SSC JE Electrical question paper with solution 2016 -Set-3

Ques.11. The parts of the armature electric circuit which take the active part in e.m.f. generation are

  1. The coil sides inside the slots
  2. The overhangs
  3. Both the coil sides inside the slots and the overhangs
  4. The commutator segments

The parts of the armature electric circuit which take an active part in E.M.F generation are the coil sides inside the slots.

Turn: Two conductors Iying in a magnetic field connected in series at the back,  so that emf induced in them is additive is known as a turn.

Coil. A coil may be a single turn coil having only two conductors, as shown in fig. it may be a multi-turn coil having more than two conductors as shown in fig. Multi-turn coils are used to develop higher voltages.

Single turn multi turn

Short-Pitched coil & Full Pitched Coil

When the coils are full pitched, the induced emf in a coil is the arithmetic sum of the emf induced in two sides of the same coil since the coil sides are displaced by 180° electrical. In this case, the two sides of the same coil are placed at the similar position of two adjacent poles (North and South).

In the case of short-pitched and overpitched coils, the resultant induced emf is reduced because the two sides would fall under the influence of the same pole at some instant. In this instance, the induced emf in the two sides will oppose each other causing a reduction in resultant emf (phase difference).

Full pitch short pitch

The advantage of short-pitched winding is that in this case the copper used for end connection is reduced substantially which reduces the cost of the machine. It also improves the commutation (reduction of sparking at brushes) because the inductance of overhang connections is reduced Moreover, it reduces the copper losses and improves the efficiency to some extent. Hence, many a time short pitch winding is used.

 

Ques.12. The function of a commutator in a DC generator is.

  1. To collect current from conductors
  2. To change DC into a.c.
  3. To conduct the current to the brushes
  4. To change A.C. into D.C

The commutator is one of a very important parts of the DC machine which rotates with the armature. The function of the commutator is to convert alternating currents induced in the armature conductors into direct currents in the external circuit in case of generator operation. In the case of a dc motor, the function of the commutator is to produce a unidirectional torque. The commutator also helps to keep the magnetic flux stationary in space.

construction of DC generator

Generally, the alternating voltage is produced in the coil, which is rotating in a magnetic field, but the direct current is required in the external circuit. For this purpose, the commutator is needed. Each commutator segment is connected to the ends of the armature coils. The commutator receives the current from the brushes, which are also placed on the rotating armature

Ques.13. Maximum efficiency will occur, when copper loss and iron loss are

  1. Unity
  2. Zero
  3. Unequal
  4. Equal

The efficiency of the transformer

Due to the losses in a transformer, the output power of a transformer is less than the input power supplied.

∴ Power Output = Power Input − Total Losses

Power Input = Power Output + Total Losses

= Power Output + Pcu + Pi

The efficiency of any device is defined as the ratio of the power output to the power Input. Therefore Efficiency

$\begin{array}{l}\eta = \dfrac{{{\text{Power Output}}}}{{{\text{Power Input}}}}\\\\\eta = \dfrac{{{\text{Power Output}}}}{{Power{\text{ }}Output{\rm{ }} + {\rm{ }}{P_{cu}} + {\rm{ }}{P_i}}}\end{array}$

Now Power Output = VICosφ

Where Cosφ is the load power factor

Let the transformer supply full load current I2 and with terminal voltage V2.

Pcu = Copper losses on full load = I22R2e

$\begin{array}{1} \eta = \dfrae{{{V_2}{1_2}Cos{ \Phi _2}}}{{{V_2}{I_21Cos{ \Phi _2} + {P_i} + g_21^2{R_{2e}}}}%\{ \text{Dividing both Numerator and Denominator By }}{{Vm{I}}_{Vm{2}}}%\ \eta = \dfrae({{V_2}Cos{ \Phi _2}}}{{{V_2}Cos{ \Phi _2} + \dfrac{{{P_i}}}{{{I_2}}} + {I_2}{R_{2e}}}}\end{array} $

 

The condition for Maximum Efficiency Of transformer

When a transformer works on a constant input voltage and frequency then efficiency varies with the load. As the load increases, the efficiency increases. At a certain load current, it achieves a maximum value. If the transformer is loaded further the efficiency starts decreasing.

