TANGEDCO AE EE Full Test - 5 - Electrical Engineering (EE) MCQ

Explanation:

Using Integration by parts, ∫ udv = uv - ∫ v du

∴ π - 2

Concept:

The definition of z-transform is given by,

Analysis:

Concept:

If vectors are perpendicular then

Calculation:

Given: and are perpendicular

Let and

We know that, If vectors are perpendicular then

⇒ -2 - 20 - λ = 0

⇒ -22 - λ = 0

∴ λ = -22

By Green’s Theorem

M = 3y

N = 6x

9² = r² = x² + y²

A =

I =

Concept:
The Laplace transform F(s) of a function f(t) is defined by:

From the time-shifting property of Laplace transform:

We know,

n = 1,

Analysis:

L [(t-a)] =

When a loss-free overhead transmission line is terminated through a resistance equal to surge Impedance of the line, there will be no reflection of travelling wave hence the value of R is 400 Ω.

Important Points

The surge impedance or characteristic impedance of a long transmission line is given by,

Z is series impedance per unit length per phase

Y is shunt admittance per unit length per phase

Surge Impedance for the transmission line is about 400 ohms it is around 40 ohms for underground cables.

Surge impedance loading (SIL):

Surge impedance loading is defined as the power load in which the total reactive power of the lines becomes zero. The reactive power generated by the shunt capacitance is consumed by the series inductance of the line.

SIL = V²/Z_C MW

Concept:

The plug setting multiplier of a relay is defined as the ratio of secondary fault current to the pick up current.

PSM = Secondary fault current/Relay current setting

Pick up current = (Rated secondary current in CT) x (Current setting)

Calculation:

Given that,

Current setting = 150% = 1.5

Relay CT ratio = 300/5

Rated secondary current = 5 A

Therefore, pickup value current of relay = 5 x 1.5 = 7.5 A

For 7.5 A, the current in the primary of the CT is

Concept:
Sound:

• A sound is a form of energy that produces a sensation of hearing in our ears.
• It is a kind of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions.
• The disturbance being handed over from one particle to the next.

Light:

• Light is a form of electromagnetic radiation that can be detected by the human eye.
• When light falls on an object, some part of the light is reflected on our eyes and we are able to see.

Explanation

• Sound waves are longitudinal waves and light waves are transverse waves.
• As we know sound waves are longitudinal waves and travel through compression and rarefactions in the medium on the other hand light waves are transverse in nature and do not require medium to travel.
• As we know that, the sound wave and lightwave travels with different velocity and have a different frequency, therefore the wavelength (λ = v/f) is different for both.
• Both sound and light waves follow the law of reflection, refraction, and interference of waves.

Therefore option 2 is correct.

Concept:
A hypothetical gas that obeys the law PV = nR̅T at all pressures and temperatures is called Ideal gas. There are two equations for Ideal Gas.

• PV = nR̅T
• PV = mRT, P = ρRT

where,
P = Absolute pressure (Pa), V = Volume (m³), n = Number of moles of the gas = m/M

Universal gas constant (8314 J/kg-mol.K), T = Absolute Temperature (K)
R = characteristic gas constant R/M , M = Molecular weight of the gas
m = Mass of gas (kg) & ρ = Density of gas (kg/m³)
[Note: Use any of the above equation as per the inputs given]
Calculation:
Given:
V = 50 lit, T = 27 °C ⇒ 300 K, P_abs = 10 MPa ⇒ 10 × 10⁶ Pa, R = 0.26 kJ/kg-K ⇒ 0.26 × 10³ J/kg-K
∵ P = ρRT
⇒ 10 × 10⁶ = ρ × 0.26 × 10³ × 300
⇒ ρ = 128.20 kg/m³

Concept:
Gay Lussac's Law: For a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.
P ∝ T
Explanation
So, the correct statement which represents Gay Lussac's Law is At constant volume, pressure is proportional to temperature.
So, option -2 is correct.
Other Related Points

• Boyles Law: At constant temperature, the pressure is inversely proportional to the temperature for an ideal gas.
• Charles Law: At constant pressure, temperature is proportional to volume for an ideal gas.
• All three laws (Boyles, Charles, and Gay Lussac's) forms Gas Laws.

