UPPCL JE 2018 Electrical question paper with Explanation 27-Aug-2018

By applying the current division rule in the given circuit to find the current in the 5-Ω resistance 

I₃ = I × (R₁R₂) ⁄ (R₁R₂ + R₂R₃ + R₃R₁)

I₃ = (50 × 7 × 3) ⁄ (7 × 3 + 3 × 5 + 5 × 7)

I₃ = 1050 ⁄ 71 = 14.79 A

Mica is an insulating and dielectric material.

When two conducting plates are brought closer and are separated by another plate that is made up of insulating material leads to the formation of the capacitor.

The main function of dielectric material is to store electrical energy. Thus dielectric materials are used in capacitors. There are four types of capacitors available depending on the dielectric material used in them.

1. Capacitors with air and gases as dielectric:- Such capacitors are used in circuits where energy loss in them should be low as well as the value of capacitance should be small. Thus, these types of capacitors are used in circuits where accuracy is the prime concern, for example, radio frequency circuits.

2. Capacitors with mineral oil as dielectric:- These capacitors give a large value of capacitance with a small amount of dielectric loss.

3. Capacitors with a combination of solid and liquid as dielectrics Paper, glass, mica, mineral oil, castor oil, etc. are used in these types of capacitors. Oil impregnated paper dielectric is used for making capacitors that should have a large value of capacitances. These types of capacitors are used in power distribution systems.

4. Capacitors with only solid as dielectric such as glass, mica, etc. These capacitors are used in laboratories. Mica has a high dielectric constant, high dielectric strength, and low dielectric loss. Further, the dielectric constant of mica does not change much with temperature. Most of the capacitors are constructed as sealed components.

Let the expression be as follows:-

V(t) = V_m sin(ωt ± φ) = 200 sin (314t + π/3)

Where φ represent the concerned phase-shift

V_m = Maximum value of the voltage  = 200 V

Angular frequency ω = 2πf

314 = 2πf

Hence frequency f = 314/2π = 50 Hz

Piezo is derived from the Greek word meaning to press and the piezoelectric eject is the production of electricity by pressure. It occurs only in insulating materials and is manifested by the appearance of charges on the surface of a single crystal that is being mechanically deformed. Piezoelectric materials have the property of becoming electrically polarized in response to applied mechanical stress. 

When a material gets electrically polarized if it is subjected to mechanical stress and it also gets strained when subjected to an electric field, the material is called piezoelectric material.

This property has an inverse: when electric stress (a voltage) is applied the material becomes strained. The strain is Directly Proportional to the applied field E. i.e., stain ∝ E.

These are the materials that possess spontaneous polarization even in the absence of an external electric field.

The polarization of the material changes with temperature and change in the polarization is given by

ΔP = λΔT

where, ΔT = Change in temperature

λ = Pyroeleetrieal coefficient.

Piezoelectric materials have the following applications:

(i) Gramophone pickups

(ii) Air transducers (car phones, hearing aids, microphones, dc.)

(iii) Ultrasonic flaw detectors

(iv) Underwater sonar transducers

(v) Filters

(vi) Frequency resonators

An overhead transmission line has groups of conductors running parallel to each other, carried on line supports. An electric transmission line conductor has four parameters: which are the series combination of resistance, inductance, shunt combination of capacitance, and conductance.

The material used as the conductor for power transmission and distribution lines must possess the following characteristics:

• Low specific resistance leads to less resistance and high conductivity.
• High tensile strength to withstand mechanical stresses.
• Low specific gravity in order to give low weight per unit volume.
• Low cost in order to use over long distances.

Copper and aluminum conductors are used for overhead transmission of electrical power. In the case of high voltage transmission, aluminum with a steel core is generally used. Sometimes cadmium, copper phosphor, bronze, copper weld, and galvanized steel are also used as transmission conductors. The choir of the conductor used for transmission purely depends upon the cost, as well as required electrical and mechanical properties.

Materials employed for transmission lines are

1. A.S.C.R
2. Cadmium copper materials.
3. Phosphor bronze materials.
4. Galvanised iron.
5. Steel cored aluminum materials.
6. Copper weld materials
7. Galvanized steel materially
8. Steel core copper

Copper: It is an ideal material for overhead lines having high electrical conductivity and greater tensile strength. Copper has high current density and its advantages are:

• A smaller cross-sectional area of the conductor is sufficient.
• The area offered by the conductor to wind loads is low.

Aluminum: Due to non-availability and the high cost of copper, it is replaced by an aluminum conductor which is low in cost and light in weight. For the same resistance, an aluminum conductor has a large diameter than the copper conductor. A larger diameter leads to a lower voltage gradient on the conducts surface and less tendency to ionize the air around the conductor.

