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

Wrong Option:-

For DC

Voltage = 15 V
Current  = 1.5 A

For AC

Voltage = 230 V
Current = 2 A
Power = 60 W

Total loss = Loss in resistance + Iron loss

Iron loss = Total Loss – Loss in resistance

P_i = P − I²R

For DC supply

R = 15 ⁄ 1.5 = 10Ω

Therefore Iron Loss is equal to

P_i = 50 − 1.5² × 10

P_i = 27.5 W

Replacing some Si atoms with atoms from Group III (boron, gallium, indium—also known as acceptor impurities), which have three valence electrons, will create a p-type material. Because four valence electrons are required to form and complete all adjacent electron-pair bonds, a hole is created by the missing bond.

A hole can be considered a positive charge which can diffuse or drift through a crystal. This becomes important when an external voltage is applied across the semiconductor, creating an electric field inside the semiconductor which then acts on the holes, causing them to move.

The resultant current in p-type material is thus primarily by positive charges, which are also referred to as majority carriers. p-type doping is illustrated in Fig.

Important Points

• The impurity atoms in the P-type extrinsic semiconductor are called acceptor atoms, as they accept an electron from the host lattice.
• In the P-type semiconductor, the number of holes in the valence band > the number of electrons in the conduction band.
• In the P-type semiconductor holes are majority charge carriers while electrons are minority charge carriers.
• In the P-type semiconductor, the Fermi level shifts towards the valence band.

Rotor conductors are skewed because of these two main reasons

Cogging:-

• The Cogging effect is also called magnetic locking. When an induction motor refuses to start even if the full voltage is applied to it, this is called cogging. This happens when the rotor slots and stator slots are the same in number or they are integer multiples of each other. due to this the opposite poles of the stator and rotor come in front of each other and get locked.
• Starting torque of an induction motor depends on the product of the magnitude of stator and rotor current and sine of the angle between both.
• If the conductors remain linear, the angle between stator and rotor current will be 180 degrees. As sin(180)=0, the starting resultant torque will be zero and thus motor will fail to start. This phenomenon is called cogging.
• Skewing makes the rotor conductor longer with the reduced cross area. This increases the rotor conductor resistance hence starting performance and the torque of an induction motor are improved.

Skewing the rotor bars prevents the locking thus preventing Cogging.

Crawling:– Crawling is a phenomenon where harmonic components introduce oscillations in torque. With the bar skewed, the amount of the bar cutting the field line grows continuously and the next bar starts cutting the field lines as the first finishes. Due to this, we get Uniform Torque.

• In a reverse-biased p-n junction diode, the positive terminal of the battery is connected to the n-type semiconductor material and the negative terminal of the battery is connected to the p-type semiconductor material.

• In reverse biasing, free electrons and holes move away from the junction. Hence, increasing the width of the depletion layer. As the depletion layer increases, the potential barrier also increases.
• The majority of charge carriers cannot move across the junction, hence current will not be allowed to flow across the diode. That is, on reverse biasing, the P-N junction diode acts as an insulator or as an Open switch.
• An ideal diode acts as an open circuit under reverse bias conditions. A practical diode offers large but not infinite resistance under reverse bias conditions.
• A diode conducts current when forward biased and blocks current when reverse biased.
• The current flowing in the reverse-biased circuit due to the minority charge carrier is known as reverse current.

Measurand: The quantity or variable being measured is called measurand.

Basically, there are three types of Force or torque that act upon the Measuring Instrument

1. Deflecting Torque
2. Controlling Torque
3. Damping Torque

Deflecting Torque: In order to move the pointer from its zero position on the scale deflecting torque is required. The deflecting torque works on the moving system to which the pointer is attached. Obviously, the magnitude of deflecting torque produced is proportional to the magnitude of the quantity being measured, say, the current I flowing through the instrument. A deflecting torque is required to overcome the inertia, damping effect, and controlling effect of the moving system.

This deflecting torque can be produced by any of the effects of current (or voltage) such as

1. Magnetic effect
2. Electrostatic effect
3. Electromagnetic effect
4. Thermal effect
5. Chemical Effect

Controlling Torque: With the help of the deflecting torque, the pointer deflection will take place on the calibrated scale but to stop the pointer at the definite position, controlling torque (Tc.) comes into action. As the deflection of the pointer increases, the controlling torque also increases and stops the pointer at the measured value.

Controlling torque is also known as restoring torque i.e., it brings back the pointer to its zero position when deflecting torque is withdrawn. The pointer attains a steady position when controlling torque becomes numerically equal to deflecting torque i.e., Tc = Td

Spring control and gravity control are used for controlling torque.

Damping Torque: At the final deflected position, when the deflecting and controlling torques are equal, the pointer starts oscillating owing to its inertia and therefore, cannot immediately settle at its final deflected position. If no extra force is provided to dampen these oscillations, the moving system will take considerable time before coming to settle to the final deflected position. This is especially undesirable if the number of readings to be taken is quite large.