Explanation:
Mohr Circle:

• It is a two-dimensional graphical representation (σ as x-axis and τ as y-axis) of the state of stress inside a body.
• The abscissa and ordinate of each point on the circle are the magnitudes of the normal stress and shear stress components, respectively.
• In other words, the Mohr circle is the locus of those points which represents the normal and shear stress on various planes passing through a point on a loaded body.

Properties of Mohr Circle:

• Centre of Mohr circle always lies on x-axis (σ-axis) i.e. Mohr circle is always symmetrical about the σ-axis.
• The co-ordinate of centre is which represents normal stress on the plane of τ_max.
• Radius of Mohr circle represents maximum shear stress i.e.
• If two-point on the circumference of Mohr circle subtends an angle 2θ at centre, then the angle between those plane will be θ.

Special case:
1) Hydrostatic loading / Hydrostatic stress:
In the case of hydrostatic fluid, equal and alike normal stress acts on two mutually perpendicular planes without any shear i.e. σ_x = σ_y = σ and τ_xy = 0.

∴ centre is at (σ, 0) and radius = 0, which represents a point on x-axis / σ-axis or normal stress axis.

 
2) Pure shear
In pure shear σ_x and σ_y = 0, τ_xy = τ

∴ centre is at origin (0, 0) and radius = τ.
 

Concept:
The N- point DFT is given as:

The number of complex additions and multiplications in direct DFT are N(N - 1) and N²
For a large value of N, it will take a large time to compute the DFT.
So, we use a different technique called fast Fourier transform (FFT) which follows the “Cooley-Tukey” algorithm.
The number of complex additions (P) and multiplications (Q) will be:


Calculation:
Given that, N = 16
Number of complex additions P = 16 log 16 = 64
Number of complex multiplications Q = 16/2 log 16 = 32

Concept:
According to Faraday's law, the induced emf in a coil (having N turns) is the rate of change of magnetic flux linked with coil,

N = number of turns in the coil
ϕ = magnetic flux link with the coil
Calculation:
Given that ϕ = (t² – 3t) m-wb and N = 200
Induced emf in coil


e = -200 (2t - 3) × 10^-3
then the induced emf in the coil at t = 4
e = - 200 (2 × 4 - 3) × 10^-3 = - 1 V

• The ideal shape of cross-section of a transformer core is circular.
• For making perfect circular cross section, each and every successive lamination steel sheet should be cut in different dimension and size.
• This is absolutely uneconomical for practical manufacturing.
• In reality, manufacturers use different groups or packets of predefined number of same dimension lamination sheets.
• The group or packet is a block of laminated sheets with a predefined optimum height (thickness).
• The core is an assembly of these blocks in such a successive manner as per their size from core central line, that it gives an optimum circular shape of the cross-section.

Concept:

The relation between the line currents in terms of the symmetrical components of currents is given below.

Ia0 = Zero Sequence Component of Current

Ia1 = Positive Sequence Component of Current

Ia2 = Negative Sequence Component of Current

a = 1∠120°, which represents the rotation of 120° in clockwise direction.

a2 = 1∠-120° or 1∠240° in anticlockwise direction or in clockwise direction, respectively.

Calculation:

Given

Ia = j3 A

Ib­ = (1 + j1) A

Ic = (-1 -j1) A

The zero sequence current:

Ia0 = j1 A

By adding a pole to the system, the steady-state response will improve.
By adding a zero to the system, the transient response will improve.

