the same nature as that of the current. Let this flux be f1.
l When this flux reaches the centre of shunt electromagnet, due to the flux , voltage
is induced in the short circuited band and due to this voltage, current starts flowing in the band which has its own flux f2.
l The difference of flux (f1 – f2) produces a rotating force due to which the
aluminium disc starts rotating and since the spindle is connected to it, the pointer also deflects on the scale to give the reading.
MEASUREMENT OF ENERGY
Energy is measured by an induction type energymeter, the arrangement for which is shown in the figure and its whole operation is divided into four parts which are explained below
:-(a) Driving System
l The driving system consists of two electromagnets – shunt electromagnet and
series electromagnet.
l The number of turns in the coil of the shunt electromagnet is more than that of
the series electromagnet.
l The coil of the series electromagnet has negligible resistance and since it carries
the load current, this coil is known as the current coil.
l The coil of the shunt electromagnet is connected across the supply and therefore,
it carries a current which is in proportion to the voltage and hence it is known as the pressure coil.
l Short circuited bands are also provided on the shunt electromagnet in order to
provide some phase difference. (b) Moving system
l The moving system consists of a disc which is mounted on a light alloy shaft.
The disc is made up of aluminium which is not magnetic but is a conducting material.
l This disc is positioned in between the air gap of the shunt and the series
electromagnet. (c) Braking system
l At the edge of the aluminium disc, a permanent magnet is positioned, which
forms the braking system of the instrument.
l It controls the speed of the aluminium disc.
l The disc acts as a current carrying conductor placed in the magnetic field (of
permanent magnet), and hence voltage is induced in it, due to which the current is produced.
Fig. 11: Induction type wattmeter
Shunt electro-magnet (P.C) S.C.bands Spindle Al disc (cc) Series electromagnet V f1 f2 Shunt Electromagnet Laminated Core Aluminium Disc Series Electromagnet Braking Magnet S C Bands PC
Fig. 12: Induction type energymeter
Moving Coil Spindle
Fixed Coil
Fig. 10: Electrodynamometer type wattmeter
l This current produces a braking torque and by adjusting the position of the permanent
magnet, we can change the braking torque and hence the speed of the disc. (d) Registering system
l A gear arrangement is there in the instrument which is in the spindle.
l It continuously records the number which is proportional to the revolutions made
by the moving system.
MEASUREMENT OF POWER FACTOR
The power factor is measured by an electrodynamic power factor meter as described below: Electrodynamic Type Power Factor Meter
l The circuit arrangement is shown in the fig. 13.
l It consists of a fixed coil, which is split up into two parts. This coil acts as a
current coil and it carries current of the circuit under test.
l Two identical coils A and B are pivoted on a spindle and are cross coupled at 90
degrees.
l Pressure coil A is connected in series with a non- inductive resistance and pressure
coil B is connected in series with a highly inductive choke.
l Both A and B are connected across the voltage, and the value of R and L are so
adjusted that the two coils have the same impedance i.e. R = wL. Thus, both of them carry the same amount of current.
l The current through coil A is in the same phase with the circuit voltage, while the
current in coil B lags the voltage by an angle nearly equal to 90o as shown in fig. 14. l Two torques are produced in the system, one acting on coil A and the other acting
on coil B.
l Since the coils are cross coupled and the torques acting on both the coils are
opposite in nature, therefore it rotates and rests at that point where the two opposite torques are equal.
l A pointer is attached to this moving coil and hence we get reading on the scale. l Torque Equation
Let the deflecting torque in A = TA=kVIMmaxcos sinf q
And the deflecting torque in B = TB =kVIMmaxcos(90-f)sin(90+q)
When the pointer comes to rest, both the torques are equal. maxcos sin
kVIM f q =kVIMmaxcos(90-f)sin(90+q) sin sin cos cos q f q = f tanq =tanf q f=
Therefore, the deflection of the instrument is a measure of the phase angle of the circuit and the instrument can be directly calibrated in terms of power factor. INSTRUMENT TRANSFORMER
The transformer used in conjunction with measuring instruments for measurement purposes is called an Instrument Transformer. To measure current, Current Transformers (CTs) are used and to measure voltage (or potential), Potential Transformers (PTs) are used. Current Transformer
l Such a transformer is used to measure the current.
l It is a step-up transformer whose primary (lv side) is connected to the line whose
current is to be measured and its secondary (hv side) is connected to the ammeter as shown in fig. 15.
l The ammeter gives a reading and this reading when multiplied by the
transformation ratio, gives the value of line current which was flowing through the line.
l By using CT, measurement is carried out using a low rating of ammeter.
Fig. 14: Phasor diagram IB I 90° IA V f S u p p ly Vol ta ge Fixed coil Lag Lead 1 A B Moving coil q L R
Fig. 13: Electrodynamic type power factor meter A 0 - 5 A Primary Secondary S
Potential Transformer
l Such a transformer is used to measure voltage.
l It is a step-down transformer whose primary (hv side) is connected to the line
whose voltage is to be measured and its secondary (lv side) is connected to a voltmeter as shown in fig. 16.
l The voltmeter gives a reading and this reading when multiplied by the
transformation ratio, gives the value of the line voltage of the line.
l By using PT, measurement is carried out using a low rating of the voltmeter and
insulation required for measuring such a high voltage is minimized. BRIDGES
Wheatstone Bridge
This bridge is used to measure the medium resistance and its arrangement is shown in fig. 17.
Let P and Q = known resistances known as ratio arms S = known variable resistance
R = unknown resistance
Kb and Kg= Battery and Galvanometer key
E = supply voltage
The value of the unknown resistance when the bridge is in balanced state is R PS Q
=
Kelvin’s Double Bridge
Kelvin’s double bridge is used to measure low resistance and its arrangement is shown in the fig. 18.
