Measurement and Instrumentation Solved Paper SSC JE (2021-2020)

Answer.4. 1%

Explanation:-

D’ Arsonval movement or PMMC:

• The Deflection of the pointer is directly proportional to the current flowing in the coil.
• The accuracy of D’ Arsonval movements used in common laboratory meters is about 1% of the full-scale reading.
• Note that D’ Arsonval moment responds for the average value of measured quantity.

Answer.3. 4%

Explanation:-

Error (E):

The difference of magnitude between measured value (A_m) and true value (A_t) is called Error.

In engineering, the error is represented with ±.

In general, the error means Absolute Error it has only magnitude.

E = |A_m – A_t|

Percentage error is given as

%E = E × 100/A_t

Application:

Given,

A_m = 48 V

A_t = 50 V

From above concept,

E = |48 – 50| = 2 V

%E = 2 × 100/50

%E = 4%

Answer.4. RMS value

Explanation:-

Thermal-Thermoelectric:

• The instrument which uses the thermocouple for the measurement of the temperature, current, and voltage type of instrument is known as the thermocouple instrument.
• It is used for both the AC and DC measurement. The thermocouple is an electric device that uses two wires of different metals.
• Thermocouple meters are AC meters that respond to the RMS value of a signal.

Answer.2. A multimeter

Explanation:-

• A multimeter is an electronic instrument. It is mainly used to measure the three basic electrical characteristics of voltage, current, and resistance.
• It can also be used to test continuity between two points in an electrical circuit.
• The multimeters can not be used to measure electrical quantities such as frequency, charge, etc.
• The multimeter has multi functionalities like, it acts like ammeter, voltmeter, and ohmmeter.
• It is a handheld device with a positive and negative indicator needle over a numeric LCD digital display.
• Multimeters can be used for testing batteries, household wiring, electric motors, and power supplies.

Answer.2. 6.25 A

Explanation:-

Current transformer:

• A current transformer is a device that is used to measure high alternating current in a conductor.

Let, Np is a number of turn in the primary winding

Ns is the number of turns in the secondary winding.

Ip and Is are primary and secondary turns respectively.

Therefore, the secondary current is given by,

I_s/I_p = N_p/N_s

Given,

N_p = 1, N_s = 8, I_p = 50 A

I_s = 50 × (1 / 8)

I_s = 6.25 A

Answer.2. 6.25 A

Explanation:-

• CRO is a very versatile instrument in the laboratory for measurement of voltage, current, frequency and phase angle of any electrical quantity.
• We cannot directly measure power by using CRO.
• The current is measured indirectly by measuring voltage drop across an impedance.
• A Lissajous figure is a pattern which is displayed on the screen when sinusoidal signals are applied to both horizontal & vertical deflection plates of CRO.
• These are used to measure the frequency of the given signals and phase difference between the signals.
• From the shape of the Lissajous pattern displayed on the CRO screen information about relative phases of signals and the frequency ratio of signals can be determined.
• It is not used for precise measurement; it depends on the type of signals.
• If one frequency is an integral multiple (harmonic) of the other, the pattern will be steady. If not, the figure will not be stationary.

Answer.4. Mass-inertia effects are maximised.

Explanation:-

• A transducer​ refers to any device that transforms mechanical phenomena into electrical phenomena or vice versa.
• The electrical transducer is a device that converts any kind of energy into an electrical signal whether it is analog or digital signals.
• An electrical transducer is also a device that is capable of converting physical quantities into a proportional electrical quantity such as voltage or electric current.

Advantages

The advantages of this transducer mainly include the following.

• Attenuation can be done easily.
• Mass inactivity effects can be reduced.
• Friction effects can be reduced.
• The o/p can be specified & recorded remotely at a distance from the sensing medium.
• The signal can be mixed to get any permutation with outputs of related transducers otherwise control signals.,
• Any system can be managed with a less power level.
• The output can be simply utilized to transmit as well as the process for measurement.

Note:-

Passive transducer or Inactive transducer is also named as an externally power-driven transducer. They derive the required power for energy change from an exterior power source. Inactive transducer do not convert energy but do influence energy conversion if they are capable of storing energy.

Answer.3. 0.99

Explanation:-

Precision: A measurement of consistency or repeatability of measurement i.e., successive reading does not differ.

