DMRC PREVIOUS YEAR SOLVED ELECTRICAL QUESTION PAPER – 2015

Factors Affecting the Resistance

The resistance R offered by a conductor depends on the following factors :

1. Length of the material (l): The resistance of a material is directly proportional to the length. The resistance of the longer wire is more.
2. Cross-Section Area (a): The resistance of a material is inversely proportional to the cross-sectional area of the material. The more cross-sectional areas allowed the passage of more number of electrons offering less resistance.
3. Nature of Material: As discussed earlier the conductor has a large number of free electrons hence it offers less resistance whereas Inductor has less number of free electrons hence which offers more resistance.
4. Temperature: The temperature of the material affects the value of the resistance. In the General case, the resistance of the material increases as its temperature increases.

So for any given material at a certain given temperature, the resistance is given as

where ρ is a constant and known as its specific resistance or resistivity.

l = Length in Meter

a = area of cross-section in m²

R = Resistance in Ohm

Unit of Resistivity

Specific Resistance depends only on temperature and material of the conductor but not on its dimensions of the conductor, on which resistance depends, and mechanical deformation such as stretching etc. As ρ depends only on the material of a conductor at a given temperature, hence it is a characteristic constant.

Absolute instrument: Absolute instrument is an instrument that indicates the quantity to be measured in terms of the constant of the instrument (dimensions, turns, etc) and in order to find out the quantity in the practical units it is necessary to multiply such deflections with an instrument constant.

No previous calibration or comparison is necessary in this case. The most common absolute instrument is the tangent galvanometer which gives the measured current in terms of the tangent of the deflected angle, the radius, and the number of turns of the galvanometer. 

Rayleigh’s current balance and Lorentz method of resistance measurement are examples of this class of instruments. Such instruments are rarely used (the use being merely confined within laboratories as standardizing instruments).

Secondary instruments: Secondary instruments are those in which the value of the electrical quantity to be measured can be determined from the deflection of the instrument only when they have been Recalibrated by comparison with an absolute instrument. The deflection of the instrument gives directly the quantity to be measured.

An example of the secondary instrument is

1. Integrating Instrument e.g (watt-hour Meter)
2. Indicating Instrument e.g (Ohmmeter)
3. Recording Instrument e.g (seismograph)
4. Comparison instrument: This instrument measure the value of an unknown quantity by comparing it with the standard. Examples are DC and AC bridges and potentiometers. They are used where high accuracy is desired.

Galvanization or galvanizing is the process of applying a protective zinc coating to steel or iron, to prevent rusting.

Eddy is a circular movement of water in a pond. Similarly, when it comes to electricity, eddies are the circular movement of currents. Eddy currents are circulating currents present in the magnetic core of the transformer. These currents occur due to the difference in magnetic flux in the core of the transformer.

In the transformer, we provide alternating current in the primary which produces alternating flux in the core, this flux links with the secondary of the transformer and induces emf in the secondary.

It may be possible that flux also links with some other conducting parts of the transformer such as the ferromagnetic core or iron body and induces local emf in these parts of the transformer which will cause a circulating current to flow in these parts causing heat loss. these currents are called eddy currents and this loss is called eddy current loss.

Eddy current losses in the transformer is given by

Eddy current losses = K_e × B_m² × f² × t²

Where K_e = Eddy’s current constant
t = thickness of the core

An atom is the smallest constituent unit of ordinary matter. Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and typically a similar number of neutrons.

Electron(-vely charged), proton(+vely charged) and neutron (electrically neutral). The mass of electrons is the lowest whereas the mass of protons and neutrons is almost the same.

mass of neutron = 1.67493 × 10^-27 kg
mass of proton = 1.67262 × 10^-27 kg
mass of electron = 9.10939 × 10^-31 kg

So, the neutron is the heaviest among the rest of the particles.

A molecule is an electrically neutral group of two or more atoms held together by chemical bonds. The molecular weight of a molecule is the sum of the atomic weights of its component atoms. Hence the molecule weight is the highest among all the given options.

Typically, three-phase motors will be started by instantly connecting the supply from the mains. In this case, the starting current is excessive and because of this, the starting torque of the motor is excessive. This torque will speed up the motor to attain its ultimate speed.

This kind of starting is applicable for small motors i.e. motors that can be rated as much as 5HP. However, the same starting approach can’t be utilized for increased capability motors. The reason being defined under.

In large motors, the starting current could be very excessive and if it is connected to the main supply, there might be an enormous voltage drop within the line. This voltage drop affects the behavior of different systems and other loads linked to the supply.

The starting current of large three-phase induction motors will be as excessive as 6 times that of the maximum current (full load current).

There are many types of Reduced Voltage Starters. Some of them are listed below.

• Star Delta (Y – Δ) Starter
• Resistance Voltage Starter
• Auto Transformer Voltage Starter

In star connection, line and phase currents are the same but the line voltage is  √3 times the phase voltage. In the delta connection, line and phase voltages are the same but the line current is √3 times the phase current. However, the power in both connections is the same, that is

√3V_LI_L cosφ.

