SSC JE Measurement & Instrumentation Solved Questions (2018-2009)

Answer.1. Kelvin’s Double Bridge

Explanation:-

Kelvin’s bridge is a modification of Wheatstone’s bridge and is used to measure values of resistance below 1Ω. In low resistance measurement, the resistance of the leads connecting the unknown resistance to the terminal of the bridge circuit may affect the measurement. In a typical Kelvin’s bridge, the range of resistance covered is 1Ω to 10 μΩ.

The Wheatstone’s bridge is not suitable for comparing two very low resistance such as metal rods because the junction resistances and resistances of connecting wires are larger compared to the low resistance to be measured.

Consider the circuit in Fig., where R_y represents the resistance of the connecting leads from R₃ to R_X (unknown resistance). The galvanometer can b connected either to point c or to point a. When it is connected to point “a” the resistance R_y of the connecting lead is added to the unknown resistance R_x, resulting in too high indication for R_x

When the connection is made to point “c” R_y is added to the bridge arm R₃ and the resulting measurement of R_X is lower than the actual value because now the actual value of R₃ is higher than its nominal value by the resistance R_y. If the galvanometer is connected to point “b” in-between points “c” and “a”, in such a way that the ratio of the resistance from “c” to “b” and the from “a” to “b” equals the ratio of resistances R₁ and R₂, then

R_cb/R_ab = R₁/R₂

The actual equation of Kelvin’s bridge is

R_x = R₁.R₃ ⁄ R₂

Answer.3. Phase Angle

Explanation:-

A multimeter is a very useful electronic instrument that can be used for the measurement of three quantities, namely voltage, current, and resistance. This instrument can also be used for both dc and ac voltages and currents. Multimeters are available in both analog and digital form. Although analog multimeters are being replaced by digital multimeters.

Answer.2. Zinc sulfide with silver as Impurity

Explanation:-

The actual conversion of light energy from the electricity occurs on the display screen when electrons strike the material called phosphor. A phosphor is a chemical that shines when exposed to electrical energy. A commonly used phosphor compound is zinc sulfide. When the pure zinc sulfide is struck by an electron beam, it gives a green glow. The exact color is given by phosphor also depends on the presence of small amounts of impurities. For example, zinc sulfide with silver metal gives a blue glow in the form of an impurity and copper metal gives a green glow in the form of impurity.

Answer.3. 4.76

Explanation:-

System voltage i.e Nominal voltage = 11000 V

Voltage Transformation ratio of potential transformer is

V₁/V₂ = N₁/N₂

V₁/105 = 100

Primary voltage = Turn ratio × Secondary voltage = 105 × 100 = 10500 V

Percentage of error is the Potential error

= (Nominal voltage − Primary voltage)/Primary voltage

(11000 − 10500)/10500

= 4.76%

Answer.1. Incorrect Position of brake magnets

Explanation:-

The energy meter is an integrating meter which measures the electrical energy consumed by a load. Induction type energy meters are very commonly used to measure the electrical energy consumed in domestic, commercial and industrial installations.

Principle

The basic principle of induction type energy meter is electromagnetic induction. When alternating current flows through two suitably located coils (current coil and voltage coil), it produces the rotating magnetic field which is cut by the metallic disc suspended near to the coils. Thus, an emf is induced in the disc which circulates eddy currents in it. 

Errors in induction type energy-meter

The following are the common errors which may creep in an energy meter:

1. Phase and speed errors
2. Frictional error
3. Creeping error
4. Temperature error
5. Frequency error

Speed error:-  Due to the incorrect position of the brake magnet, the braking torque not correctly developed. This can be tested when the meter runs at its full load current alternatively on loads of unity power factor and a low lagging power factor. The speed can be adjusted to the correct value by varying the position of the braking magnet towards the center of the disc or away from the center and the shielding loop. If the meter runs fast on inductive load and correctly on non-inductive load, the shielded loop must be moved towards the disc. On the other hand, if the meter runs slow on no inductive load, the brake magnet must be moved towards the center of the disc.