If a > b, then it is a lag compensator
If a < b, then it is a lead compensator
To improve the transient response, the zero should be nearer to the origin. Which is possible if b > a
Therefore, the lead compensator will improve the transient response.
Important Point
Lead compensator:
Transfer function:

If it is in the form of , then a > 1
If it is in the form of , then a < b
Maximum phase lead frequency:
Maximum phase lead:
ϕm is positive
Pole zero plot:

The zero is nearer to the origin.
Filter: It is a high pass filter (HPF)
Effect on the system:

• Rise time and settling time decreases and Bandwidth increases
• The transient response becomes faster
• The steady-state response is not affected
• Improves the stability

Lag compensator:
Transfer function:
If it is in the form of , then a < 1

If it is in the form of , then a > b
Maximum phase lag frequency:
Maximum phase lag:

ϕm is negative

Pole zero plot:

The pole is nearer to the origin.
Filter: It is a low pass filter (LPF)
Effect on the system:

• Rise time and settling time increases and Bandwidth decreases
• The transient response becomes slower
• The steady-state response is improved
• Stability decreases

Concept:

The entropy of a probability distribution is the average or the amount of information when drawing from a probability distribution.

It is calculated as:

bits

pi is the probability of the occurrence of a symbol.

Application:

The number of outcomes = 64.

Since all the outcomes are equally likely, the probability of each outcome happening is:

The information associated with each outcome will be:

∴ The information associated with each outcome is of 6 bits.

Concept:

• In the field of communication different types of propagation method are used for electromagnetic wave.
  • Ground wave propagation: If the radio waves have a frequency less than 2 MHz, then this method is used to communicate from one place to another via earth surface.
    • It gives the best efficiency at receiving end.
  • Sky wave propagation: If the radio frequency is between 2 MHz to 30 MHz then it can be communicated via sky wave by ionosphere reflection of a wave toward earth.
    • This type of propagation is used by short wave broadcast service.
    • Ionosphere act as a reflecting surface for this propagation.
    • It extends its height from 65 to 400 km above the earth surface.
  • Space wave Propagation: It is also known as line-of-sight (LOS) propagation. If the frequency is above 40 MHz then for communication we use this method.
    • Space wave is used in line-of-sight as well as space communication.
    • Because of LOS type of communication sometimes it is blocked by objects in between.
    • Examples are- Television Broadcast, microwave links, satellite communication etc.

Explanation: 

• For waves of frequency:
  • Less than 2 MHz – Ground wave propagation
  • Up to 30 MHz to 40 MHz – Sky wave propagation
  • More than 40 MHz – Space wave propagation

So, Option 3 is correct.

Concept:
Electric field intensity between two parallel conducting plates can be calculated as:
E = V/L
Where E = Electric field intensity
V = supply voltage supplied by the source.
l = distance by which parallel conducting plates are separated.
Application:
Given:
l = 0.05 mm
E = 8 kV/mm
The maximum voltage that can be applied before breakdown is:
8 × 0.05 = 0.4 kV

• A magnetic tape recorder is used to record data which can be retrieved and reproduced in electrical form again. This recorder can record signals of high frequency.
• Speed of the motor plays an important role in the fine recording of audio signals on magnetic tape recorder.
• A motor circuit of a tape recorder comprises a mechanical switch in which a movable contact is connected to a first contact in response to the depression of a recording or reproduction button, and also to a second contact in response to the depression of a fast feeding or rewinding button.
• A motor control circuit is connected to a D.C. power source through the first contact of the mechanical switch to provide a motor speed suitable for the recording or reproduction.
• An output terminal of a constant voltage circuit connected to the D.C. power source is connected to the motor through a switching transistor.
• The switching transistor is rendered conducting in response to the closing of the second contact of the mechanical switch, causing an output from the constant voltage circuit to be supplied to the motor to rotate the motor at a high speed suitable for the fast feeding or rewinding.