The starting current in an induction motor is proportional to the input voltage per phase to the motor. If V_LL is the line to line voltage applied to the motor,

I_ST ∝ E_LL

The voltage drop in the stator impedance is small compared to the applied voltage and can be neglected.

V_LL = E_LL

Therefore, the starting current in an induction motor is proportional to the supply voltage. If a reduced voltage is applied to the motor at starting, the starting current also will be reduced accordingly. While the starting current is reduced, causing a lesser voltage drop during starting, a lower starting current means a lower starting torque.

The most popular and effective means of reduced voltage starting is achieved by means of star-delta starters. In this method, the motor windings are connected in star configuration during starting and then switched over to Delta once the machine has picked up sufficient speed (about 75% of the speed).

By connecting the motor in the star configuration, the reduction in voltage corresponds to 1/√3 = 0.577. The reduction in starting current when compared to DOL starting is 33.3%. But the starting torque also gets reduced and this is a disadvantage. If this method is to be used, we must make sure that the load torque is not more than 50% of the rated torque.

The TRIAC is a three-terminal semiconductor device for controlling current. It gains its name from the term TRIode for Alternating Current.

A triac is a device that operates like an SCR for an AC circuit. The triac conducts during both halves of the AC waveform. This means that the output of a triac is AC, not DC as is the case with an SCR. The schematic symbol of a triac is shown in Figure.

The triac is a three-terminal device. One terminal is called the gate, the terminal closest to the gate is called main terminal 1 (MT I), and the remaining terminal is called main terminal 2 (MT 2). The gate voltage must be the same polarity as MT2 to turn on the triac. The Device is triggered by applying the small gate pulse. The triac will continue to conduct until the current flowing through it decreases below its minimum holding current level.

CAUSES OF LOW POWER FACTOR

1. The induction motors work at a low lagging power factor at light loads and an improved power factor with increased loads.
2. The transformers have a lagging power factor because they draw magnetizing current.
3. Miscellaneous equipment like arc lamps, electric discharge lamps, welding equipment, etc., operates at a low power factor.
4. The industrial heating Fumaces operate at a low lagging power factor.
5. The variation of load on the power system also causes a low power factor.

Normally, the power factor of the whole load on a large generating station is in the region of 0.8 to 0.9. However, sometimes it is lower and in such cases In order to improve the power factor, some devices taking leading power should be connected in parallel with the load. This can be achieved by the following equipment

1. Static capacitors
2. Synchronous condenser
3. Phase advancers

Static Capacitor:-

• The power factor can be improved by connecting capacitors in parallel with the equipment operating at a lagging power factor.
• The capacitor (generally known as the static capacitor) draws a leading current and partly or completely neutralizes the lagging reactive component of the load current.
• This raises the power factor of the load. For three-phase loads, the capacitors can be connected in delta or star.

Synchronous condenser

A synchronous condenser is a synchronous motor running without the mechanical load. The Synchronous motor takes a leading current when over-excited and therefore behaves as a capacitor. When such a machine is connected in parallel with the supply, it takes a leading current which partly neutralizes the lagging reactive component of the load. Thus the power factor is improved.

Phase Advancer:

There are special commutator machines, which are used to improve the power factor of the induction motor. When the supply is given to the stator of an induction motor, it takes a lagging current. So, the induction motor has low lagging power factor. For compensating this lagging current, a phase advancer (mounted on the same shaft) is used. It supplies MMF to the rotor circuit at slip frequency.

Note:- For more detail check SSC JE CONVENTIONAL PAPER 2017 QUES 5(D) : SSC JE CONVENTIONAL PAPER 2017

Volt is the electrical unit of voltage or potential difference (symbol: V).

One Volt is defined as energy consumption of one joule per electric charge of one coulomb.

1V = 1J/C

One volt is equal to the current of 1 amp times the resistance of 1 ohm:

1V = 1A ⋅ 1Ω

Why is the electric field inside a conductor zero? 

• Let a plane conductor that has no initial charge be placed in a uniform static electric field in free space, as shown in Fig.

• Every free electron of the conductor will experience an electric force equal to eE, where e is the value of the charge of an electron and E is the intensity of the applied field.
• The electrons will move in the opposite direction of the applied field until they reach the bottom surface of the conductor and then get distributed on the conductor surface in the form of a surface charge.
• The positive charges, which are generated in the conductor after the migration of the electrons, move to the top surface and get distributed over a thin layer.
• The charges cannot move beyond the conducting surfaces because the medium surrounding them is an insulator.
• The surface charges produce an induced electric field within the conductor. As the induced field is directed from the top surface having a positive charge towards the bottom surface, it is opposite to the applied field.

When the magnitude of the induced field becomes equal to that of the applied field, the net field intensity inside the conductor will become zero That is the Electric field due to the charges inside the conductor being directed opposite to the electric field outside which the field inside the conductor originated.

Remember: The charges move in a conductor so as to kill the external field

Consequently, no further movement of charges will take place. That is, the static condition will be reached after a brief transient period during which charges move to the surfaces. External field lines terminate on the bottom surface and emerge from the top surface, as shown in the figure.

Since field intensity inside a good conductor is zero, the potential gradient, which is numerically equal to the field intensity, is also zero. Accordingly, the potential has the same value everywhere inside a good conductor.