The formula of an average value of current is

I_avg = 0.637 × I_m

Where I_m = peak or maximum value of current

45 = 0.637 × I_m

I_m = 70.643 A

The instantaneous value of the sine wave for any angle of rotation is expressed by the following formula

I = I_msinθ

Hence the instantaneous value of current for an angle of 30° is

I = 70.643 × sin30°
= 70.643 × .5

I = 35.32

There are several important characteristics of series circuits. Remember the following basic rules for series circuits:

1. The same current flows through each part of a series circuit.
2. The total resistance of a series circuit is equal to the sum of the individual resistances.
3. The voltage applied to a series circuit is equal to the sum of the individual voltage drops.
4. The voltage drop across a resistor in a series circuit is directly proportional to the size of the resistor.
5. If the circuit is broken at any point, no current flows.

The voltage across a resistor is often called a “voltage drop.”

Now suppose two resistors of 10Ω and 20Ω are connected in series and the current in the circuit is 2A.

Therefore voltage drop across 10 ohms resistance is

V = I x R = 2 x 10 = 20 V

Voltage drop across 20 ohm resistor is

V = I x R = 2 x 20 = 40 V

Hence it is clear that the different resistors have a different voltage drop

The semiconductor is divided into two types. One is an Intrinsic Semiconductor and the other is an Extrinsic semiconductor.

Intrinsic Semiconductors

A sample of the semiconductor in its purest form is called an intrinsic semiconductor. The impurity content in the intrinsic semiconductor is very very small, of the order of one part in 100 million parts of the semiconductor.

Extrinsic Semiconductor

In order to change the properties of intrinsic semiconductors a small amount of some other material is added to it. The process of adding other material to the crystal of intrinsic semiconductors to improve its conductivity is called doping. The impurity added is called dopant.

The doped semiconductor material is called extrinsic semiconductors. The doping increases the conductivity of the basic intrinsic semiconductors hence the extrinsic semiconductors are used in practice for the manufacturing of various electronic devices such as diodes, transistors, etc.

Depending upon the type of impurities, the two types of extrinsic semiconductors are,

1. N-TYPE
2. P-TYPE

N-TYPE Impurity

The impurity material having five valence electrons is called the pentavalent atom. When this is added to an intrinsic semiconductor, it is called donor doping as each impurity atom donates one free electron to an intrinsic material. Such an impurity is called donor impurity. Examples of such impurities are arsenic, bismuth, phosphorous, etc. This crests an extrinsic semiconductor with a large number of free electrons called an n-type semiconductor.

P-TYPE Impurity

Another type of impurity used is the trivalent atom which has only three valence electrons. Such an impurity is called acceptor impurity. When this is added to an intrinsic semiconductor, it crests more holes and is ready to accept an electron hence the doping is called acceptor doping. Examples of such impurities are gallium, indium, and boron. The resulting extrinsic semiconductor with a large number of holes is called a p-type semiconductor.

Hence the extrinsic semiconductor may have either a large number of electrons or holes

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta (∆) or star (Y).

In a three-phase system, the order in which the voltages attain their maximum positive value is called Phase Sequence. The order in which the phase voltages of a 3-phase system attain their peak or maximum positive values is called the phase sequence of the system.

The phase sequence RYB normally means that the red phase is followed by the yellow phase, which is followed by the blue phase. When the voltage of the red phase is at its positive maximum value, the voltage of the Y-phase will be 120° (2π/3) behind its positive maximum value and that of the B-phase 240° behind its positive maximum value as shown in fig.

Then Red phase  V_RN = Vm sinθ
Yellow Phase V_YN = Vm sin(θ – 120°)
Blue Phase V_BN = Vm sin(θ – 240°)
or V_BN = Vm sin (θ + 240°)

If the red phase voltage, V_RN is taken as the reference voltage so the voltage in the yellow phase lags V_RN by 120°, and the voltage in the blue phase lags V_YN also by 120°. But we can also say the blue phase voltage, V_BN leads the red phase voltage, V_RN by 120°.

As the three individual sinusoidal voltages have a fixed relationship between each other of 120^o they are said to be “balanced” therefore, is a set of balanced three-phase voltages their phasor sum will always be zero as Va + Vb + Vc = 0

Ripple Factor (r): It is the ratio of the root mean square (RMS) value of AC component to the DC component in the output and is given by

For full-wave rectifier

I_rms = Im/√2

I_dc =2I_m/π

Substituting the value in the above expression we get

$\begin{array}{l}\gamma = \sqrt {{{\left[ {\dfrac{{{I_m}/\sqrt 2 }}{{2{I_m}/\pi }}} \right]}^2} – 1} \\\\\gamma = \sqrt {\dfrac{{{\pi ^2}}}{8} – 1} \\\\\gamma = 0.48\end{array}$

Note:- The ripple factor of half-wave rectifier is 1.21.