DMRC JE Electrical 9th- April- 2018 Paper With Solution and Explanation

Plug setting multiplier of the relay is referred to as the ratio of the fault current in the relay to its pick up current.

The current transformer ratio is 500 / 5. So, the CT can be provided a rated current of 5 Amps to the relay coil.

Now the relay setting is 50%, then the relay can be operated for 5 × ( 50 / 100 ) = 2.5 Amps.

This is the pick-up current of that relay.

We know that the fault current is 2000 Amps. Hence, the fault current in the secondary of the CT is 5 × ( 2000 / 500) = 20 Amps.

Therefore PSM of the relay is,

PSM = 20 / 2.5 = 8

That means the fault current in the secondary of the CT is 8 times greater than the operating current of relay coil.

• Semiconductor materials lie in the range between Conductor and Insulator. Pure germanium has a resistivity of 60Ω cm.
• Pure silicon has a considerably higher resistivity, in the order of 60,000Ω cm.
• As used in semiconductor devices, however, these materials contain carefully controlled amounts of certain impurities, which reduce their resistivity to about 2 Ω cm at room temperature and this resistivity decreases rapidly as the temperature rises.

Clip-on type transformer:

• • A Clip-on type current transformer is also known as a clamp-on type current transformer.
  • Clamp meters rely on the principle of magnetic induction to make non-contact AC current measurements.
  • Electric current flowing through a wire produces a magnetic field. Since alternating current frequently reverses polarity, it causes dynamic fluctuations in the magnetic field which are proportional to the current flow.
  • A current transformer inside the clamp meter senses the magnetic fluctuations and converts the value to an AC current reading. This type of measurement is convenient for measuring very high AC currents.
  • While measuring, the primary is connected to the feeder and the secondary is connected to the ammeter. The current transformer steps down the high feeder current to low current which can be measured by using an ammeter.

REACTANCE

Reactance is the property of resisting or impeding the flow of alternating current or voltage in inductors (coils) and capacitors. It is part of the total opposition to the flow o. AC, also expressed in ohms, is extra to resistance.

There are two types of reactance:

Inductive reactance is the opposition in an inductive circuit (with a coil). When the apply voltage to an inductor a magnetic field is created that slows the current down while the voltage is allowed to build up freely. The amount of back emf depends on the rate of change of the current, in that, the larger its frequency, the larger will be the reverse current, so the effect decreases with a decrease in frequency.

Capacitive reactance exists in a capacitive circuit. and it decreases with an increase in frequency. Unlike inductive reactance, changes to the current occur before any changes to voltage-current now lead to the voltage because when you first apply a voltage, the current will be at its highest value, but the voltage will be at its lowest.

Capacitive reactance is also measured in ohms and is inversely proportional to AC frequency, meaning that when the frequency is high reactance is low, and when it is low reactance is high. Capacitors, therefore, act as low resistance to high frequency and high resistance to low frequencies.

Fig. shows phasor diagrams for series RLC circuit for three different keeping values of both L, and C constant.

For any frequency f is lower than resonant frequency fo, inductive reactance is less than capacitive reactance. Hence the voltage drop VL is less than the voltage drop across the capacitor which is V_C. So the current I leads the resultant supply voltage V and so the circuit behaves as a capacitive circuit at the frequencies which are less than f_o.

At f = f_o, the inductive reactance equals capacitive reactance. Hence the voltage V_Lis equal to V_C. The two voltages cancel each other and the resultant voltage is the same as the voltage V_R. So the voltage and current are in phase. The circuit behaves as the pure resistive circuit at resonating frequency with a unity power factor.

Similarly, for any frequency f higher than resonant frequency f_o, capacitive reactance is very much less than inductive reactance. Hence the voltage drop V_L is more than the voltage drop across the capacitor which is V_C. So the current I lags the resultant supply voltage V and so the circuit behaves as an inductive circuit at the frequencies which are more than f_o.

The effective or r.m.s. value of alternating current is that steady current (d.c.) which when flowing through a given resistance for a given time produces the same amount of heat as produced by the alternating current when flowing through the same resistance for the same time. It is also called the virtual value of a.c. and is represented by I_rms or I_eff or I_v.

For example, when we say that r.m.s. or effective value of an alternating current is 5A, it means that the alternating current will do work (or produce heat) at the same rate as 5A direct current under similar conditions.

To determine r.m.s. value of a sinusoidal alternating current, we have to first square it, then take its mean over one cycle or half-cycle and then take the square root (note that r.m.s. value is calculated by making reverse operation, that is, the first square, then take mean and then take square root).

Square of current i = I_m sinθ = I²_m sin²θ

Its mean over one cycle is calculated by integrating it from 0 to 2π and dividing by the time period of 2π.