p and q = first set of ratio arms P and Q = second set of ratio arms S = known variable resistance R = unknown resistance r = lead resistance
E and KG= Battery and Galvanometer key
Also, p P q =Q
The value of unknown resistance when the bridge is in a balanced state is P
R S
Q
=
Maxwell’s Induction Bridge
This bridge is used to measure self inductance is shown in fig. 19. R1 = resistance of the coil (unknown)
L1 = inductance of the coil (unknown)
R2, R4 = known non-inductive resistances
R3 = variable resistance L3 = known inductance r3 = internal resistance of L3 At balanced condition, 2 1 3 3 4 ( ) R R R r R = + 2 1 3 4 R L L R = Q – factor = 3 3 3 L R r w + V
Fig. 16: Potential transformer
Fig. 17: Wheatstone bridge
b d G P S R E Kb a c Q KG
Fig. 18: Kelvin’s bridge G P b Q e d a R I p f q KG S c E K B
Fig. 19: Maxwell’s Induction Bridge
a b R2 R3 I1 c R4 d I2 I2 E R1 E1 E 2 E4 Z4 Z2 E3 Z3 D L3 Z1 L1 I1
Maxwell’s Inductance-Capacitance Bridge
This bridge is also used to measure self inductance. Its circuit diagram and vector diagram is shown in fig. 20 and 21 respectively
R1 = resistance of the coil (unknown)
L1 = inductance of the coil (unknown)
R2, R3, R4 = known non-inductive resistances
C = known variable capacitor At balanced condition, 2 3 1 4 R R R R = 1 2 3 L =CR R Q – factor = wCR4 Desaultay Bridge
This bridge is used to measure the value of capacitance circuit diagram is shown in fig. 22. I I a I1 C1 b R2 I1c I2 R4 d I2 C3 D
Fig. 22: Desaultay Bridge C1 = unknown capacitor
C3 = known variable capacitor
R2,R4 = known standard resistance
1 1 1 3 1 3 I I E E j C j C = = w w At balanced condition, 4 3 1 2 R C C R = Anderson Bridge
This bridge is used to measure self inductance. Its circuit diagram and vector diagram are shown in fig. 24 and 25 respectively
Bridge arrangement I I a b R3 r c R4 d I2 I = I – I R 2 C IC E e I1 r1 R2 I1 R1 1L D c
Fig. 24: Anderson bridge At balanced condition 2 3 1 1 4 R R R r R = -2 1 3 4 3 4 4 [ ( )] R L C R R r R R R = + + I2 E1 I R1 1 I ,I1 2 E I R =E1 2 2 I j L1 w 1
Fig. 21: Vector diagram
I , I1 2 E = I R4 2 4
2 1 2
E = I R
E
Fig. 23: Vector diagram
IC I2 I1 IR ICr E1 I R2 3 I RR 4 E I (R +r )1 1 1 E =I R2 1 2 I j L1 w 1 I j c C w = Fig. 25: Vector diagram Fig. 20: Maxwell’s inductance
-capacitance bridge I I a c b Z4 Z3 R3 c d D E IRR4 IC I2 I2 I1R1 L1 Z1 R2 I1 Z2
POTENTI OMETER
A potentiometer is a three terminal device shown in fig. 26 which is used as a variable resistor. The outer terminals are fixed, while the middle terminal can vary; the middle terminal is either in the screw-shape or in the form of a control shaft along with a wiper. The screw moves over the resistive element and shows continuous variation in the resistance of the element, which is connected between the outside and the middle terminal of the potentiometer. A potentiometer is basically used to control the voltage of the circuit. Although there is one more application of the potentiometer: it can be used as a rheostat by connecting its middle terminal with an outside terminal. (A rheostat is mainly used to control the circuit current.)
DIGITAL VOLTMETERS
Digital voltmeters are the instruments which measure AC or DC voltages and display the results in a numeric form. This method is more advantageous than the analog method as observational errors are eliminated. There are two types of digital voltmeters – ramp type voltmeter and potentiometric digital voltmeter.
Ramp Type Voltmeter
l The fig. 27 shows the arrangement of a ramp type voltmeter.
l Input comparator receives two voltages – one from the input and the other from
the ramp generator.
l the instant when both the voltages are equal, the comparator generates a pulse
which opens the gate.
l The ramp voltage continuous to decrease till it reaches the ground level. At this
instant, another comparator generates a pulse and closes the gate.
l The time elapsed between this opening and closing of gate is as indicated in the
timing diagram as shown in fig. 28.
l During the time interval, pulses from a clock pulse generator pass through the
gate and are counted by the counter and the result is displayed at the read out.
l The sample rate multivibrator sends a pulse to the counters which sets the reading
of the display again back to zero. Potentiometric Digital Voltmeter
l Arrangement of this type of voltmeter is shown in the given fig. 29.
l The input voltage to be measured is applied to a comparator which is also known
as the error detector.
l The value of feedback voltage depends upon the position of the sliding contact. l The unknown voltage and feedback voltage are compared in the comparator and
the output of the comparator is the difference between the voltages which is known as the error signal.
l This signal is amplified and is fed to the potentiometer adjustment device which
moves the sliding contact of the potentiometer.
l The sliding contact moves to such a place where the unknown voltage equalizes
feedback voltage and when this happens, the sliding contact comes to rest.
l The position of the potentiometer adjustment device at this point is indicated in
numeric form on the display. MULTIMETER
A Multimeter is a measuring instrument which is used to measure several functions like current, voltage and resistance. Multimeters are of two types: analog and digital. In an analog multimeter, a micro ammeter is used which consists of a pointer and a deflection scale; whereas in digital Multimeter, the measured value is displayed in numerals on a digital screen, the display can either be in the seven segment format or in the liquid style display of an LCD. Nowadays, digital multimeters are preferred over analog for all types of measurements. But analog multimeters are still used when we have to monitor the values which rapidly vary over a wide range.
110
Display I/O port V I R - + Transistor testing Fig. 30: Multimeter Error Signal On Known Voltage Feedback voltage Sliding contact Error Amplifier Potentiometer adjustment device Read out 0 0 0 0 Comparator Ref. Voltage source R +-Fig. 29: Potentiometric digital voltmeter
+12 V Unknown Voltage 0 -12 V Gating time interval Clock Pulses Ramp voltage Time t
Fig. 28: Timing diagram
I/P Voltage Ranking & attenuator Input Comparator Clock Osc. Ramp Gen. Sample rate MV Gate Stop Pulse Ground Comp. Counter Start Pulse Read out 0 0 0 0
Fig. 27: Ramp type voltmeter Top view
Side view
Pin No-1
Main applications of multimeter: (a) Measuring of AC and DC (b) Measuring voltage and current (c) Measuring resistance
(d) Testing of continuity in circuit
PHASE AND FREQUENCY MEASUREMENT Phase Measurement
In phase measurement, phase of the signal which is fed into the system is compared with the phase of the signal responded by the system. The difference between the phases of both the signals is recorded as phase difference, and it is due to the electrical properties of the system. The fig. 31 shows the phase difference or phase shift between the applied and responded signal:
In time and frequency domain, phase shift is defined in terms of time instead of angle. During a complete cycle, time taken by a signal to constitute a 3600 phase shift is
given as — T = 1 360f Or T = 1 360f
There is a device named Phase Analyzer, which is used to display the phase-frequency curve over +1800 to –1800 ranges. There are different types of phase measurement
processes –
(1) Complex impedance (2) Group delay
(3) Deviation from linear phase
(4) Amplitude modulation –to– phase modulation conversion Frequency Measurement
Frequency is defined as the number of oscillations or repetitions of a signal per unit of time. Three methods are used for frequency calculations:
(1) Counting – Since we know that frequency is inversely proportional to time, i.e. F = T1
So, by calculating the number of oscillations of a signal or events which occur in a specific time period, we can calculate the frequency of that signal.
