SSC JE 2016 Electrical question paper (Set-2)

Neither one unit of large capacity generator nor a large number of small capacity generators is used to fulfill total demand at any time of the plant. A compromise is made between the two alternatives. So, a number of generating units of different capacities are used. Also, all units are not operated simultaneously. Types of the different units are given below.

Types of the different Generating units are as given below.

1. Firm power: It is the power that should always be available, even in emergency conditions.
2. Prime power: Prime power is the mechanical, hydraulic, or thermal power that is always available for conversion into electrical power.
3. Hot reserve: This reserve generating capacity is always ready for operation but is not in service.
4. Cold reserve: This reserve generating capacity is available for service but is not ready for immediate operation.
5. Spinning reserve: This reserve generating capacity is connected to the bus and is ready to take the load.

Reserve margin: It is the rated capacity in service minus actual loading on the generator.

BASIC PRINCIPLES OF ELECTRICAL MACHINES

In any machine, the currents in all the windings combine together to produce the resultant flux. The field system produces flux. Voltages are induced in the windings such as those of an armature. When the armature carries current, the interaction between the flux and the current produces torque. Current produced by the relative motion of stator/rotor conductor or magnet is called induced current, set up by an induced electromotive force or EMF. EMF is produced when a current-carrying conductor is placed in a rotating magnetic field. Where either field is rotating or conductor.

These are the basic facts on which the action of the machine depends. The windings of the electrical machines are mainly of three types:

1. Coil winding:- The winding consists of coils wound on all poles of the machine and connected together to form a suitable series or parallel circuit. The coils may be wound on the stator or on the rotor, forming the salient or non-salient poles of the machine. DC supply is given to these windings and they produce a field proportional to the magnitude of the current through the windings. If the poles are on the stator, a stationary field is produced in the airgap.  As the currents are dc they do not vary with time.
2. Polyphase winding:- This is a distributed winding. Individual conductors are distributed in slots in a suitable way, connected into a number of separate circuits—one for each phase. A three-phase supply is used. This type of winding is mainly used for the stator. When supplied with three-phase currents it produces a rotating field in the airgap. This is of a constant magnitude but rotating in space at a constant (synchronous) speed.
3. Commutator winding:- This is on the rotor. The armature has open slots and the conductors are located in these slots and are connected to the commutator segments in a continuous sequence.

TYPES OF ELECTRICAL MACHINES

The type of a machine depends on how a particular type of combination of the above windings is used on the stator and the rotor.

A synchronous machine has a coil winding and a polyphase winding. Generally, the polyphase winding is on the stator while the coil winding is on the rotor. The coil winding on the rotor produces a field and with the rotation of the rotor, this moves in space at the speed of the rotor. The voltage will be induced in the staler polyphase winding (three-phase). The magnitude of the voltage depends on the strength of the de field and the frequency corresponding to the speed of the rotor when driven as a generator.

In the case of motor action, the polyphase winding is supplied with three-phase currents. This produces a rotating field in the air gap. This, when it reacts with the dc field produced by the current in the rotor, makes the machine run as a motor at synchronous speed. The construction of the field system may be on the stator or the rotor.

A dc machine has a coil winding for the poles on the stationary part. This produces the stationary field in the space in the air gap due to dc in the field windings wound on the poles. The armature or the rotor has a commutator type of winding with stationary brushes for connecting to the external circuit. The machine can work as a motor or as a generator, depending on the current input to or output from the armature.

An induction machine has a polyphase winding both on the stator and the rotor. The three-phase winding on the stator produces a rotating magnetic field. This is cut by the closed circuit of the rotor, thereby producing an induced voltage in the winding due to the transformer action. This produces a current in the winding which reacts with the flux to produce torque. The machine runs as an induction motor on the induction principle.

Wooden Poles:

This is one of the simplest forms of the line support. Generally, wooden poles are used. They are cheap, easily available, and have good insulating properties. These poles must be straight, strong, and free from knots. The poles should be properly seasoned to prevent rapid decay because of crakes. An aluminum, zinc, or cement cap is used at the top of the wooden pole to prevent decay due to snow and rain. They are widely used for distribution purposes up to 22 kV and short spans (up to 60 metros). In cities where timber is easily available and the cost of transportation of steel tower is more, single and double pole structures either A or H type are widely used for overhead lines for 130 kV and for the span of 150 meters as shown in Fig.

Wooden poles generally rot below the ground level and to prevent this preservative compounds such as creosote oil is used.