Mean value of alternating current

$\begin{array}{l}{\text{Mean of square}}\\\\ = 1/2\pi \int\limits_0^{2\pi } {{I^2}_m} {\sin ^2}\theta d\theta \\\\{\text{RMS Value}}\\\\{\rm{I = }}\sqrt {1/2\pi \int\limits_0^{2\pi } {{I^2}_m} {{\sin }^2}\theta d\theta } \\\\{\sin ^2}\theta = \dfrac{{1 – \cos 2\theta }}{2}\\\\{\rm{I = }}\sqrt {\dfrac{{{I^2}_m}}{{4\pi }}\int\limits_0^{2\pi } {(1 – \cos 2\theta } )d\theta } \\\\ = \sqrt {\frac{{{I^2}_m}}{{4\pi }}\left[ {\theta – \dfrac{{\sin 2\theta }}{2}} \right]_0^{2\pi }} \\\\ = \sqrt {\dfrac{{{I^2}_m}}{{4\pi }}} \times 2\pi \\\\ = \sqrt {\dfrac{{{I^2}_m}}{2}} \\\\I = \frac{{{I_m}}}{{\sqrt 2 }} = 0.707\end{array}$

If we calculate the r.m.s. value for half cycle, it can bc seen that we will get the same value by calculating as

$\begin{array}{l}{\text{Mean of square}}\\\\ = 1/\pi \int\limits_0^\pi {{I^2}_m} {\sin ^2}\theta d\theta \\\\{\text{RMS Value}}\\\\{\rm{I = }}\sqrt {1/\pi \int\limits_0^\pi {{I^2}_m} {{\sin }^2}\theta d\theta } \\\\{\sin ^2}\theta = \dfrac{{1 – \cos 2\theta }}{2}\\\\{\rm{I = }}\sqrt {\frac{{{I^2}_m}}{{2\pi }}\int\limits_0^\pi {(1 – \cos 2\theta } )d\theta } \\\\ = \sqrt {\dfrac{{{I^2}_m}}{{2\pi }}\left[ {\theta – \dfrac{{\sin 2\theta }}{2}} \right]_0^\pi } \\\\ = \sqrt {\dfrac{{{I^2}_m}}{{2\pi }}} \times \pi \\\\ = \sqrt {\dfrac{{{I^2}_m}}{2}} \\\\I = \dfrac{{{I_m}}}{{\sqrt 2 }} = 0.707\end{array}$

Hence the r.m.s. value or effective value or virtual value of alternating current is 0.707 times the peak value of alternating current for the half-cycle as well as for the full cycle.

Almost the whole of the world uses a frequency of 50Hz and a voltage of 220-240(higher voltages for better efficiency in transmission). The exception, where 60Hz is used (with a voltage of 110-120), is the Americas (North and South) and the Caribbean (and parts of Japan and Korea).

The reasons for India’s A.C (ALTERNATING CURRENT) frequency is maintained at 50Hz are very interesting.

IT STARTS FROM THE BEGINNING OF ELECTRICITY-

Early in the history of electricity, Thomas Edison’s General Electric company was distributing DC electricity at 110 volts in the United States.

Then Nikola Tesla devised a system of three-phase AC electricity at  240 volts. Three-phase meant that three alternating currents slightly out of phase were combined in order to even out the great variations in voltage occurring in AC electricity. He had calculated that 60 cycles per second or 60Hz was the most effective frequency.

Tesla later compromised to reduce the voltage to 120 volts for safety reasons. With the backing of the Westinghouse Company, Tesla’s AC system became the standard in the United States.  Westinghouse chose 60 Hz because the arc light carbons(arc lamps) that were popular at that time worked better at 60 Hz than at 50 Hz.

Europe goes to 50Hz and 230V

Meanwhile, the German company AEG started generating electricity and became a virtual monopoly in Europe.
They decided to use 50Hz instead of 60Hz to better fit their metric standards, but they stayed with 120V.

Europe stayed at 120V AC until the 1950s, just after World War II.  They then switched over to 220V for better efficiency in electrical transmission. Great Britain not only switched to 220V, but they also changed from 60Hz to 50Hz to follow the European lead.  Since many people did not yet have electrical appliances in Europe after the war, the change-over was not that expensive for them.

U.S stays at 120V, 60Hz

The United States also considered converting to 220V for home use but felt it would be too costly, due to all the 120V electrical appliances people had.  A compromise was made in the U.S. in that 240V would come into the house where it would be split to 120V to power most appliances.
Certain household appliances such as the electric stove and electric clothes dryer would be powered at 240V.

India got 50Hz because it was colonized by England, which when they developed their electrical systems, choose 50 Hz.