(2) Frequency counter – A frequency counter is an electronic device which is used to display the frequency of a signal in Hertz. In a frequency counter, with the help of transducer, the processes which are not electrical in nature are converted into electronic signals. These processes are known as cyclic processes, and they include mechanical vibrations, rate of rotating shaft, etc. These electronic signals are then applied to the frequency counter, where digital logic counts the number of cycles of a specific time interval. The results obtained are displayed on the digital display. This device is used to determine a frequency up to 100 GHz. (3) Heterodyne or frequency conversion method – In this method, the signal whose
frequency is to be measured is nonlinearly mixed up with a reference signal of known frequency. The difference of frequency between these two signals is small enough to be measured by the frequency counter. The rest of the procedure for frequency calculation is followed by the frequency counter. This method is suitable for high frequency calculation.
Phase difference
Q-METER
Q-meter is a device which is used to determine the quality factor of a circuit. Generally, this device is used in radio frequency circuits, where it is desirable to know how much amount of energy is dissipated from the system in a non-ideal reactive form. Q-factor is given
as-Q =2 Peak EnergyStored
Energy dissipated per Cycle
p´
OSCILLOSCOPES
l Block diagram of the cathode ray oscilloscope is shown in the fig. 32.
l The cathode ray tube (CRT) generates the electron beam, accelerates it to a high
velocity, focuses it and deflects the beam to produce the image on a phosphor screen.
l The power supply block provides the input required by the CRT to generate the
beam.
l Horizontal and vertical amplifiers are required to strengthen the weak signal and
also to focus it correctly on the screen.
l The time base generator provides the potential of variable frequency to be applied
to the x-plate.
l The function of the vertical delay line is to allow the operator to observe the
leading edge of the signal waveform by delaying the signal drive. POTENTIOMETRIC RECORDER
A Potentiometric recorder is a device which is used to record and monitor the voltage which a voltmeter measures. The most important application of Potentiometric recorder is that it enables us to monitor even minute unattended voltages during a measurement, which varies over a wide range of 0 – 500 V. This device is highly sensitive in nature and produces accurate results. The gain adjustment panel of recorder helps in determining the sample voltage over full-scale recorder deflection. The differential voltage determined by the recorder is not impaired in any way due to its high leakage resistance, which is approximately 500,000 Mega Ohms.
ERROR ANALYSIS
There are three basic types of errors which are obtained while taking measurements in lab with any electrical system and these are –
(1) Random Error (2) Systematic Error (3) Gross Error
(1) Random Error : Those uncontrolled or uncertain fluctuations which randomly affect the results of experiments are called random errors. Examples include the change in temperature due to sunlight around temperature sensors, air fluctuations caused by opening and closing of doors, etc. This error type is difficult to remove but can be solved by calculating the estimated standard deviation of collected data.
(2) Systematic Error : Instrumental mistakes, methodological and personal mistakes fall under this category. Instrumental errors can be caused in many ways, for e.g. an improper placement of device. Methodological errors are caused because of the selection of wrong alternatives for experiment, and personal mistakes are caused by observers and performers like noting down incorrect readings, etc. These errors can be easily eliminated by careful observation and correct operation of instruments.
(3) Gross Error : This error is caused either by an instrument failure or the carelessness of the experimenter. In order to minimize this error, a set of precision measurements must be taken by the experimenter.
Fig. 32: Oscilloscopes Input Signal To all Circuit Electron Gun To CRT CRT Electron beam Screen HV Supply Time/division Vertical
amplifier DelayLine
Horizontal amplifier Time base generator Trigger Circuit LV Supply
SOME SOLVED EXAMPLES
1. A DC ammeter has a resistance of 0.1 ohm and its current range is 0 – 100 A. If this range is to be extended to 0 – 500 A, then the meter requires the following shunt resistance:
(a) 0.010 ohms (b) 0.011 ohms
(c) 0.025 ohms (d) 1.00 ohms
Solution : Maximum current which can flow through the ammeter is 100 A.
So, the value of the shunt resistance which is required to measure the 500 A current must be chosen in such a way that 400 A current flows through the shunt.
From current division formula, (I I R- a) shunt =I Ra a
Therefore, 100 0.1 ( ) (500 100) a shunt a a I R R I I = ´ = ´ - -Thus, 1 0.1 0.025 4 shunt R = ´ = W
Hence, option (c) is the correct answer.
2. The setup in the fig. 1 is used to measure resistance R. The ammeter and voltmeter resistances are 0.1 ohm and 2000 ohm, respectively. Their readings are 2 A and 180 V respectively, yielding a measured resistance of 90 ohm. The percentage error in the measurement is
(a) 2.25% (b) 2.35%
(c) 4.5% (d) 4.71%
Solution : From Ohm’s law, the current flowing through voltmeter,
180 0.09 2000 V V I A R = = =
Therefore, actual ammeter current should be 2 0.09 1.91A- =
Therefore, actual value of resistance should be = 1.91180 = 94.24 ohm The percent error = 94.24 90 100 4.71%
90
- ´ =
Hence, option (d) is the correct answer.
3. Two wattmeters, which are connected to measure the total power on a three – phase system supplying a balanced load, read 10.5 kW and – 2.5 kW respectively. The total power and the power factor, respectively, are
(a) 13.0 kW, 0.334 (b) 13.0 kW, 0.684
(c) 8.0 kW, 0.52 (d) 8.0 kW, 0.334
Solution : We know that the total power of the circuit when measured by the two-wattmeter method is the algebric sum of the readings of the two two-wattmeters. Therefore, P W= 1+W2=10.5 ( 2.5) 8+ - = W
To find the power factor, firstly we have to calculate the value of f Therefore,
1 1 2 1 1
1 2
3 ( ) 3 (10.5 ( 2.5) 3 13
tan tan tan
10.5 ( 2.5) 8 W W W W f= - ´ - = - ´ - - = - ´ + + -1 0 tan (2.81458) 70.44 f= - =
Power factor = cos f = cos 70.440= 0.334 Hence, option (d) is the correct answer.