The average of the measured value is given by,

$\overline {{X_n}} = \sum \frac{{{X_n}}}{n}$

Where X_n is the recorded readings, n is no. of recorded readings.

Precision for particular reading is given by,

$ = 1 – \left| {\frac{{Respective\:Reading – \overline {{X_n}} }}{{\overline {{X_n}} }}} \right|$

Calculation:

The average measurement value

$\overline {{X_n}} = \frac{{98 + 101 + 99 + 100 + 102}}{5}$

The 3rd reading precision is given as

$\begin{array}{l} = 1 – \left| {\frac{{99 – 100}}{{100}}} \right|\\\\ = 1 – \frac{1}{{100}} = 0.99\end{array}$a

Answer.1. 0.9

Explanation:-

Sensitivity(S) of instrument is defined as change in output with respect to change in input

$\frac{{d{V_0}}}{{d{V_i}}} = \frac{{\Delta {V_0}}}{{\Delta {V_i}}}$

V₀ = Output voltage of instrument

V_i = Input voltage of instrument

Application:

Given:

ΔV₀ = 0.18 V

ΔV_i =0.2 V

S = 0.18/2 = 0.9

Answer.2. Strain gauge; strain

Explanation:-

Active transducers:

• Active transducers are those which do not require any power source for their operation.
• They work on the energy conversion principle. They produce an electrical signal proportional to the input (physical quantity).
• Piezoelectric, thermocouple, and photovoltaic cell transducers are some examples of active transducers.

Passive transducers:

• Transducers which require an external power source for their operation is called a passive transducer.
• They produce an output signal in the form of some variation in resistance, capacitance, or any other electrical parameter, which then has to be converted to an equivalent current or voltage signal.
• LVDT, strain gauge, RVDT, etc is an example of a passive transducer.

Strain Gauge:

• Strain Gauge is a passive transducer that converts a mechanical elongation or displacement produced due to a force into its corresponding change in resistance R, inductance L, or capacitance C.
• It uses the variation in electrical resistance in wires to sense the strain produced by a force on the wires.
• A strain gauge is basically used to measure the strain in a workpiece.

Answer.4. ADC and DAC

Explanation:-

Analog Meter:

• An Analog meter (indicating instrument) is fitted with a pointer which indicates on a scale the value of the quantity being measured.
• The moving system of such an instrument is usually carried by a spindle of hardened steel, having its ends tapered and highly polished to form pivots that rest in hollow-ground bearing, usually of sapphire set in steel screws.
• In some instruments, the moving system is attracted to thin ribbons of a spring material such as beryllium-copper alloy, held taut by tension springs mounted on the frame of movement.

Answer.3. Electrodynamometer meter

Explanation:-

Advantages of Electrodynamic instruments:

• Air cored coils are used, they are generally free from hysteresis and eddy current errors when used on AC circuits.
• These instruments can be used for both DC. and AC measurements.
• It is the most accurate instrument for measuring AC signals with frequencies lower than 200 Hz.
• It has precision grade accuracy when used as a wattmeter.
• Less power consumption.

Disadvantages of Electrodynamic instruments:

• Air-cored coils are used, the operating magnetic field of these instruments is so weak that considerable errors may be introduced due to stray magnetic fields and in order to protect them, they must be shielded with cast-iron cases.
• Energy must be used to create two magnetic fields, such instruments are relatively insensitive or having low sensitivity.
• The power required is generally greater than that required by the permanent-magnet type owing to the greater weight of the moving parts.
• Dynamometer-type ammeters and voltmeters have uneven scales. However, the dynamometer wattmeter has a uniform scale.
• They are more expensive than the permanent-magnet-type instruments

Answer.2. Watt

Explanation:-

Answer.3. Electrodynamometer meter

Explanation:-

Moving-Iron Instruments (MI):

• Moving-iron instruments are generally used to measure alternating voltages and currents.

Permanent Magnet Moving Coil (PMMC):

• A Permanent Magnet Moving Coil (PMMC) meter also known as a D’Arsonval meter or galvanometer is an instrument that allows you to measure the current through a coil by observing the coil’s angular deflection in a uniform magnetic field.

Electrostatic Instrument

• The instrument whose working depends on the principle of attraction or repulsion of electrodes that carry electrical charges such type of instrument is known as the electrostatic instrument.
• In other words, the instrument which uses the static electric field for producing the deflecting torque is known as the electrostatic instrument.
• The electrostatic instrument is used for measuring the high and low voltage and also the power of the given circuit.