From a technical point of view operating 50 Hz versus 60 Hz would not make much difference but, to achieve it, either the prime movers – for example, steam turbines, gas turbines, and diesel engines would need to be able to tolerate a 20% increase in speed or the alternators they drive – which produce the electricity would need to be completely rebuilt with extra poles and windings so that they could continue to run at the same rotational speed.

We could have chosen any other frequency other than 50/60 Hz, but 50/60 HZ is an optimum frequency that keeps the transmission losses to tolerable limits.

A Bipolar Junction Transistor (BJT) is a three-layer, two junction semiconductor device consisting of either two N-type and one P-type layer of material (NPN transistor) or two P-type and one N-type layer of material (PNP transistor). If a thin layer of N-type Silicon is sandwiched between two layers of P-type silicon. This transistor is referred to as PNP. Alternatively, in an NPN transistor, a layer of P-type material is sandwiched between two layers of N-type material.

The term bipolar is to justify the fact that holes and electrons participate in the injection process into the oppositely polarised material. If only one carrier is employed (electron or hole). it is considered a unipolar device.

CIRCUIT CONFIGURATION OF A BIPOLAR JUNCTION TRANSISTOR

A transistor has three terminals: an emitter (E), base (B), and collector (C) and two junctions as emitter-base junction and collector-base junction. Each of these junctions requires two terminals for a biasing arrangement.

When a transistor is connected to a circuit, it requires four terminals, i.e. two input terminals and two output terminals. Therefore, one of the three transistor terminals (emitter, base, and collector) is used as a common terminal between input and output. Depending upon the common terminal, the transistor may be connected to the three different configurations such as common emitter (CE), common base (CB), and common collector (CC) configurations.

Common Emitter Configuration:

In the common-emitter configuration, the emitter of a transistor is connected to a common terminal between input and output as shown in Fig. The input signal is applied between the emitter and base terminals. The output will be obtained from the collector and emitter terminals. The common emitter configuration of the transistor is the most commonly used one in circuits.

Common Emitter Current Gain β

The current gain, beta (β), is defined for the common-emitter configuration of a BJT and can be defined in two forms: the dc current amplification factor (β_dc) and the ac current amplification factor (β_ac).

The dc current gain β_dc is defined as the ratio of collector current to base current at a constant V_CE under dc biasing conditions.

${\beta _{dc}} = \dfrac{{{I_C}}}{{{I_B}}}$

Similarly, the ac current gain, β_acis defined as the ratio of change in collector current to a corresponding change in base current at a given V_CE under ac signal conditions.

Since the collector current is the output current for a common-emitter configuration and the base current is the input current.

${\beta _{ac}} = \dfrac{{{I_C}}}{{{I_B}}}$

A common-emitter configuration offers the following characteristics:

• The transistor circuit will have a moderately high input impedance
• Low output impedance
• Moderately high current gain
• Moderately high voltage gain and very good and wide range of frequency response and hence find dominant applications in voltage, current and power amplifiers.

Relation between α and β

$\begin{array}{l}{I_E} = {I_B} + {I_c}\\\\\dfrac{{{I_c}}}{\alpha } = \dfrac{{{I_c}}}{\beta } + {I_c}\\\\{\text{Dividing both sides of the equation by }}{I_c}\\\\\dfrac{1}{\alpha } = \dfrac{1}{\beta } + 1\\\\{\text{On Solving}}\\\\\alpha = \dfrac{\beta }{{\beta + 1}}\\or\\\\\beta = \dfrac{\alpha }{{1 – \alpha }}\end{array}$

Note :- For common base configuration current amplification factor is α

For common collector configuration, current amplification factor is Γ

[ninja_tables id=27501]

The synchronous motor is a truly constant speed motor. This is the specialty of this motor. Yet, it has very limited applications. To develop a steady torque, its rotor must be rotating at synchronous speed, Ns. This is the major defect of synchronous motors. Either it runs at synchronous speed, or it does not run at all.

The stator field rotates at synchronous speed due to the three-phase currents supplied to its windings.  In order to develop a continuous unidirectional torque, it is necessary that the stator and rotor poles do not move with respect to each other. This is possible only if the rotor also rotates at synchronous speed. Therefore Magnetic Locking between the poles is necessary to do so.

The concept of Magnetic Locking

• Synchronous motor work on the principle of magnetic locking.
• When two unlike strong unlike magnets poles are brought together, there exists a tremendous force of extraction between those two poles. In such conditions, the two magnets are said to be magnetically locked.

• If now one of the two magnets is rotated, the other magnets also rotate in the same direction with the same speed due to the strong force of attraction.
• This phenomenon is called magnetic locking 

For magnetic locking conditions, there must be two unlike poles and the magnetic axes of these two poles must be brought very nearer to each other.