Advantages of Wooden Poles

• They are cheap and readily available.
• They are light in weight so easy to install.
• They have a good life, i.e., approximately 20 years.
• They can be directly buried in the ground or anchor-based and hence no special foundation is required.

Disadvantages of Wooden Poles

• They start rotting underground.
• They cannot be used for voltage higher than 22 kV.
• They require regular inspection.
• They have less mechanical strength.

The op-amp is known as the differential amplifier because it amplifies the voltage difference of the inverting and non-inverting terminals. A third terminal represents the operational amplifier’s output port which can both sink and source either a voltage or a current. 

PROPERTIES OF THE IDEAL OPERATIONAL AMPLIFIER

An ideal op-amp should have the following properties:

1. Gain must be infinite
2. Output voltage must be zero when input voltages are the same or when both are zero
3. The input resistance must be infinite
4. The output resistance must be zero
5. The common-mode rejection ratio (CMMR) must be infinite

Now coming back to the Question

Input offset voltage(v_io ) is the voltage that must be applied between input terminals of OPAMP to ensure zero output for zero input. 

v_io = |v₊ – v_–| 

As non-inverting terminal of the given op-amp is connected to the ground. 

V₊ = 0 
V_io = |0 – v_–| = v_– 
V _– = R₁ /(R₁ + R_F )v_o 
V_o = (1+R_F /R₁ )v_– 
V_o = (1+R_F /R₁)v_io 
V₀ = [1+(1×10⁶ )/(1×10³ )]×1×10^-3 
Vo = [1+(1×10³ )]×1×10^-3 

As 1<<1000 therefore it can be neglected 

Vo = 1×10³ ×1×10^-3 = 1 V

The strain is defined as the deformation of materials caused by the action of stress. A body subjected to external forces is in the condition of both stress and strain. Stress cannot be measured directly. As there is a relationship between stress and strain, the effect of stress can be shown by the measurement of the strain. Thus, the stress occurring in a body can be computed if sufficient strain information is available. The measurement helps in knowing better about any structure, whether it is strong enough for the purpose or it may fail in use.

Measurement of Strain Using Electrical Resistance Strain Gauges

Strain gauges are made up of a long, thin strip of conductive material arranged in a zigzag manner. Load cells typically contain multiple strain gauges aligned and wired in a Wheatstone bridge circuit. When stress is applied to a strain gauge, the resistance of the strain gauge changes and unbalances the Wheatstone bridge, resulting in a signal output (voltage) that is proportional to the stress.

When a strain gauge is expanded or contracted by an external force, it experiences a change in electrical resistance. By bonding a strain gauge to the surface of a test specimen with an electrical insulator between them, the strain gauge changes dimension according to the expansion or contraction of the test specimen, resulting, in a change in resistance. This resistance is measured using the Wheatstone bridge which is the indication of the strain of the specimen at that point.

Types of Strain Gauges There are basically two types Of strain gauges unbonded and bonded.

Unbonded Resistance Strain Gauge: In general, the basic usage of the unbonded strain gauge is a displacement transducer. It can be constructed in a variety of configurations. The unbonded resistance strain gauge uses a strain-sensitive wire (or wires) with one end fixed and the other end attached to a movable element. Strain, induced on the wire by the displacement of the movable element, produces a change in resistance proportional to the displacement of the movable element. The unbonded strain gauge can measure the very small motion of the order of 50,μm and very small forces. The device is less robust than the bonded gauge and was developed at a time when the bounding technique was not reliable. With the advancement of improved bonding cement, unbonded wire strain gauges have become less common.

2. Bonded Resistance Strain Gauge: Bonded resistance strain gauge can be grouped into those that require an adhesive to fix the gauge so the pressure-sensing element (metal foil and strain sensitive wires) and those attached to the strain-sensing element by techniques that effectively make the strain gauge an integral part of the strain-sensing element (thin film and semiconductor).

In the rotating machine whether it is AC or DC machine the type of losses are almost the same 

The various losses in a d.c. the machine, whether it is a motor or a generator, is categorized amplified into three groups as:

1. Copper losses.
2. Iron or core losses.
3. Mechanical losses
4. Stray Load Losses

Copper Losses

Copper losses are also called Electrical losses, winding losses or Ohmic losses. The copper losses are the losses taking place due to the current flowing in a winding. There are basically two windings in a d.c. machine namely armature winding and field winding. The copper losses are proportional to the square of the current flowing Through these winding; Thus the various copper losses can be given by

1. Armature copper losses (I²_aR_a)
2. Shunt field winding losses (I²_shR_sh)
3. Series field winding losses(I²_seR_se)

Core Losses

Core losses are also known as iron losses or Magnetic losses. These Losses are constant and Independent of the load. They are induced in the machine due to hysteresis and eddy currents produced in the core produced when the magnetization is changing. They mainly occur in the armature teeth and core as also in the pole shoe.