Induction Type Instrument

• We use induction type instrument for AC measurement only. This is because the induction phenomenon only occurs in AC. An induction instrument has multi use. For example, we use the instruments as ammeters, voltmeters, wattmeters, and energy meters.

Answer.3. Electrodynamometer meter

Explanation:-

Deflecting torque of the PMMC meter is given as,

T_d = NBAI = GI

Where,

Td = deflecting torque in N-m

B = flux density in air gap, Wb/m2

N = number of turns of the coils

A = effective area of the coil in m2

I= current passing through the meter, amperes

G = constant = NBA

The spring control provides a restoring (controlling) torque given as,

TC = Kθ (Nm)

K = spring constant (Nm/degree)

θ = angle of deflection in degree

For the final steady-state deflection condition

Td = Tc

GI = Kθ

Current I = (K/G) θ …..(1)

Calculation:

Given Deflecting torque is directly proportional to current, then the scale of the ammeter is linear and the meter is PMMC type.

Given data

I₁ = 5 A, θ₁ = 80°

For I₁ current let the deflection be θ₁

I₂ = 2.5 A , θ₂ = ?

For I₂ current let the deflection be θ₂

From equation(1),

The current passing through the ammeter is directly proportional to the deflection of the pointer

I ∝ θ

$\begin{array}{l}\frac{{{I_1}}}{{{I_2}}} = \frac{{{\theta _1}}}{{{\theta _2}}}\\\\\frac{5}{{2.5}} = \frac{{{{80}^ \circ }}}{{{\theta _2}}}\end{array}$

θ₂  = 40°

Answer.2. 5/3 Ω resistance in parallel

Explanation:-

Given that: Rm = 5 Ω

$\begin{array}{l}{R_m} = \frac{{{V_m}}}{{{I_m}}}\\\\{R_{sh}} = \frac{{{R_m}}}{{M – 1}}\end{array}$

M= Multiplying factor = (Required full scale deflection) / (Initial full scale deflection)

Where,

Rsh = Series resistance

Rm = Meter resistance

Vm = Potential difference across the meter

Im = Meter current

Calculation:

Given –

Rm = 5 Ω

$\begin{array}{l}M = \frac{1}{{250 \times {{10}^{ – 3}}}} = 4\\\\{R_{sh}} = \frac{5}{{4 – 1}} = \frac{5}{3}\:{\rm{\Omega }}\end{array}$

Rsh = 5 / 3 Ω 

Answer.2. Thermal effect

Explanation:-

• The instruments which use the heating or thermal effect of the current for knowing their magnitude such type of instrument is known as the hot wire instrument.
• The hot wire instrument is used for both the AC and DC current.
• Hotwire instrument works on the principle of the thermal effect, that the length of the wire increases because of the heating effect of the current flow through it.
• When the current is passed through the fine platinum-iridium wire it gets heated up and expands.
• The sag of the wire is magnified, and the expansion is taken up by the spring.
• This expansion causes the pointer to deflect, indicating the value of the current.
• This expansion is directly proportional to the heating effect of the current and hence directly proportional to the square of the RMS value of the current.
• Therefore, the meter may be calibrated to read the rms value of the current.​

Answer.4. Indicating instruments

Explanation:-

Based on their nature of the operation, instruments can be classified into three types.

Indicating Instruments: These indicate the quantity being measured by means of a pointer which moves on a scale. These instruments indicate the instantaneous value of the electrical quantity being measured at the time at which it is being measured.

Example: Ammeter, Voltmeter, Wattmeter

Recording Instruments: These instruments record continuously the variation of any electrical quantity with respect to time. In principle, these are indicating instruments but so arranged that a permanent continuous record of the indication is made on a chart or dial.

Any electrical quantity like current, voltage can be recorded by a suitable recording mechanism.

Example: A potentiometric type of recorder used for monitoring temperature records the instantaneous temperatures on a strip chart recorder.

Integrating Instruments: These instruments record the consumption of the total quantity of electricity, energy etc. during a particular period of time. These instruments give reading for a specific period of time but no indication of reading for a particular instant of time.

Example: Ampere-hour meter, Energy meter, kilovolt ampere-hour meter.

Answer.1. 6.5 V / μm

Explanation:-

The linear variable differential transformer (LVDT) is a type of electrical transformer used for measuring linear displacement (position).