4. The circuit in fig. 2 is used to measure the power consumed by the load. The current coil and the voltage coil of the wattmeter have 0.02 ohm and 1000 ohm resistances respectively. The measured power compared to the load power will be
(a) 0.4 % less (b) 0.2 % less
(c) 0.2 % more (d) 0.4 % more I2 R V A 1000W 20A Unity PF 1000 200V 0.023W W Fig 1: Fig 2:
Solution : We know that the reading which we get from a wattmeter comprises the power which is consumed by the load and the power which is lost across the current coil of the galvanometer.
Therefore,
Power consumed by the load, P V I= ´
Or,P=200 20 4000´ = W
And power loss across current coil, p I R= 2
Therefore, p=20 (0.02) 82 = W
Thus, ideally the wattmeter should show 4000Was the final reading, but due to the loss, the reading which is shown by the wattmeter is 4000W + 8W = 4008W
So, the measured power is 4008 4000 100 0.2% 4000
-´ = more than the actual load power.
Hence, option (c) is the correct answer.
5. A galvanometer with a full scale current of 10 mA has a resistance of 1000 ohms shown in fig. 3. The multiplying power (the ratio of measured current to galvanometer current) of a 100 ohm shunt with this galvanometer is
(a) 110 (b) 100
(c) 11 (d) 10
Solution : We know that a shunt is always connected in parallel with a galvanometer. In the question, it is given that the internal resistance of galvanometer is 1000 ohms and the value of shunt resistance is 100 ohms.
From the current division formula, Let measured current = I
Current through galvanometer, I1=1100100 I
Multiplying factor power =
1 I I On substituting the values, we get Multiplying factor = 100
1100
I I
= 111 Hence, option (c) is the correct answer.
6. A moving coil of a meter has 10 turns, and a length and depth of 100 mm and 20 mm respectively. It is positioned in a uniform radial flux density of 200 mT. The coil carries a current of 50 mA. The torque of the coil is
(a) 200 mNm (b) 100 mNm
(c) 2 mNm (d) 1 mNm
Solution : Given, uniform radial flux density, B=200 10´ -3T length, l=100 10´ -3m
depth, d=20 10´ -3m current, I=50 10´ -3A number of turns, N=10
As we know that torque, T =BldIN mNm
Thus, T=(200 10 ) (100 10 ) (20 10 ) (50 10 ) 10´ -3 ´ ´ -3 ´ ´ -3 ´ ´ -3 ´ Therefore, T =0.0002Nm=200mNm
Hence, option (a) is the correct answer. I1 I2 I 1000 100W W Fig 3:
7. A dc A-h meter is rated for 15 A, 250 V. The meter constant is 14.4 A-second/rev. The meter constant at rated voltage may be expressed as
(a) 3750 rev/kWh (b) 3600 rev/kWh
(c) 1000 rev/kWh (d) 960 rev/kWh
Solution : Given,
Meter constant = 14.4A-sec/rev and 1sec 1
3600hr
=
Therefore, the meter constant can be written as 14.4 / 3600A hr rev -also, A hr V W hr rev rev - ´ = -thus, 14.4 / 250 1 / 3600 Ah rev Wh rev ´ = now, 1 1 1000 Wh= kWh so, 1 / 1 / 1000 / 1000
Wh rev= kWh rev= rev kWh Hence, option (c) is the correct answer.
8. A moving iron ammeter produces a full scale torque of 240 mNm with a deflection of 120 degrees at a current of 10 A. The rate of change of self inductance (mH radian/ ) of the instrument at full scale is
(a) 2.0 mH/radian (b) 4.8 mH/radian (c) 12.0 mH/radian (d) 114.6 mH/radian Solution : Full scale torque in a moving coil instrument,
2 1 2 dl T I dq =
On substituting the value of current and torque in the above equation, we get 6 1 2 240 10 (10) 2 dl dq -´ = Thus, 240 10 6 50 dl dq -´ = Therefore, 6 6 240 10 50 4.8 10 H/radian 4.8 μH/radian q -´ = = ´ = dl d
1. The Q-meter works on the principle of
[2005, 1 Mark] (a) mutual inductance (b) self inductance
(c) series resonance (d) parallel resonance 2. A PMMC voltmeter is connected across a series
combination of a DC voltage source V1 = 2V and an AC voltage source V2(t) = 3 sin (4t). The voltmeter reads
[2005, 1 Mark] (a) 2 V (b) 5 V (c) æçç2+ 23ö÷÷ è øV (d) 17 V 2 æ ö ç ÷ ç ÷ è ø
3. A variable w is related to three other variables x, y, z as w = xy/z. The variables are measured with meters of accuracy ± 0.5% reading, ± 1% of full scale value and ± 1.5% reading. The actual readings of the three meters are 80, 20 and 50 with 100 being the full scale value for all three. The maximum uncertainty in the measurement of
w will be [2006, 2 Marks]
(a) ± 0.5 % rdg (b) ± 5.5% rdg (c) ± 6.7% rdg (d) ± 7.0 rdg
4. An energy meter connected to an immersion heater (resistive) operating on an AC 230 V, 50 Hz, AC single phase source reads 2.3 units (kWH) in 1 hour. The heater is removed from the supply and now connected to a 400V peak to peak square wave source of 150 Hz. The power in kW dissipated by the heater will be
[2006, 2 Marks]
(a) 3.478 (b) 1.739
(c) 1.540 (d) 0.870
5. Consider the following statements with reference to the
equation ddpt [2006, 2 Marks]
(1) This is a point form of the continuity equation (2) Divergence of current density is equal to the decrease
of charge per unit volume per unit at every point (3) This is Maxwell's divergence equation
(4) This represents the conservation of charge Select the correct answer.