Phase Error:- The phase error is introduced because the shunt magnet flux does not lag behind the supply voltage by exactly 90° due to some resistance of the coil and iron losses. The angle of lag is slightly less than 90°. Because of this error, the torque is not zero at zero power factor of the load and Therefore, energy meter registers some energy even though the actual energy passing through the meter is zero at zero power factor.

In order to remove this error, the flux produced by the shunt magnet should be made to lag behind the supply voltage exactly by 90°. This is accomplished by adjusting the position of copper shading band provided on the central limb of the shunt magnet. An error on the fast side, under these conditions, can be eliminated by bringing the shading band nearer to the disc and vice versa.

Friction Error:- This error is introduced due to friction at the rotor bearing and in the register mechanism. Because of this error, an unwanted braking torque acts on the moving system and meter registers less energy than the actual energy passing through it.

This error is compensated by placing two short-circuited bands on the outer limbs of the shunt magnet. These bands embrace the flux contained in the two outer limbs of the shunt magnet. An emf is induced and the current circulates through them. This causes phase displacement between the enclosed flux and the main gap flux. As a result of this, small driving torque is exerted on the disc solely by the pressure coil which compensates, the frictional torque. The amount of this corrective torque is adjusted by the variation of the position of the two bands and it should be just sufficient to overcome the frictional torque without actually rotating the disc at on-load.

Creeping Error:- The slow but continuous rotation of the energy meter when only the pressure coil is excited and no current is flowing through the current coil is called creeping. This error may be due to excessive friction compensation, excessive voltage supply, stray magnetic field, etc.

In order to prevent creeping at no-load, two holes of the same radius are drilled in the disc on the opposite side of the spindle. This causes sufficient distortion of the field to prevent continuous rotation. The disc remains stationary when one of the holes comes under one of the poles of the shunt magnet.

Temperature Error:- By the change of temperature, the parameters of the coils change slightly which introduces a small error in the meter. However, this error is negligible and there is no need to provide any means to eliminate this error.

Frequency Error:- Since the energy meters are used normally at the fixed frequency, therefore they are designed and adjusted to have a minimum error at declared supply frequency which is normally 50 Hz in India.

Answer.4. Wheatstone Bridge

Explanation:-

A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The primary benefit of a Wheatstone bridge is its ability to provide extremely accurate measurements.

Under the balanced condition, the following relation is obtained

R₁/R₂ = R₃/R₄

If R₁ is unknown resistance then

R₁ = R₂ × (R₃/R₄)

A Wheatstone bridge can measure any resistance, but it only has a small range. High and low resistances will make the choice of galvanometer harder, and the response less linear. Moreover, while measuring low resistances, the resistance of copper strips and the connecting wires become comparable to the unknown low resistance and hence cannot be neglected. Hence Wheatstone bridge is used to measure the value of medium resistance.

Note:-

The inductance of an inductive coil is generally measured by the usual inductive circuit like Maxwell-Wein Bridge, Hay Bridge, Anderson’s bridge, etc.

The Anderson’s bridge gives the accurate measurement of the self-inductance of the circuit.

Answer.1. ωC₄R₄

Explanation:-

In this bridge, the unknown inductance is measured by comparison with a standard variable capacitance It is much easier to obtain standard values of variable capacitors with an acceptable degree of accuracy

The configuration of Maxwell’s inductance-capacitance bridge and the associated phasor diagram balanced state are shown in Figure

The unknown inductor L₁ of effective resistance R₁ in the branch AB is compared with the standard known variable capacitor C₄ on arm CD. The other resistances R₂, R₃, and R₄ are known as non-inductive resistors.

The bridge is preferably balanced by varying C₄ and R4, giving independent adjustment settings.

Under the balanced condition, no current flows through the detector. Under such conditions, currents in the arms AB and BD are equal (I₁). Similarly, currents in the arms AC and CD are equal (I₂). Under the balanced condition, since nodes B and D are at the same potential, voltage drops across arm BD and CD are equal (V₃ = V₄); similarly, voltage drops across arms AB and AC are equal (V₁ = V₂).