The load current at which efficiency attain the maximum value is denoted as I2m and the maximum efficiency is denoted as ηmax.

The efficiency is the function of load i.e Load current I2 assuming cosφ2constant. The secondary terminal voltage V2 is also assumed to be constant.

For the maximum value of cosφ, and the denominator must have the least value. The condition for maximum A, obtained by differentiating the denominator with respect to I2 and equate to zero, thus 

To determine the maximum efficiency differentiate the denominator 

$/begin{array}{1} dfrac{d}{{d{I_2}}}Veft( {\dfrac{{{V_2}Cos{\Phi _2}}}{{{V_2}Cos{ \Phi _2} + \dfrac{{{P_i}}} {{{I_2}}} + {I_2}{R_{2e}}}}} \right) \\\{ \text{or }}\dfrac{{{P_i}}}{{{I_2}}} + {R_{2e}} = o \\VI_21^2{R_{24} = {P j}\end{ array}$

 

Copper-loss (variable) (I2R) = core loss Pi (constant)

Hence the efficiency will be maximum at a load in which the total copper loss in the windings is equal to the core loss. A transformer is designed such that its efficiency is generally maximum at a load slightly lower than the full-load. This is because the transformer generally works at a load lower than the full-load rating (when a transformer is installed, its rating is chosen higher than the estimated load). Thus by design, the transformer is put to work at near maximum efficiency.

 

Ques.14. Which of the following circuit conditions does a metal oxide varistor (MOV) protect against?

  1. High Current
  2. High Voltage
  3. High circuit Noise
  4. High crosstalk

A varistor is a voltage-dependent resistor used as a device to protect delicate electrical circuits from sudden, drastic changes in voltage. The variation in the resistance they offer to the flow of current under varying voltage is the basis of their use. Varistor materials offer high resistance at low voltages and low resistance at high voltages.

A varistor is coupled with the main electrical circuit in an alternative pathway. Normally when the voltage in the circuit is low this device does not conduct any current because they offer high resistance to the flow of current and hence current flows through the main circuit. But as soon as a drastic increase in voltage occurs, its resistance falls off and it allows most of the current to pass through, thus protecting the main circuit from damage. Varistors are used in voltage stabilizers and for motor speed control.

There are two types of varistors

Silicon Carbide Varistor or Carborundum crystal Varistor:- These varistors are made from silicon carbide mixed with a suitable ceramic binder material. The mixture la prefixed to the desired shape and then wintered (compressed under heat) under controlled conditions to the produced hard ceramic body.

Silicon-carbide varistors have a high power-handling capability and are used in high-voltage surge (lightning) arresters. The devices tend to draw considerable current in the normal state, and so they are commonly used in series with a gap that provides an open circuit until a surge occurs. This property makes silicon-carbide varistors unsatisfactory for low-voltage clamping operation. Newer zinc-oxide lightning arresters have better nonlinear characteristics and can be used without a gap. They are essentially crowbar devices but perform almost like clamping devices.

Metal oxide Varistor:- They are made from the mixture of zinc oxide, bismuth oxide, and other powdered metals, which are pressed into the disc and then sintered above 1200°C

At very low voltage they provide infinite resistance (open circuit) and when the applied voltage exceeds rated voltage they appear as a short circuit and thus protect, the component they shunt.