(a) Only 2 and 4 are true (b) 1, 2 and 3 are true (c) 2, 3 and 4 are true (d) 1,2 and 4 are true
6. R1 and R4 are the opposite arms of a Wheatstone bridge as are R3 and R2. The source voltage is applied across R1 and R3. Under balanced conditions which one of the
following is true? [2006, 2 Marks]
(a) 1 3 4 2 R R R R = (b) 1 2 3 4 R R R R = (c) 1 2 4 3 R R R R = (d) R 1 = R2 + R3 + R4 7. A 200
1 Current Transformer (CT) is wound with 200 turns on the secondary on a toroidal core. When it carries a current of 160 A on the primary, the ratio and phase errors of the CT are found to be –0.5% and 30 min respectively. If the number of secondary turns is reduced by 1, the new ratio error (%) and phase error (min) will
be respectively [2006, 2 Marks]
(a) 0.0, 30 (b) –0.5, 35
(c) –1.0, 30 (d) –1.0, 25
8. A current of 8 6 2(sin t 30 )- + w + ° A is passed through three meters. They are at centre zero PMMC meter, true rms meter and a moving iron instrument. The respective readings (in ampere) will be [2006, 2 Marks]
(a) 8, 6, 10 (b) 8, 6, 8
(c) –8, 10, 10 (d) –8, 2, 2
9. The time/div and voltage/div axes of an oscilloscope have been erased. A student connects a 1 kHz, 5 V p-p square wave calibration pulse to channel 1 of the scope and observes the screen to be as shown in the upper trace of the figure. An unknown signal is connected to channel 2 (lower trace) of the scope. If the time/div and V/div on both channels are the same, the amplitude (p-p) and period of the unknown signal are respectively.
[2006, 1 Mark]
(a) 5 V, 1 ms (b) 5V, 2 ms (c) 7.5 V, 2 ms (d) 10 V, 1 ms
10. A sampling wattmeter (that computes power from simultaneously sampled values of voltage and current) is used to measure the average power of a load. The peak to peak voltage of the square wave is 10 V and the current is a triangular wave of 5A (p-p) as shown in the figure. The period is 25 ms. The reading in watt will be [2006, 1 Mark]
0 0
(a) zero (b) 25 W
(c) 50 W (d) 100 W
11. A bridge circuit is shown in the figure below. Which one of the sequences given below is most suitable for balancing the bridge? [2007, 2 Marks]
R2 R4
R3 R1
–jX4 jX1
(a) First adjust R4 and then adjust R1 (b) First adjust R2 and then adjust R3 (c) First adjust R2 and then adjust R4 (d) First adjust R4 and then adjust R2
12. The probes of a non-isolated, two-channel oscilloscope are clipped to points A, B and C in the circuit of the adjacent figure. Vin is a square wave of a suitable low frequency. The display on Ch1 and Ch2 are as shown on the right. Then the "Signal" and "Ground" probes S1, G1 and S2, G2 of Ch1 and Ch2 respectively are connected to
points. [2007, 1 Mark] GND12 C B A R L Vin Ch1 Ch2 (a) A, B, C, A (b) A, B, C, B (c) C, B, A, B (d) B, A, B, C
13. The ac bridge shown in the figure is used to measure the impedance Z.
If the bridge is balanced for oscillator frequency f = 2 kHz, then the impedance Z will be [2008, 2 Marks]
~
D 15.9 1 m H 3 00W 500W 0.3 98 H 300 m W Oscillator D Z A C B (a) (260 + j0) W (b) (0 + j200) W (c) (260 – j200) W (d) (260 + j200) W14. The sinusoidal signals p(w1t) = A sin w1t and q (w2t) are applied to X and Y inputs of a dual channel CRO. The Lissajous figure displayed on the screen is shown below
Y
The signal q (w2t) will be represented as
[2008, 2 Marks] (a) q(w2t) = A sin w2t, w2 = 2w1 (b) q(w2t) = A sin w2t, w2 = 1 2 w (c) q(w2t) = A cos w2t, w2 = 2w1 (d) q(w2t) = A cos w2t, w2 = 1 2 w
15. Two 8-bit ADCs, one of single slope integrating type and other of successive approximate type, take TA and TB times to convert 5 V analog input signal to equivalent digital output. If the input analog signal is reduced to 2.5 V, the approximate time taken two ADCs will respectively,
be [2008, 1 Mark] (a) TA, TB (b) A B 2 T ,T (c) A B 2 T ,T (d) A B 2 2 T ,T
16. The figure shows a three-phase delta connected load supplied from a 400V, 50Hz, 3-phase balanced source. The pressure coil (PC) and current coil (CC) of a wattmeter are connected to the load as shown, with the coil polarities suitably selected to ensurer a positive deflection. The wattmeter reading will be [2009, 2 Marks]
Z1 Z 2 PC CC C z = (100 + J0) 2 W b a 3-Phase Balanced supply 400 volts 50 Hz. z= (100 +J0) 1 W (a) 0 (b) 1600 Watt (c) 800 Watt (d) 400 Watt
17. An average reading digital multimeter reads 10 V when fed with a triangular wave, symmetric about the time axis. For the same input, an rms reading meter will read
[2009, 2 Marks] (a) 20 3 (b) 10 3 (c) 20 3 (d) 10 3
18. The measurement system shown in the figure uses three sub-systems in cascade whose gains are specified as G1, G2 and
3
1
G . The relative small errors associated with
each respective subsystem G1, G2 and G3 are e1, e2 and e3. The error associated with the output is
[2009, 1 Mark] G2 G1 3 1 G Input Output (a) 1 2 3 1 e + e + e (b) 1 2 3 . e e e (c) e + e - e1 2 3 (d) e + e + e1 2 3
19. The pressure coil of a dynamometer type wattmeter is [2009, 1 Mark] (a) highly inductive (b) highly resistive
(c) purely resistive (d) purely inductive
20. The two inputs of a CRO are fed with two stationary periodic signals. In the X-Y mode, the screen shows a figure which changes from ellipse to circle and back to ellipse with its major axis changing orientation slowly and repeatedly. Which of the following inference can be
made from this? [2009, 1 Mark]
(a) The signals are not sinusoidal
(b) The amplitudes of the signals are very close but not equal
(c) The signals are sinusoidal with their frequencies very close but not equal
(d) There is a constant but small phase difference between the signals
21. The Maxwell's bridge shown in the figure is at balance. The parameters of the inductive coil are [2010, 2 Marks]
R3 R4 R2
~
R j L + w – /(j wC4) (a) 2 3 4 4 2 3 R R R R L C R R = = (b) 4 2 3 2 3 4 R C R R R R L R = = (c) 4 4 2 3 2 3 R R , L C R R R R = = (d) 4 4 2 3 2 3 R L , R C R R R R = =22. An ammeter has a current range of 0–5 A, and its internal resistance is 0.2 W. In order to change the range to 0 – 25A, we need to add a resistance of [2010, 1 Mark] (a) 0.8 W in series with the meter
(b) 1.0 W in series with the meter (c) 0.04 W in parallel with the meter (d) 0.05 W in parallel with the meter
23. A wattmeter is connected as shown in the figure. The
wattmeter reads [2010, 1 Mark]
~
Wattmeter Current coil Potential coilZ1
Z2
(a) zero always
(b) total power consumed by Z1 and Z2 (c) power consumed by Z1
(d) power consumed by Z2 24. A 41
2 digit DMM has the error specification as : 0.2%
or reading + 10 counts. If a dc voltage of 100 V is read on its 200 V full scale, the maximum error that can be expected in the reading is [2011, 2 Marks]
(a) ± 0.1% (b) ± 0.2%
(c) ± 0.3% (d) ± 0.4%
25. Consider the following statements :
(i) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the current coil.