Sensitivity is defined as the ratio between the output signal and the measured property.

Here the output of LVDT is a voltage signal and the measured quantity is displacement.

Sensitivity(S) = output voltage / displacement measured

Given, RMS output voltage = 2.6 V

Displacement = 0.4 μm

S = 2.6 / 0.4

Sensitivity = 6.5 V / μm

Answer.1. a and d

Explanation:-

The permanent magnet moving coil (PMMC) instrument uses two permanent magnets to create a stationary magnetic field. These types of instruments are only used for measuring the DC quantities.

Electrolytic meters are exclusively DC ampere-hour meters, measuring an electric quantity directly and electric energy only indirectly, on the assumption that the pressure of the supply is constant.

Dynamometer type instrument is used for the measurement of A.C. as well as D.C. quantity. It is equally accurate on AC and DC circuits.

Shaded-pole type and induction type instruments are only used for AC measurements.

Answer.4. Manual setting of polarity and zeroing is required

Explanation:-

Digital instruments:

Definition: Instruments that are used to express the measuring quantity in numeric format is known as Digital Instruments.

Principle: Quantization is the basis of the working of a digital instrument. It is an act of transforming an analog signal into its digital form.

Advantages of Digital Instruments:

• Highly accurate measurement.
• Numeric data representation format provides better readability.
• Energy consumption is very less.
• Better resolution: Reading may be carried to any number of significant figures by merely positioning the decimal point

Manual setting of polarity and zeroing is required in analog meters which is a disadvantage for analog meters and it was automatically adjusted in digital instruments.

Answer.2. ∝ θ

Explanation:-

In spring control instrument, the controlling torque is given by,

T_c = K_cθ

And deflecting torque

T_d ∝ I

At equilibrium position, T_C = T_D

⇒ I ∝ θ

Hence in spring control, the scale is uniform.

Answer.4. By connecting 0.2041 Ω resistance in parallel with the instrument

Explanation:-

We can extend the range of ammeter by keeping a shunt resistance as shown:

Rm = internal resistance of the coil

Rsh = Shunt resistance

I = Required full-scale range

Im = Full scale deflection of current

As the two resistances, Rm and Rsh are in parallel, the voltage drop across the resistance will be equal.

Given:

Meter resistance (Rm) = 10 Ω

Full scale deflection current (Im) = 40 mA

Required full scale reading (I) = 2 A

∴ The required shunt resistance that should be connected in parallel/shunt will be:

$\begin{array}{l}{R_{sh}} = \frac{{{R_m}}}{{\left[ {\frac{I}{{{I_m}}} – 1} \right]}}\\\\{R_{sh}} = \frac{{10}}{{\left( {\frac{2}{{40 \times {{10}^{ – 3}}}} – 1} \right)}} = 0.2041\:{\rm{\Omega }}\end{array}$

Answer.1. Induction type

Explanation:-

1. PMMC instruments are only used in DC measurements.

2. MI instruments can be used for both AC & DC measurements.

3. Rectifier type instruments are used for both AC & DC measurements.

4. Induction type instruments are only used for AC measurements.

5. Thermocouple meters can be used for both DC as well as AC quantities.

Answer.4. 

Explanation:-

When two sinusoidal signals of the same frequency and magnitude are applied two both pairs of deflecting plates of CRO, the Lissajous pattern changes with the change of phase difference between signals applied to the CRO

When 0 < ϕ < 90o or 270o < ϕ < 360o

The Lissajous pattern is of the shape of an Ellipse having a major axis passing through the origin from the first quadrant to the third quadrant.

When 90o < ø < 180o or 180o < ø < 270o

The Lissajous Pattern is of the shape of an Ellipse having a major axis passing through the origin from the second quadrant to the fourth quadrant.

Explanation:

The given inputs are: Em sin (ωt) V, Em sin (ωt + 30°) V

The phase difference between both the inputs = 30°

The Lissajous pattern on the screen of a CRO is an ellipse with a major axis in quadrant 1 and quadrant 3.

Answer.2. High resistance, series

Explanation:-

To increase the ranges of a voltmeter, we need to connect a high multiplier resistance in series with voltmeters. Multipliers are used for the range extension of voltmeters. The multiplier is a non-inductive high-value resistance connected in series with the instrument whose range is to be extended. The combination is connected across the circuit whose voltage is to be measured.