Metal oxide varistor

Metal-oxide varistors (MOVs) are solid-state device and is usually connected in parallel across the input power supply. Metal-oxide varistors (MOVs), the most common clamping devices, are available for use at a wide range of voltages and currents. The range of parameters includes:

  • Voltages as low as 4 V for data lines u to several thousand volts for power systems
  • Peak pulse currents from a few amperes to tens of thousands of amperes
  • Energy dissipation from less than 1 to over 10,000 joules.
  • MOVs are low in cost, compact in size, easy to apply, and are among the most frequently used devices for transient protection. One disadvantage of the MOV is that its operating characteristics deteriorate with repeated transients. Although this problem has been reduced with improved technologies, MOV life under frequent transient conditions must be considered.

 

Ques.15. The frequency and time domain are related through

  1. Laplace transform only
  2. Fourier integral only
  3. Laplace transform or Fourier integral
  4. Both Laplace transform and Fourier integral

Frequency domain conversion: It is the analysis of mathematical functions or signals with respect to frequency, rather than time. Commonly, a time-domain graph shows signals over time, whereas a frequency domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. The spectrum of frequency components is the frequency domain representation of the signal.

A spectrum analyzer is a tool commonly used to visualize real-world signals in the frequency domain. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid to be able to recombine the frequency components to recover the original time signal. A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called a transform. The most common transforms between time and frequency are

  • Fourier transform, which converts the time function into a sum of sine waves of different frequencies, each of which represents a frequency component. Fourier transform of a function is a complex function of a real variable (frequency). The inverse Fourier transform converts the frequency domain function back to a time function.
  • Fourier series: it is used for repetitive signals as oscillating systems. A Fourier series is a way to represent a wave-like function as the sum of simple sine waves. It decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials). The Fourier transform of a function of time itself is a complex-valued function of frequency, whose absolute value represents the amount of that frequency present in the original function, and whose complex argument is the phase offset of the b, basic sinusoid in that frequency.
  • Laplace transform: the Laplace transform of a function is a complex function of a complex variable. The Laplace transform is an integral transform. It takes a function of a positive real variable t (often time) to a function of a complex variable s (frequency). Laplace transformation from the time domain to the frequency domain transforms differential equations into algebraic equations and convolution into multiplication. It has many applications in the sciences and technology.
  • Z-transform: in mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation. It can be considered as a discrete-time equivalent of the Laplace transform. This similarity is explored in the theory of time scale calculus.
  • Wavelet transform: a wavelet series is a representation of a square-integrable (real-or complex-valued) function by a certain orthonormal series generated by a wavelet. It is used for data compression in image analysis.

 

Ques.16. _________ should be provided as the working space around the main switchboard according to Indian Electricity Rule 51.

  1. 0.523 m
  2. 1 m
  3. 0.638 m
  4. 0.814 m

According to Indian Electricity Rule 51, every switchboard shall comply with the following provisions, namely:

  1. A clear space of more than 1m in width shall be provided in front of the switchboard;
  2. If there are any attachments or bare connection at the back of the switchboard, the space (if any) behind the switchboard shall be either Less than 20 cm or more than 75 cm in width, measured from the furthest outstanding part of any attachment or conductor;
  3. If the space behind the switchboard exceeds 75 cm in width, there shall be a passageway from either end of the switchboard clear to a height of 1.8 m.
  4. In case of installations provided in premises where inflammable materials including gases and/or chemicals are produced, handled, or stored, the electrical installations, equipment, and, apparatus shall comply with the requirements of flame-proof, dust-tight totally enclosed of any other suitable type of electrical fittings depending upon the hazardous zones as per the relevant Indian Standard Specifications.

 

Ques.17. Moire fringes are used to measure rotary displacement along with

  1. Contact type encoders only
  2. Optical encoders only
  3. Contact type encoders and optical encoders
  4. None of these

The word ‘Moire’ is derived from silk fabric which when superimposed on itself exhibits light and dark bands. Optical encoders are common displacement sensors that utilize the Moire effect.

Optical encoders are commonly used for measuring angular or linear position, velocity, and directional movement. A typical optical encoder consists of a light source, a disk on which a pattern is etched, a sensing head.