(ii) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the voltage coil circuit. [2011, 1 Mark] (a) (i) is true but (ii) is false
(b) (i) is false but (ii) is true (c) both (i) and (ii) are true (d) both (i) and (ii) are false
26. A dual trace oscilloscope is set to operate in the alternate mode. The control input of the multiplexer used in the y-circuit is fed with a signal having a frequency equal to [2011, 1 Mark] (a) the highest frequency that the multiplexer can operate
properly
(b) twice the frequency of the time base (sweep) oscillator
(c) the frequency of the time base (sweep) oscillator (d) half the frequency of the time base (sweep) oscillator
27. The bridge circuit shown in the figure below is used for the measurement of an unknown element Zx. The bridge circuit is best suited when Zx is a [2011, 1 Mark]
D
~
R2 R4 R1 Zx Vs C1 +(a) low resistance (b) high resistance (c) low Q inductor (d) lossy capacitor
28. An analog voltmeter uses external multiplier setting. With a multiplier setting of 20 kW, it reads 440 V and with a multiplier setting of 80 kW, it reads 352 V. For a multiplier setting of 40 kW, the voltmeter reads [2012, 2 Marks]
(a) 371 V (b) 383 V
(c) 394 V (d) 406 V
29. For the circuit shown in the figure, the voltage and current
expressions are [2012, 1 Mark]
1 3
( ) E sin( ) E sin(3 )= w + w
v t t t and
1 1 3 3 5
( ) I sin(= w - f +) I sin(3w - f +) I sin(5 )w
i t t t t
The average power measured by the Wattmeter is
L oa d v t( ) + – i t( ) Wattmeter (a) 1 1 1cos 1 2E I f (b) 12[E I1 1cosf +1 E I1 3cosf +3 E I1 5] (c) 12[E I1 1cosf +1 E I3 3cosf3] (d) 12[E I1 1cosf +1 E I3 1cos ]f1
30. The bridge method commonly used for finding mutual
inductance is [2012, 1 Mark]
(a) Heavyside Campbell bridge (b) Schering bridge
(c) De Sauty bridge (d) Wien bridge
31. A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent Magnet Moving Coil (PMMC) meter connected across the same load reads [2012, 1 Mark] 10V 5V – 5V 0 10 12 20 Time (ms) V t( ) (a) 4 V (b) 5 V (c) 8 V (d) 10 V
32. The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is [2013, 1 mark]
– + 100 kW 14.14 sin (314t) V Volt-meter 1 kW (a) 4.46 (b) 3.15 (c) 2.23 (d) 0
33. Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V, V1 and V2 as indicated. The correct relation among the voltmeter
readings is [2013, 1 mark] V V1 V2 –j 1W –j 2W (a) V V1 V2 2 2 = + (b) V = V1 + V2 (c) V = V1V2 (d) V = V2 – V1
34. A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as R5 = 300 W. Other bridge resistances are R1 = R2 = R3 = 300 W. The maximum permissible current through the strain gauge is 20 mA. During certain measurement when the bridge is excited by maximum permissible voltage and
the strain gauge resistance is increased by 1% over the nominal value, the output voltage V0 in mV is
[2013, 2 marks] + – R5 R1 R2 R3 V0 – + Vi (a) 56.02 (b) 40.83 (c) 29.85 (d) 10.02
35. In an oscilloscope screen, linear sweep is applied at the (a) vertical axis [2014, Set-1, 1 Mark] (b) horizontal axis
(c) origin
(d) both horizontal and vertical axis
36. The reading of the voltmeter (rms) in volts, for the circuit shown in the figure is _________.
1jW 1/jW 1jW 1/jW V 100 sin( t)w R = 0.5W [2014, Set-1, 2 Marks] 37. The dc current flowing in a circuit is measured by two ammeters, one PMMC and anothrr electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is 0.2 Wb/m2,
and the area of the coil is 80 mm2. The electrodynamometer
ammeter has a change in mutual inductance with respect to deflection of 0.5 mH/deg. The spring constants of both the metres are equal. The value of current, at which the deflections of the two meters are same, is _________.
[2014, Set-1, 2 Marks] 38. The total power dissipated in the circuit, shown in the figure,
is 1 kW. 10 A 2 A 1 W XC1 XC2 XL R V Load 200V A.C. Source
The voltmeter, across the load, reads 200 V. The value of XL
39. Two ammeters X and Y have resistances of 1.2 W and 1.5 W respectively and they give full-scale deflection with 150 mA and 250 mA respectively. The ranges have been extended by connecting shunts so as to give full scale deflection with 15A. The ammeters along with shunts are connected in parallel and then placed in a circuit in which the total current flowing is 15A. The current in amperes indicates in ammeter X is _________. [2014, Set-2, 2 marks] 40. An LPF wattmeter of power factor 0.2 is having three voltage settings 300 V, 150 V and 75 V, and two current settings 5 A and 10 A. The full scale reading is 150. If the wattmeter is used with 150 V voltage setting and 10 A current setting, the multiplying factor of the wattmeter is _________.
