DMRC JE Electrical 2014 Paper With Solution and Explanation

Electrostatic instruments are the only instruments that are directly voltage-sensitive and do not depend on a current for their operation. Basically, electrostatic instruments are all voltmeters. Practically such instruments may be used for the measurement of current and power but both the types of measurements require measurement o the voltage across a known impedance. The main advantage of such instruments is the measurement of high voltages in both a.c. and d.c. circuits without any errors due to eddy current losses and hysteresis.

The operation of all the electrostatic instruments is based on the principle that there exists a force between the two plates with opposite charges. This force can be obtained using the principle that the mechanical work is done is equal to the stored energy if there is a relative motion of plates.

In electrostatic instrument deflecting torque is proportional to

$\theta = \dfrac{1}{2}\dfrac{{{V^2}}}{K}\dfrac{{dC}}{{d\theta }}$

Where K = spring constant
C = capacitance between the plate

Since the deflection is proportional to the square of the voltage to be measured, the instrument can be used on both ac and dc. The instrument exhibits a square-law response and hence the scale is nonuniform.

Advantages of Electrostatic Instrument

1. They can be manufactured with very high accuracy.
2. The instruments may be calibrated with d.c., and yet the calibration would be valid for a.c. also since the deflection is independent of the waveform of the applied voltage.
3. Since no iron is used for their construction, they are free from hysteresis, eddy current losses, and temperature errors.
4. Once the discs are charged, no more current is drawn from the circuit and the instrument represents infinite impedance.

The Schering Bridge is an electrical circuit used for measuring the insulating properties of electrical cables and equipment.It is also used for power factor measurement. It is an AC bridge circuit, developed by Harald Schering. It has the advantage that the balanced equation is independent of frequency.

In this diagram:

C₁ = capacitor whose capacitance is to be determined,
R₁ = a series resistance representing the  dielectric loss  component in the capacitor C1,
C₂ = a standard capacitor,
R₃ = a variable non-inductive resistance,
C₄ = a variable capacitor,
R₄ = a non-inductive resistance in parallel with the variable capacitor C₄.

The bridge is balanced by successive variations of R3 and C4 until the detector shows no deflection.

At balance C₁ = C₂R₄/R₃

Note:-

Maxwell bridge is used to measure the value of unknown inductance.

Heaviside bridge is used to measure mutual inductance in terms of a known self-inductance.

Kelvin bridge is used to measure the value of low resistance

Exciting current is the current which flows through the transformer primary when the transformer is under no load. Even on a no-load, a small amount of current is drawn from the primary side, to set up the required magnetic flux in the magnetic core. This current is known as the  “No Load Current” or magnetization current.

The no-load current is about 3-5% of the full load current and it accounts for the losses in a transformer.

In no-load conditions, only iron losses occur. Copper losses are zero in this condition as secondary current is zero and primary current is negligibly small.

Iron Loss (Pi)

The power loss in a transformer that takes place in its iron core is known as iron loss. In the transformer, flux set up in the core remains constant from no load to full load. Hence this power loss in a transformer is independent of load and is also known as constant losses of a transformer.

This power loss in a transformer has two components named hysteresis loss and eddy current loss. To determine the iron loss, an open circuit test of the transformer is performed.

Now coming back to the question………

Current transformers are used to perform two tasks. Firstly, they step down the heavy power system currents to low values that are suitable for the operation of the relays and other measuring instruments (meters) connected to their secondary windings.

Secondly, they isolate the relays and meters circuits from the high voltages of the power system. The standard current ratings of the secondary windings of the CTs.

CT Error

In practice, it is said that the current transformation ratio I₂/I₁ is equal to the tums ratio N₁ / N₂. But actually, it is not so. The current ratio is not equal to the turns ratio because of magnetizing and core loss components of the exciting current.

In ideal CT the secondary current is given as

${I_S} = \dfrac{{{I_P}}}{N}$

But in practical CT the ratio is

${I_S} = \frac{{{I_P}}}{N} – {I_O}$

Thus, the actual CT does not reproduce the primary current exactly in the secondary side both in magnitude and phase due to exciting current I_O. The exciting current Io is the main source of errors in both measuring and Protective CTs. The error in magnitude is due to an error in CT ratio which is called “ratio error” and the error in phase is called “phase-angle error.”

Ratio error (current Error)

The actual transformation ratio (Na) is not equal to the rated (nominal) transformation ratio (N) since the primary current is contributed by the exciting current. The error introduced due to this difference in CT ratios is termed a ratio error or current error. The ratio error in percentage is expressed as

Ratio Error = (Nominal Ratio – Actual Ratio)/Actual ratio

The ratio error is largely dependent upon the value of the iron-loss component I_C of the exciting current.

The ratio error is considered to be positive when the actual ratio of the CT is less than the nominal ratio, i.e., when the secondary current, for a given primary current, is high.

Creeping in the energy meter is the phenomenon in which the aluminum disc rotates continuously when only the voltage is supplied to the pressure coil, and no current flows through the current coil. In other words, the creeping is the kind of error in which the energy meter consumes a very small amount of energy even when no load is attached to the meter.