• Consider a synchronous motor whose stator is wound for 2 poles.
• The stator winding is excited with 3 phase A.C supply and rotor winding with D.C supply respectively. Thus two magnetic fields are produced in the synchronous motor.
• When the 3 phase winding is supplied by 3 phase A.C supply then the rotating magnetic field or flux is produced.
• This magnetic field or flux rotates in space at a speed called synchronous speed.
• When the rotor speed is about synchronous, the stator magnetic field pulls the rotor into synchronism i.e. minimum reluctance position and keeps it magnetically locked. Then rotor continues to rotate with a speed equal to synchronous speed.
• The rotating magnetic field or rotating flux has a fixed relationship between, the number of poles, the frequency of a.c supply, and the speed of rotation.
• The rotating magnetic field creates an effect that is similar to the physical rotation of magnets in space with a synchronous speed.
• So for rotating magnetic field
  Where f = supply frequency
  P = Number of poles

• Suppose the stator poles are N₁ and S₁ which are rotating at a speed of N_s and the direction of rotation is clockwise.
• When the field winding on a rotor is excited by the D.C source, it produces the two stationary poles i.e N₂ and S_2.
• To establish the magnetic locking between the stator and rotor poles the, unlike poles N1 and S2 or N2 and S1 should be brought near to each other.
• As stator poles are rotating and due to magnetic locking the rotor poles will rotate in the same direction of the rotating magnetic field as that of stator poles with the same speed N_s.
• Hence synchronous motor rotates at only one speed which is synchronous speed.
• The synchronous speed depends on the frequency therefore for constant supply frequency synchronous motor speed will be constant irrespective of the load change.

At zero speed or at any other speed lower than synchronous speed, the rotor poles rotate slower than the stator field. Therefore, in one cycle of rotation of the stator field, the N-pole of the rotor is for some time nearer to the N pole of the stator and for some other time nearer to the S-pole of the stator.

As a result, the torque developed is for some time clockwise and for some other time anticlockwise. Consequently, the average torque developed remains zero. Hence the Synchronous Motor Run either on Synchronous Speed Or Not at all.

Interpoles In DC Machine

• In DC machine One way to reduce the effects of armature reaction is to place small auxiliary poles called “interpoles” between the main field poles. The interpoles have a few turns of large wire and are connected in series with the armature.
• One of the disadvantages of armature reaction is brush shifting, therefore a person is always required to adjust the brush position in the machine at every load change. We observe that sparking in the brushes can be avoided if the voltage in the coils undergoing commutation is made zero.
• This method tries to do just the same. Small poles called commutating poles or interpoles are introduced in between the main poles along the geometrical neutral axis. Brushes are also set on this axis and kept fixed at this position for all the loads. The interpole winding has fewer turns of heavy copper conductors.

• Interpoles are connected in series with the armature winding so that they carry full armature current, as shown in Fig. As the load on the machine is increased, the current passing through the interpoles also increases, hence the flux produced by the interpoles is very large. Consequently, the large voltage is induced in the conductor that opposes the voltage due to the neutral plane shift and the net result is that they neutralize each other.
• Note that the interpoles can be used equally effectively in motors as well as in generators. When the mode of operation of the machine changes from the motor to the generator, the currents in the armature and the interpoles is reverses in direction. Therefore, their voltage effects cancel each other out.

Thus, we can conclude that:

1. In a generator, interpoles must have the same polarity as the next upcoming pole.
2. In a motor, interpoles must have the same polarity as the previous main pole.

The mmf induced on the interpoles must be sufficient enough to neutralize the effect of armature reaction and to produce enough field in the interpole winding to overcome the reactance voltage due to commutation.

Another important function of the interpole is to neutralize the cross-magnetizing effect of the armature reaction, as shown in Fig. Here, vector F_M represents the MMF due to the main poles, F_A represents the cross-magnetizing mmf due to the armature reaction and F_C represents the interpole mmf which is directly opposite to the F_A so that they cancel each other out.

It is important to note here that the interpoles do not affect the flux distribution under the pole faces. So, even by using the interpoles in the machine, the flux weakening problem is not completely eliminated. Most medium-sized general-purpose motors correct the sparking problems with the interpoles and just live with the flux weakening problems.

Main Functions of the Interpole

1. The interpole neutralizes the reactance voltage and gives a spark-free commutation.
2. It neutralizes the cross-magnetizing effect of armature reaction so that the brushes are not required to be shifted from their original position for any load.

Load factor = Average load x time / Maximum Demand x time

0.5 = 600 / Max. Demand in kW × 24

Max. Demand = 600 / 24 × 0.5 = 50 kW

When load factor is increased by 0.8.then the energy consumed in 24 hrs

Energy consumption = Load factor × max. demand × 24

= 0.8 × 50 × 24 = 960 kWh