[2014, Set-3, 1 Mark] 41. The two signals S1 and S2, shown in figure, are applied to Y
and X deflection plates of an oscilloscope.
t v 1 T 2T S1 t v 1 T 2T S2
The waveform displayed on the screen is
[2014, Set-3, 1 Mark] (a) X Y 1 -1 (b) X Y 1 -1 (c) X Y 1 -1 (d) X Y 1 -1
42. A periodic waveform observed across a load is represented by
V(t) = ìí- + w p £ w < p1 sin1 sin+ wtt 60£ w < ptt 612
î
The measured value, using moving iron voltmeter connected across the load, is [2014, Set-3, 2 Marks]
(a) 3 2 (b) 2 3 (c) 3 2 (d) 2 3
43. In the bridge circuit shown, the capacitors are loss free. At balance, the value of capacitance C1 in microfarad is
_________. [2014, Set-3, 2 Marks]
1. What is the correct sequence of the following types of ammeters and voltmeters with increasing accuracy? 1. Moving-iron
2. Moving-coil permanent magnet 3. Induction
Select the correct answer using the codes given below
(a) 1, 3, 2 (b) 1, 2, 3
(c) 3, 1, 2 (d) 2, 1, 3
2. The total current I = I1 + I2 in a circuit is measured as I1 = 150
±1 A, I2 = 250 2A± , where the limits of error are given as
standard deviations. I is measured as
(a)
(
400 3 A±)
(b)(
400 2.24 A±)
(c)(
400 1/ 5 A±)
(d)(
400 1 A±)
3. A C.R.O. is operated with X and Y settings of 0.5 mV/cm and 100 mV/cm. The screen of the C.R.O. is 10 cm × 8 cm (X and Y). A sine wave of frequency 200 Hz and r.m.s. amplitude of 300 mV is applied to the Y-input. The screen will show
(a) One cycle of the undistorted sine wave (b) Two cycle of the undistorted sine wave
(c) One cycle of the sine wave with clipped amplitude (d) Two cycle of the sine wave with clipped amplitude 4. A Wien-bridge is used to measure the frequency of the
input signal. However, the input signal has 10% third harmonic distortion. Specifically signal is 2 sin 400 pt + 0.2 sin 1200 pt (with t in sec.). With this input the balance will (a) Lead to a null indication and setting will correspond to
a frequency of 200 Hz.
(b) Lead to a null indication and setting will correspond to 260 Hz.
(c) Lead to a null indication and setting will correspond to 400 Hz.
(d) Not lead to null indication
5. Measurement of an unknown voltage with d.c. potentiometer loses its advantage of open circuit measurement when (a) primary circuit battery is changed.
(b) standardisation has to be done again to compensate for drifts.
(c) Voltages larger than the range of the potentiometer are measured.
(d) range reduction by a factor of 10 is employed in the potentiometer to improve resolution.
6. A set of independent current measurements taken by four observers was recorded as: 117.02 mA, 117.11 mA, 117.08 mA and 117.03 mA. What is the range of error?
(a) ±0.045 (b) ±0.054
(c) ±0.065 (d) ±0.056
7. Which of the following bridges can be used for inductance measurement?
1. Maxwell’s bridge 2. Schering bridge 3. Wein-bridge 4. Hay’s bridge 5. Wheatstone bridge
Select the correct answer using the codes given below
(a) 1 and 2 (b) 2 and 3
(c) 3, 4 and 5 (d) 1 and 4
8. The secondary winding of a current transformer is open when current is flowing in the primary then,
(a) there will be high current in primary. (b) there will be very high secondary voltage. (c) the transformer will burn out immediately. (d) the meter will burn out.
9. Which one of the following digital voltmeters is most suitable to eliminate the effect of period noise?
(a) Ramp type digital voltmeter (b) Integrating type digital voltmeter
(c) Successive approximation type digital voltmeter (d) Servo type digital voltmeter
10. Match List - I (Instrument) and List - II (Error) and select the correct answer using the code given below the lists:
List - I List - II
A. PMMC voltmeter 1. Eddy current error B. AC ammeter 2. Phase angle error C. Current transformer 3. Braking system error D. Energy meter 4. Temperature error Codes: A B C D (a) 2 3 4 1 (b) 4 1 2 3 (c) 2 1 4 3 (d) 4 3 2 1
11. Which of the following can be used/modified for measurement of angular speed?
1. LVDT 2. Magnetic pick-up
3. Tacho-generator 4. Strain gauge Select the correct answer using the code given below (a) Only 1 and 2 (b) Only 2 and 3
(c) Only 3 (d) Only 2, 3 and 4
12. A meter has full scale deflection at 90° at a current of 1 A, the response of meter is square law. Assuming spring control, the current for a deflection of 45° will be
(a) 0.25 A (b) 0.50 A
(c) 0.67 A (d) 0.707 A
13. The sensitivity of voltmeter using 0 to 5 mA meter movement is
(a) 50 W/volt (b) 100 W/volt
14. The full scale deflection current of a meter is 1 mA and its internal resistance is 100 W. This meter is to have full deflection when 100 V is measured. What is the value of series resistor to be used?
(a) 99.99 kW (b) 100 kW
(c) 99.99 W (d) 100 W
15. Calculate the maximum velocity of the beam of electrons in a CRT having a cathode anode voltage of 1000 V. Assume the electrons to leave the cathode with zero velocity. Charge of electron = 1.6 × 10–19 C and mass of electron
= 9.1 × 10–31kg.
(a) 0.1875 × 106 m/s (b) 0.1875 × 107 m/s
(c) 0.1875 × 108 m/s (d) 0.1875 × 109 m/s
16. In the Maxwell bridge as shown in the figure below, the values of resistance Rx and inductance Lx of a coil are to be
calculated after balancing the bridge. The component values are shown in the figure at balance. The values of Rx and Lx
will respectively be LX RX 750 W 4000 W 2000 W 0.05 Fm R4 (a) 375 W, 75 mH (b) 75 W, 150 mH (c) 37.5 W, 75 mH (d) 75 W, 75 mH
17. A simple dc potentiometer is to be standardised by keeping the slider wire setting at 1.0183 V. If by mistake, the setting is at 1.0138 V and the standardisation is made to obtain a source voltage of 1.0138 V, then the reading of the potentiometer will be (a) 1.0138 V (b) 1.0183 V (c)
(
)
2 1.0138 V 1.0183 (d) (1.0138)2 V18. Two-wattmeter method is employed to measure power in a 3-phase balanced system with the current coils connected in the A and C lines. The phase sequence is ABC. If the wattmeter with its current coil in A-phase line reads zero, then the power factor of the 3-phase load will be
(a) zero lagging (b) zero leading (c) 0.5 lagging (d) 0.5 leading
19. A digital voltmeter uses a 10 MHz clock and has a voltage controlled generator which provides a width of 10 m sec per volt of unit signal. 10 volt of input signal would correspond to a pulse count of
(a) 500 (b) 750
(c) 1000 (d) 1500
20. In a digital voltmeter, the oscillator frequency is 400 kHz and the ramp voltage fills from 8 V to 0 V in 20 m sec. The number of pulses countered by the counter is
(a) 800 (b) 2000
(c) 4000 (d) 8000
21. A high frequency a.c. signal is applied to a PMMC instrument. If the rms value of the a.c. signal is 2 V, then the reading of the instrument will be
(a) zero (b) 2 V
(c) 2 V (d) 4 2V
22. A current i = (10 + 10 sin t) amperes is passed through an ideal moving iron type ammeter. Its reading will be
(a) zero (b) 10 A
(c) 150A (d) 10 2A
23. In PMMC instrument, the central spring stiffness and the strength of the magnet decrease by 0.04% and 0.02% respectively due to a rise in temperature by 1°C. With a rise in temperature of 10°C, the instrument reading will (a) increase by 0.2% (b) decrease by 0.2% (c) increase by 0.6% (b) decrease by 0.6% 24. Standard cell
(a) Will have precise and accurate constant voltage when current drawn from it is few microamperes only. (b) Will have precise and accurate constant voltage when
few milliamperes are drawn from it.