Creeping occurs due to

1. Overcompensation for friction.
2. The supply voltage is more than the normal voltage
3. Stray magnetic field
4. Vibration

To eliminate this, two holes are drilled in the disc 180° opposite to each other. When this hole comes under the shunt magnet pole, it gets acted upon by a torque opposite to its rotation. This restricts its rotation, under no-load conditions.

Synchronous motor excitation refers to the DC supply given to the rotor which is used to produce the required magnetic flux.

Power Factor = Useful Power /Magnetizing or Apparent Power

The magnetizing power or current does not contribute to the active power and is purely reactive. Therefore, any electromagnetic device which draws excitation for its magnetic circuit from an AC system will have a lagging power factor.

Normal excitation– In this case, the synchronous machine gets the required flux through the DC voltage supplied. Hence the motor works on unity p.f.

Under excitation:– As field current reduces, the flux will start reducing, to keep this flux constant the armature draws high magnetizing current or lagging reactive VA  from the bus. Hence in this case the motor is said to operate under a lagging power factor and the motor is said to be under-excited.

At zero field current, the motor acts as a synchronous reluctance motor. A reluctance motor is a synchronous motor with no field winding or Permanent magnet excitation at all. In this case, the magnetizing current is fully taken from the bus.

If we increase field current in the reverse direction to keep flux constant draws more currents. During this process, the load angle increases. At one point, the reverse field force dominates reluctance torque and rotor slips are pole pitch and align to the opposite pole. The instant angle aligns to the opposite pole the flux will be very high to reduce this flux current drop steeply to synchronous motor value. This torque is reluctance + synchronous motor torque.

or

The Back emf will go to zero when the field is reduced, so the Current input will be increased. But when the Field increases (though in the reverse direction) the back emf will cause the current to reduce.

• Starting torque is directly proportional to the rotor resistance of an induction motor.
• The resistance of the squirrel-cage induction motor cannot be varied as compared to the slip ring induction motor.
• In the squirrel-cage induction motor, the rotor has very low fixed resistance, therefore, the starting torque is low due to the low power factor and high reactance.
• In the SLIP RING induction motor the ends of the rotor windings are externally connected by a variable rheostat (resistance is varied in order to give it proper starting and running current).
• So more the resistance, more the torque. When we add resistance to the rotor the torque is high, the slip is high and the current is reduced.
• Therefore slip ring induction motor is used for providing high starting torque

All single-phase induction motors have two stator windings, a main (running) winding and an auxiliary (starting) winding. If the two winding currents are shifted in time phase, a rotating field is created which is necessary for the production of starting torque. The time phase displacement between auxiliary winding current Ia and main winding current Im is obtained by putting the suitable capacitor in series with auxiliary winding.

Hence The capacitor increases the starting torque by producing a greater phase shift between the current in the run winding and the current in the start winding.

To increase the Power factor we can connect the capacitor in parallel.

Resistivity ρ of a conductor is given by

ρ = 0.57 Ω-m

Distribution transformers are used for lower voltage distribution networks as a means of end-user connectivity. (11kV, 6.6 kV, 3.3 kV, 440V, 230V) and are generally rated less than 200 MVA. Distribution transformers depend on the typical load cycle for which it has to supply power.

Consider a distribution transformer, the load(secondary side) may be connected or disconnected according to the consumer. But the distribution transformer would be continuously energized from the supply(feeders) as the load is unexpected(we don’t know at what time the load is connected or disconnected).

Such transformers, therefore, are designed to have minimum core losses. Whereas power transformer is designed to have minimum copper losses

Corona loss can be minimized by controlling the following factors:

1. The frequency of supply: Corona loss increases as the supply frequency increases.
2. The radius of the conductors: Generally corona loss increases when decreasing the radius of the conductor. In order to prevent this, bundled or hollow large diameter conductors must be used.
3. The distance between the two conductors: To prevent corona spacing between the conductors must be increased.
4. Air Pressure: In hilly areas, the corona effect is more dominant due to reduced pressure.
5. Using Smooth conductor: Since corona loss is higher at sharp corners of the conductors, due to the presence of the highly non-uniform field, increasing the conductor radius as a whole can reduce the corona effect significantly. More the imperfections on the conductor surface will be Corona.

A transistor has three doped regions, as shown in Fig.  Notice that for both types, the base is a narrow region sandwiched between the larger collector and emitter regions.

• Usually, the emitter-base junction is forward biased and the collector-base junction is reverse biased and also termed an Active Region. In this type of connection Transistor work as an amplifier.
• The emitter region of a transistor is heavily doped. Its job is to emit or inject current carriers into the base.
• The base region is very thin and lightly doped. Most of the current carriers injected into the base from the emitter do not flow out the base lead. Instead, most of the current carriers injected into the base pass on to the collector.
• The collector region is moderately doped and is the largest of all three regions.
• The collector region attracts the current carriers that are injected into the thin and lightly doped base region. Incidentally, the collector region is the largest of all three regions because it must dissipate more heat than the emitter or base