Gauss law for electric field:
Gauss's law states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge.
The net flux of a given electric field through a given surface, divided by the enclosed charge should be equal to a constant.
Integral form:
Differential form: ∇ . E = ρ/ε0
Gauss law for magnetic field:
Gauss's law for magnetism is one of the four Maxwell's equations. It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field.
It is equivalent to the statement that magnetic monopoles do not exist.
Integral form:
Differential form: ∇ . B = 0
Gauss law can’t be represented by:
Maxwell's Equations for time-varying fields:

A split-phase motor has no capacitance in the auxiliary circuit. A phase shift with respect to the main current is achieved by using narrow conductors to achieve a high resistance to reactance ratio.

Increasing the resistance means that the auxiliary winding can only be used during starting, otherwise, it would overheat.
A split-phase motor has significantly lower torque at starting than any of the capacitor motors due to the reduced phase angle between main and starting winding currents.

Torques developed by a split-phase motor is proportional to the sine of the angle between I_m and I_s

Open-loop control system:
The open-loop control system can be described by a block diagram as shown in the figure below.

These are the systems in which the control action is independent of output and other state variables.
Ex: Traffic signals, washing machine and bread toaster, systems having no sensor, etc.
Advantages:

• Simple construction and design
• Cost is less
• Maintenance is easy
• No problem of instability
• Convenient to measure when the output is difficult to measure

Disadvantages:

• These are less accurate, and their accuracy depends on the calibration.
• Inaccurate results are obtained with parameter variations within the system.
• Recalibration of the controller is required time to time to maintain accuracy.

Closed-loop control system:
The open-loop control system can be described by a block diagram as shown in the figure below.

These are the systems in which the control action depends on the output. These systems have a tendency to oscillate.
Ex: Temperature controllers, speed control of the motor, systems having sensors, etc.
Advantages:

• More accurate
• Non-linear distortions are less
• Output is less sensitive to parameter changes within the system
• Bandwidth increases

Disadvantages:

• Design is complicated
• More expensive
• May become unstable, if there are malfunctions in the feedback.

State transition matrix:
It is defined as inverse Laplace transform of |sI - A|^-1
⇒ L^-1 |sI - A|^-1 = e^At = ϕ(t)
Properties:
State transition matrix, ϕ(t) = e^At

Application:

By taking inverse Laplace transform,

180-degree conduction with star connected resistive load:

The configuration of the three-phase inverter with star connected resistive load as shown in the figure. The following convention is followed.

• A current leaving a node point a, b or c and entering the neutral point n is assumed to be positive.
• All the three resistances are equal, R_a = R_b = R_c = R

In this mode of operation, each switch conducts for 180°. Hence at any instant of time three switches remain on. There are six possible modes of operation in a cycle and each mode is of 60° duration and the explanation of each mode is as follows:

The general expression of an amplitude-modulated wave for a single-tone message signal is given as:
s_AM(T) = [A_c + A_mcosω_mt] cosω_ct
where ω_m = Frequency of the message signal
ω_c = Carrier signal frequency
The expression can be written as:
s_AM(T) = A_c cosω_ct + A_mcosω_mtcosωc_t
We observe that the amplitude modulated signal has both the carrier frequency and the shifted frequency as shown:

Concept:

During the operation of the transformer, to maintain the sane exciting current the flux must be the same.

Calculation:

Given that, f₁ = 50 Hz, f₂ = 60 Hz

V₁ = 200 V

Anti-Aliasing Filter:

• An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal.
• It blocks the higher frequency contents in a signal to restrict it to a maximum frequency.
• Anti-aliasing filters are commonly used at the input of the digital signal processing system's analog-to-digital converter.

Important Point
Aliasing is explained with the help of the spectrum as shown:

The atoms in these materials have permanent magnetic moments, and a phenomenon called exchange coupling takes place in which the magnetic moments of nearby atoms line up with one another. This forms domains, small neighbourhoods where the magnetic moments are aligned. Typical dimensions of domains are 0.1 to 1 mm.

When a ferromagnetic material is not magnetized it still has domains, but the domains have random magnetization directions. If an external field is turned on two things happen. Domains aligned with the field grow at the expense of domains aligned against the field, and the magnetization direction within each domain tends to shift towards the direction of the applied field.