(c) Will continue to have constant voltage irrespective of loading conditions.
(d) Can supply voltages up to 10 V.
25. If the reading of the two wattmeters are equal and positive in two-wattmeter method, the load pf in a balanced 3-phase 3-wire circuit will be
(a) zero (b) 0.5
(c) 0.866 (d) unity
26. A voltage of {200 2 sin 314t 6 2 sin 942t 30+
(
+ °)
(
)
8 2 cos 1570t 30 }V
+ + ° is given to a harmonic distortion meter. The meter will indicate a total harmonic distortion of approximately
(a) 4.55% (b) 6.5%
(c) 7.5% (d) 8.5%
27. In the measurement of power on balanced load by two-Wattmeter method in a 3-phase circuit, the readings of the Wattmeters are 3 kW and 1 kW respectively, the latter being obtained after reversing the connections to the current coil. The power factor of the load is
(a) 0.277 (b) 0.554
(c) 0.625 (d) 0.866
28. A CRO screen has ten divisions on the horizontal scale. If a voltage signal 5 sin (314 t + 45°) is examined with a line base setting of 5 m sec/div, the number of cycles of signal displayed on the screen will be
(a) 0.5 cycles (b) 2.5 cycles
(c) 5 cycles (d) 10 cycles
29. A 0-10 mA PMMC ammeter reads 4 mA in a circuit. Its bottom control spring snaps suddenly. The meter will now read nearly
(a) 10 mA (b) 8 mA
30. A Lissajous pattern, as shown in figure below, is observed on the screen of a CRO when voltages of frequencies fx and
fy are applied to the x and y plates respectively. fx : fy is then
equal to
(a) 3 : 2 (b) 1 : 2
(c) 2 : 3 (d) 2 : 1
31. Two voltmeters have the same range 400 V. The internal impedances are 30,000 ohms and 20,000 ohms. If they are connected in series and 600 V be applied across them, the readings are
(a) 360 V and 240 V (b) 300 V and 300 V (c) 400 V and 200 V (d) None of these
32. A meter has a full-scale angle of 90° at a current of 1 A. This meter has perfect square-law response. What is the current when the deflection angle is 45°?
(a) 0.5 A (b) 0.65 A
(c) 0.707 A (d) 0.87 A
33. Which of the following electronic instruments (or equipment) can be used to measure correctly the fundamental frequency component of a waveform and its higher harmonics?
1. Cathode ray oscilloscope 2. Vacuum tube voltmeter 3. Spectrum analyzer 4. Distortion factor meter
Select the correct answer using the codes given below
(a) 1 and 2 (b) 2 and 3
(c) 3 and 4 (d) 1 and 4
34. In d.c. potentiometer measurements, a second reading is often taken after reversing the polarities of the d.c. supply and the unknown voltage, and the average of the two reading is taken. This is with a view to eliminate the effects of (a) ripples in the d.c. supply
(b) stray magnetic fields (c) stray thermal emf’s (d) erroneous standardisation
35. Electrostatic instruments are normally used for (a) low current measurements
(b) high current measurements (c) low voltage mesurements (d) high voltage measurements
36. A certain oscilloscope with 4 cm × 4 cm screen has its own sweep output fed to its input. If the x and y sensitivities are same, the oscilloscope will display a
(a) triangular wave (b) diagonal line
(c) sine wave (d) circle
37. Which instrument has necessarily the ‘square law’ type scale?
(a) Permanent magnet moving coil. (b) Hot wire instruments
(c) Moving iron repulsion (d) None of the above
38. In a single-phase power factor meter, the controlling torque is (a) provided by spring control
(b) provided by gravity control
(c) provided by stiffness of suspension (d) not required
39. In electrodynamometer type wattmeter, the inductance of pressure coil produces error. The error is
(a) constant irrespective of the power factor of the load (b) higher at higher power factor loads
(c) higher at lower power factor loads (d) highest at unity power factor loads
40. If an induction type energy meter runs fast, it can be slowed down by
(a) lag adjustment (b) light load adjustment
(c) adjusting the position of braking magnet and moving it closer from the centre of the disc
(d) adjusting the position of braking magnet and moving it away from the centre of the disc.
41. The reflecting mirror mounted on the moving coil of a vibration galvanometer is replaced by a bigger size mirror. This will result in
(a) lower frequency of resonance & lower amplitude of vibration
(b) lower frequency of resonance but the amplitude of vibration is unchanged
(c) higher frequency of resonance & lower amplitude of vibration
(d) higher frequency of resonance but the amplitude of vibration is unchanged
42. In calibration of a dynamometer Wattmeter by potentiometer, phantom loading arrangement is used because
(a) the arrangement gives accurate results.
(b) the power consumed in calibration work is minimum. (c) the method gives quick results.
(d) the onsite calibration is possible.
43. The accuracy of Kelvin’s double bridge for the measurement of low resistance is high because the bridge
(a) use two pairs of resistance arms
(b) has medium value resistance in the ratio arms. (c) uses a low resistance link between standard and test
resistances
(d) uses a null indicating galvanometer.
44. In a Q meter measurement to determine the self-capacitance of a coil, the first resonance occurred at f1 with C1 = 300 pF.
The second resonance occurred at f2 = 2f1, with C2 = 60 pF.
The self-capacitance of coil works out to be
(a) 240 pF (b) 60 pF
(c) 360 pF (d) 20 pF
45. Which one of the following statements is correct? The deflection of hot wire instrument depends on (a) r.m.s. value of the a.c. current
(b) r.m.s. value of the a.c. voltage (c) average value of the a.c. current (d) average value of the a.c. voltage