Steel-cored aluminum (ACSR): For transmission of high voltages, multi-stranded (composite) conductors, such as stranded copper conductors, hollow copper conductors, and aluminum conductor steel reinforced (ACSR) are used. An ACSR conductor has a central core of galvanized steel wire covered with successive layers of aluminum strands, which are electrically in parallel. Because of galvanized steel wire, the tensile strength of the conductor is increased, so that the sag is reduced. It reduces the tower height and is useful for increasing the span length.

Another advantage of the ACSR is that the diameter of the conductor may be increased so that the effect of the corona is less. When compared with the equivalent copper conductor, the breaking strength of ACSR is high, whereas its weight is less.

Copper base alloy:- Copper and copper-base alloys are unique in their physical properties. When alloyed with zinc, tin, lead, nickel, silicon, aluminum, etc., they are used as cast. Their tensile strength is of the order of 150-170 MN/m². However, rolling, drawing and another hot and cold working can increase their tensile strength to 280 MN/m² for annealed material and to a maximum of 450 MN/m² for the hard-drawn wire. Cold-drawn copper is used for the conductor in overhead transmission lines, bus bars, etc. where high mechanical strength is needed. Annealed copper due to its flexibility is used in cables. As an insulated conductor, hard-drawn copper is used for commutator segments in electrical machines since it can withstand wear on the parts of the brushes.

Cadmium copper:- Co, when alloyed with cadmium, chromium, silver, and tellurium in a small percentage increases its strength at the cost of reduced conductivity. It is used for rotor bars, transmission line conductors, and traction collector wires. Copper-containing 0.7 to 1.0 percent cadmium has greater strength and better resistance to wear. It is commonly used for contacts and telephone wires. Copper-containing the small percentage of silver is a special type of high conductivity copper and is used for rotor conductors of large turbo-generators and commutators.

Cadmium copper is costlier than copper. They will be economical for a line with long spans and small cross-sections.

In the parallel connection, all of the positive electrodes are connected to one line, and all of the negative electrodes are connected to the other.

Any point on the positive side can serve as the positive terminal of the battery and any point on the negative side can be the negative terminal.

Hence the potential difference across each cell remains the same. All the cells connected in parallel should have the same voltage otherwise the cells with higher voltage will supply current to the cells with lower voltage.

Note:- In the series combination of cells, the positive terminal of one cell is connected to the negative terminal of the other cell, and so on. In this case, the voltages add up and the series combination is also called the series-aiding combination. Since the same current flows through all the cells in the series combination, the current rating of the combination does not increase. In fact, the current rating of the combination will be the current rating of the weakest cell.

Permittivity, ε, also called electric permittivity, is a constant of proportionality that exists between electric displacement (D) and electric field intensity (E) i.e D = εE. The vacuum permittivity is equal to 8.85 x 10^-12  farads per meter (F/m). 

Permittivity is the measure of capacitance that is encountered when forming an electric field in a particular medium. A high permittivity tends to reduce an electric field presence. For instance, the capacitance of a capacitor can be raised by increasing the permittivity of the dielectric material.

As given in the above question

W₁ = 1700 W

W₂ = 1100 W

The power factor of the two wattmeters is

tanØ =  √3[(W₁ – W₂) / (W₁ + W₂)]

tanØ = √3[(1700 – 1100) ⁄ (1700 + 1100)]

Φ = 19°

Power factor = cosφ = cos19° = 0.945 lag

Since an induction motor always run on lagging power factor

In leading power factor the circuit is capacitive in nature where the current “leads” the voltage by an angle φ

Most electrical power when produced at the power plants is produced as three-phase AC voltage. Electrical power is also transmitted in the form of three-phase voltage over long-distance power-transmission lines. At its destination, the three-phase voltage can be changed into three separate single-phase voltages for distribution into the residential areas.

Although single-phase systems are used mainly for residential power distribution systems, there are some industrial and commercial applications of single-phase systems. Single-phase power distribution usually originates from three-phase power lines so electrical power systems are capable of supplying both three-phase and single-phase loads from the same power lines.

The single-phase two-wire system consists of a two-conductor circuit (Phase and neutral) with constant voltage available between the conductors. The load is connected across the two lines. For safety reasons, one of the conductors can be grounded to form the neutral line. If the live conductor comes in contact accidentally with the neutral conductor, the voltage of the live conductor will be dissipated throughout a relatively large body of earth and thereby rendered harmless.