Hysteresis losses occur due to the reversal of the magnetization of the armature core. So, the hysteresis loss can be obtained as:

Hysteresis Loss = K_h × B_M^1.67 × f × v watts

where
Kh = Hysteresis constant depends upon the material
Bm = Maximum flux density
f = frequency
v = Volume of the core

The eddy current loss exists due to eddy currents. When the armature core rotates, it cuts the magnetic flux and e.m.f. gets induced in the core. This induced e.m.f. sets up eddy currents which cause power loss. Ibis loss is given by,

Eddy current losses = K_e × B_m² × f² × t²

Where K_e = Eddy current constant
t = thickness of the core

Mechanical Losses

These losses are produced due to friction and windage (friction with air) caused by machine rotation. Hence, these are named mechanical losses. Some power is required to overcome mechanical friction and wind resistance at the shaft. They depend on the speed of the machine. The mechanical losses are also constant for a d.c. machine

Bearing friction loss generally depends on the type of bearing used and on the viscosity of the lubricant.

Brush friction loss is proportional to the contact area and the brush pressure. It also depends on other factors like the material of the brush and commutator, their polish condition, and the temperature at the contact surface.

 Stray Load Losses

The magnetic and mechanical losses together are called stray losses. Stray load losses are losses that are produced in the machine when they are loaded. They cannot be considered with the main losses listed above. These losses include:

(a) Additional core loss resulting from armature reaction distortion.

(b) Copper loss due to short circuits produced in coils, segments, and brushes during commutation.

(c) Copper loss due to non-uniform distribution of current in large-sized armature conductors.

Stray load losses are very small in value and therefore, they are very difficult to calculate. In small machines, they can be neglected but for large machines, they are generally considered to be 1% of the output power in total.

The voltage across the resistance R2 can find out by voltage divider rule.

Voltage Divider Rule (VDR)

The voltage divider rule provides a useful formula to determine the voltage across any resistor when two or more resistors are connected in series with a voltage source. The voltage across the individual resistors can be given in terms of the supply voltage and the magnitude of individual resistances as follows

I = V ⁄ (R₁ + R₂ + R₃)

V₁ = I.R₁ = V.R₁ ⁄ (R₁ + R₂ + R₃)

Similarly

V₂ = I.R₂ = V.R₂ ⁄ (R₁ + R₂ + R₃)

Hence for the given question the voltage across the resistance R₂

V₂ = V.R₂ ⁄ (R₁ + R₂)

V₂ = 20 × 40 ⁄ (20 + 40)

V₂ = 13.33 Volt

Force on a straight conductor carrying current placed in a magnetic field can be found by using Fleming’s left-hand rule. 

The forefinger represents the direction of the magnetic field, the thumb represents the direction of motion of the conductor, and the middle finger Ives the direction of the current.

In a purely inductive circuit, the rate of change of current is opposed by the reactance of the coil, and the effect of this opposition is to make the current lag behind the applied voltage or be out of phase by 90°. The waveforms of current and voltage in a purely inductive circuit are shown in Fig. 

The current lags the voltage by 90°, as V has reached its maximum at point A when the current is zero at point B.

Battery cycle and depth of discharge One discharge and charge period are referred to as a battery cycle. A major factor affecting battery life is the depth of discharge i.e. how much the battery is discharged and how often. The depth of discharge of a battery is a measure in the percentage of the amount of energy that can be removed from a battery during a cycle.

Limiting the depth of discharge will make the battery last longer. If discharged beyond its recommended depth of discharge, the life of a battery will be considerably reduced.  As the rate of discharge is increased, the cell terminal voltage, that is, the voltage at the output terminals of the cell drops because the internal resistance results in voltage drops within the cell due to the flow of current from the cell. These losses result in increased internal heating within the cell and reduced available energy.

It is suggested that lead-acid batteries not be discharged beyond 80%, even if the battery is designed for deep discharge. Lead-acid batteries that are deeply discharged may suffer from a permanent loss of capacity due to sulphation, acid dilution, and a greater tendency for freezing. The fully charged lead-acid cell has 2.25 Volts. The 80% of this voltage is nearly 1.8 Volts.