Answer.1. Change in thermal conductivity

Explanation:-

Pirani Gauge:

The pirani gauge consists of a Wheatstone’s bridge circuit in which all resistance elements are arranged in four arms as shown in the Fig.. The measuring cell denoted by X4 consists a wire filament and is connected to a vacuum pressure system. Another arm consists a reference cell denoted by Y which is evacuated. This reference cell consists a temperature compensating reference compensating reference wire filament. The remaining two arms consists two equal value resistors.

Initially when the system is at atmospheric pressure the resistance bridge is balanced. A constant voltage is applied to bridge all the time using regulated power supply. When resistances of the filament in measuring and reference cell are equal then no current flows through galvanometer. When the filament of the measuring cell is subjected to vacuum, pressure, it causes change in the conductivity of the gas surrounding filament. Thus equilibrium temperature of a filament also changes. The bridge balance condition gets disturbed. The current under unbalanced condition is indicated by the galvanometer G. Thus the bridge unbalance current can be calibrated interms of the vacumm pressures. The range of pirani gauge is 2 to 200 microns Hg.

1. It is based on a hot metal wire suspended in a tube that is exposed to gas pressure media.

2. The Pirani gauge measures the vacuum pressure dependent thermal conductivity from the heated wire to the surrounding gas.

3. The heated Pirani sensor filament is typically made of a thin (< 20 μm) Tungsten, Nickel or Platinum wire.

4. As gas molecules collide with the filament wire, heat is transported from the hot wire.

5. The heat loss is a function of the gas pressure and at low pressure the low gas density and long mean free path between gas molecules provides low thermal conductivity.

6. At high pressure, the high gas density and short mean free path between molecules will result in high thermal conductivity.

Answer.4. 2.7 mA

Explanation:-

Probable error (ξρ) :

It is defined as A range within one probable error on either side of the mean that will include 50% of the data values.

Probable error is the coefficient of correlation that supports finding out about the accurate values of the coefficients.

Probable error is

${\xi _\rho } = 0.6745 \times \frac{{(1 – {r^2})}}{{\sqrt N }} = 0.6745{\rm{\;}}\sigma .$

σ = Standard error (Standard deviation)

r = Correlation coefficient of ‘n’ pairs of observations for any random sample

N = Total number of observations.

Calculation:

Given that, standard deviation (σ) = 4 mA

Probable error = 0.6745 × 4 = 2.7 mA

Answer.4. Static Error

Explanation:-

The deviation of the measured value from the true value or actual value is called error. It is also known as static error.

Static error (E) = A_m – A_t

Where A_m = measured value

A_t = true value

Answer.1. Thermocouple

Explanation:-

Thermocouple:

• The thermocouple is an electrical device containing junctions of two dissimilar metal joints. It is used as temperature sensors.
• It works on the principle of the thermoelectric effect or the Seebeck effect which means which states that the temperature difference between two dissimilar electric conductors produces a voltage difference between them.
• This potential difference is used to measure temperatures.

Answer.2. Graticule

Explanation:-

CRO is a cathode-ray oscilloscope used to measure amplitude, frequencies, and phase angles of sinusoidal signals.

Graticule: graticule is the grid on the display screen of an oscilloscope that comprises the horizontal and vertical axes. The graticule is used to visually measure waveform parameters.

Important points:

Focus in CRO: The electron beams entering the field at angles other than the normal to the equipotential surfaces will be deflected towards the normal and the beam is thus focused towards the center of the tube axis.

Aquadag: The aquadag coating has two functions: it maintains a uniform electric field inside the tube near the screen, so the electron beam remains collimated and is not distorted by external fields, and it collects the electrons after they have hit the screen, serving as the return path for the cathode current.

Intensity control: Intensity control is provided for adjustment of the brightness of the spot on the screen. It is accomplished by varying the voltage between the first and second anodes.

Answer.3. Halved

Explanation:-

• A pH meter is a scientific instrument that measures the concentration of hydrogen-ion in water based solutions.
• Indicates acidity or alkalinity.
• Expressed as pH.
• The pH scale measures how acidic or basic a substance is.
• The pH scale ranges from 0 to 14.
• A pH of 7 is neutral. A pH less than 7 is acidic. A pH greater than 7 is basic.
• Both H+ and OH- ions are always present in any solution. A solution is acidic if the H+ are in excess. A solution is basic, if the OH- ions are in excess.