Under the balance condition, the unknown quantities i.e resistor R₁ and C₁ can be determined by the

R₁ = R₂ × R₃ ⁄ R₄

&

L₁ = C₄ × R₂ × R₃

It is interesting to note that both in Maxwell’s Inductance Bridge and Inductance-Capacitance Bridge, the unknown Inductor L1 was always associated with a resistance R1. This series resistance has been included to represent losses that take place in an inductor coil. An ideal inductor will be lossless irrespective of the amount of current flowing through it.

However, any real inductor will have some non-zero resistance associated with it due to the resistance of the metal wire used to form the inductor winding. This series of resistance causes heat generation due to power loss. In such cases, the Quality Factor or the Q-Factor of such a lossy inductor is used to indicate how closely the real inductor comes to behave as an ideal inductor.

The Q-factor of an inductor is defined as the ratio of its inductive reactance to its resistance at a given frequency. Q-factor is a measure of the efficiency of the inductor. The higher the value of Q-factor, the closer it approaches the behavior of an ideal, lossless inductor. An ideal inductor would have an infinite Q at all frequencies.

The Q-factor of an inductor is given by the formula Q = ωL/R, where R is its internal resistance R (series resistance) and ωL is its inductive reactance at the frequency ω_o.

Q-factor of an inductor can be increased by either increasing its inductance value (by using a good ferromagnetic core) or by reducing its winding resistance (by using good quality conductor material, in special cases may be superconductors as well).

In Maxwell’s Inductance-Capacitance Bridge, Q-factor of the inductor under measurement can be found at balance condition to be

Q = ωL₁/R₁

or

Q = (ωC₄ R₂ R₃) ⁄ (R₂ × R₃/R₄ )= ωC₄ R₄

The above relation for the inductor Q factor indicates that this bridge is not suitable for the measurement of inductor values with high Q factors since in that case, the required value of R₄ for achieving balance becomes impracticably high.

Answer.1. Megger

Explanation:-

The principal purpose of testing the insulation is to verify that there are no inadvertent connections between live conductors and between live and Earth before the installation is energized. Tests are required between live conductors (e.g. between phases and between phase(s) and neutral) and between all live conductors and Earth.

Insulation resistance of the installation depends on many factors such as atmospheric conditions, humidity, dirt, etc. As such its calculation is not possible, but it can be readily measured. Normally the insulation resistance is quite high and can be measured by an instrument called megger usually used for the measurement of high resistance. The main object in performing this test is to ascertain whether the complete wiring is sound enough to avoid leakage current.

Insulation testing megger is a portable instrument used for testing the insulation resistance of a circuit, and for measuring the resistance of the order of megaohms in which the measured value of resistance is directly indicated on a scale.

Answer.2. 2

Explanation

The deflection sensitivity of a magnetic deflection cathode ray tube is defined as the amount of spot deflection on the screen when the potential of 1 volt is applied to the deflection plate.

In most CROs, the deflection sensitivity is expressed as the ratio of input voltage to the length of the trace.

In the electrostatic deflection, the spot la deflected on the screen by applying voltages on the vertical or the horizontal deflecting plates. The dc or peak-to-peak ac voltage applied to the deflects ing plates to displace the spot by 1 mm on the screen is termed the deflection factor. The reciprocal of the deflection factor is called the deflection sensitivity. The deflection factor la usually expressed in V/mm and deflection sensitivity in mm/V.

Deflection sensitivity of the CRO is given as

Deflection sensitivity = 1/deflection factor

Deflection sensitivity = 1/0.5 = 2 m/V

Answer.3. 8

Explantion:-

The sensitivity of a voltmeter is given in ohms per volt. It is determined by dividing the sum of the resistance of the meter (R_m) plus the series resistance (R_s), by the full-scale reading in volts. In equation form, sensitivity is expressed as follows:

Sensitivity (S) = (R_m + R_s) ⁄ V_fld

or

Sensitivity (S) = Sensitivity = Ohm/Volt = 1/Volt/Ohm = 1/Ampere

S = 1/125 = 0.008A

S = 8 mA