The Moire fringe principle has also been used for optical transducers and encoders. The Moire fringe method is basically an optical method of amplifying displacement by using two identical gratings.  The opaque lines are at right angles to the length of the grating. When two gratings of the same pitch are mounted face to face with the rulings inclined at an angle θ to each other, a set of dark bands called Moire fringes are obtained. When one grating pattern is moved with respect to the other at right angles to its lines, the Moire fringe pattern travels at right angles to the direction of movement.

Moire Fringes 2

The measure of movement depends on the relative distance traveled by the gratings. Analysis of the geometric relationship between the Moire fringes and the grating pair enables displacement to be computed. This principle has been applied to measuring length, angle, straightness, and circularity of motion.

Example:-

The Moire technique is traditionally used for precise displacement measurements. Figure shows the Moire fringe generated by superimposing two gratings. The period of the Moire fringe is much large than that of the gratings. When the angle between the grating lines is increased, the period of the Moir fringe decreases. Translating a grating in a direction perpendicular to the grating lines, the Moire fringe moves in the direction parallel to the grating lines with a magnified displacement. When the two gratings are parallel, the magnification of the displacement is maximized.

Moire Fringes 1

 

Ques.18. A dominant wave is characterized by

  1. Lowest attenuation
  2. Highest attenuation
  3. Lowest cut off wavelength
  4. Highest cut off wavelength

Dominant Wave:- Dominant wave is the electromagnetic wave that has the lowest cutoff frequency in a given Uniconductor waveguide. A wave mode with the lowest cut-off frequency is generally used for practical studies.

Note:- Some Other Important Definition:-

Waveguides: Waveguides are the hollow metallic tube of virtually any consistent cross-sectional shape through which an electromagnetic wave travels by reflection and not by conduction.

Mode: Mode is a distinct field configuration obtained by solving Maxwell’s equation for the particular waveguide.

Degenerate Mode: Two or more modes having the same cut-off frequency are said to be degenerate modes

 

Ques.19. Determine the value of maximum power (in W) transferred from the source to the load in the circuit given below

ques.19o

  1. 30
  2. 25
  3. 20
  4. 37.5

Statement of the theorem: Maximum power transfer theorem is stated as “in a dc network maximum power will be consumed by the load or maximum power will be transferred from the source to the load when the load resistance becomes equal to the internal resistance of the network as viewed from the load terminals.

Step-1: Converting the current source into the equivalent voltage source

ans.19a

Step:2 Open circuit voltage terminal across A and B is calculated as

ans.19b

 

Applying Kirchoff’s Voltage Law in the given circuit

12V − 3I − 3I − 18V = 0

−6V = 6I

I = −1A

The voltage across terminal A & B is

V = 18 − 3 × 1 = 15V

Step:-3

Equivalent Resistance Req across terminal A and B by short-circuiting the voltage source is

ans.19c

= 3Ω || 3Ω = (3 x 3)/(3 + 3) 

Req = 3/2Ω

Step:-4 

Thevenin equivalent circuit across RL is

ans.19d

For maximum Power transfer, RL = Rs = 1.5Ω

Current I, = Vs ⁄ (RL + Rs)

I = 15  ⁄ (1.5 + 1.5)

I = 15 ⁄ 3 = 5A

Maximum Power = I2RL = 52 × 1.5 = 37.5 W

 

Ques.20. The electric field from ‘a’ to ‘b’ will be

Ques.20

  1. Increasing
  2. Decreasing
  3. Remain the same
  4. Zero

The electric field intensity at a point tat a distance R from Q) due to a point charge Q in free space can be obtained as 

E = Q/(4π εoR2

Where

Q: Charge placed (in Coulumb) 
R: distance between charge placed and point where the electric field is to be calculated 

E ∝ 1/R2 

Electric field intensity is inversely proportional to the  distance between the charge

b > a  i.e Radius of b > Radius of a

Therefore electric field at point ‘b’ will decrease from point ‘a’.

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