UPPSC AE Electrical 13 Dec 2020 Official Paper II (Previous Year Paper)

The correct answer is 300%.

• Crop intensity is referred to as the number of crops grown in the same field in one agriculture year.
• The formula to calculate any crop intensity is:
• ​Crop intensity= Total cropped area / Total sown Area)X100
• ​In this case, the number of different crops is 3.
• So, here the rotation intensity of Maize – Mustard – Mung crop is 300%.

The correct answer is Lentil.

• Lentil is not a Kharif Crop among the given options.

Key Points

• India has many growing seasons due to the prevalence of high temperatures over a long period. The different crop seasons are:​
• Kharif Crop​
• Crops are sown at the beginning of the southwest monsoon and harvested at the end of the South-West monsoon.
• Sown in June-July when rains first begin.
• Harvested in September-October.
• Requires a lot of water and hot weather to grow.
• Important crops: Jowar, Bajra, Soybean, Rice, Maize, Cotton, Jute, Groundnut, Sugarcane.
• Rabi crop
• Crops need a relatively cool climate during the period of growth but a warm climate during the germination of their seed and maturation.
• Sown in October-November.
• Harvested in April-May.
• Important Crops: Wheat, Barley, Gram, Linseed, Mustard, Masur, Lentil and Potatoes, Tobacco.

The correct answer is Postal Service Schemes.

• The Department of Posts launched a scheme called Five Star Villages.
• It is to ensure universal coverage of flagship postal schemes in rural areas of the country.
• The scheme is being launched on a pilot basis in Maharashtra.
• It bridges the gaps for generating public awareness and reach of postal products and services, mainly in interior villages.
• Under the Five Star Village scheme, all postal products and services are going to be made available and marketed, and publicized at the village level.
• The schemes covered under the Five Star scheme include:
• ​Savings Bank accounts, Recurrent Deposit Accounts, NSC / KVP certificates.
• Sukanya Samridhi Accounts/ PPF Accounts.
• Funded Post Office Savings Account linked India Post Payments Bank Accounts.
• Postal Life Insurance Policy/Rural Postal Life Insurance Policy.
• Pradhan Mantri Suraksha Bima Yojana Account / Pradhan Mantri Jeevan Jyoti Bima Yojana Account.

The correct answer is Dominic Thiem.

Key Points

• US Open Men's single title- Dominic Thiem (from Austria).
• US Open Women's single- Naomi Osaka (from Japan).
• The 2020 US Open was the 140^th edition of tennis US open and the second Grand Slam event of the year.
• It was held on outdoor hard courts at the USTA Billie Jean King National Tennis Center in Queens, New York.
• It was held without spectators due to the COVID 19 pandemic.

The correct answer is a.

Key Points

• The ancient name of Sarnath is Isipatana.
• ​Sarnath has been variously known as Mrigadava.
• Just 10 km north-east of Varanasi, near the confluence of the Ganga and Varuna Rivers in Uttar Pradesh, was Initially known as Isipatana.

Additional Information 

• The ancient name of Kannauj is Mahoday.
• Kannauj is one of the most ancient place in India having a rich archeological and cultural heritage.
• The ancient name of this place is Kanyakubja or Mahodya (as per Balmiki Ramayana, Mahabharat and Puran) later name kanyakubja was changed as Kannauj the present name of the District.
• ​The ancient name of Mandsaur is Dashpur.
• ​Mandsaur was known as Dashpur in ancient times.
• It is also said that the name originated from Mandodri, wife of Ravana. And the ancient name Dashpur was named after her husband Dashanand, the other name of Ravana.
• The ancient name of Talkad is Banvasi.
• Banavasi is an ancient town in Uttara Kannada in the state of Karnataka.

The correct answer is Chirand​.

Key Points

• Chirand is the early farming site located on the northern bank of the river Ganga together with two other rivers Sarayu and Son.
• Chirand is an archaeological site in the Saran district of Bihar.
• It is the first known site of the Neolithic age.
• It has a large pre-historic mound (a rounded mass projecting above a surface) containing various artifacts.
• The mound is known for its continuous archaeological record from the Neolithic age (about 2500–1345 BC) to the reign of the Pala Dynasty, which ruled this place during the pre-medieval period.
• This is probably one of the youngest date of early farming known from the Gangetic basin.

Additional Information

• T. Narsipur is a place located in the Mysore district in the Indian state of Karnataka.
• This is the place in South India where Kumbhamela is held every three years.
• The word 'Narasipura' is the name of the town, which is derived from the famous Gunja Narasimhaswamy temple that is located on the right bank of the Kabini river.

The correct answer is Mohsin Fanni.

• The author of the ‘Dastane Mazahib’ which discusses the Din-i-Ilahi of Akbar, was Mohsin Fanni.
• Din-i Ilahi “the religion of God,” was a system of religious beliefs introduced by the Mughal emperor Akbar in 1582 CE.
• Akbar's idea was to combine Islam and Hinduism into one faith, but also to add aspects of Christianity, Zoroastrianism, and Jainism.
• Akbar took a deep personal interest in religious matters.
• He founded an academy, the Ibadat Khana, “the House of Worship,” in 1575, where representatives of all major faiths could meet to discuss questions of theology.

​

Akbar

• Akbar was born as Abu'l-Fath Jalal ud-din Muhammad Akbar on October 15, 1542.
• Akbar succeeded his father, Humayun, in 1556 when he was 13 years old.
• Akbar was given the nickname 'the Great' because of his many accomplishments.
• Akbar started a new religion that was based on the teachings of major religions like Hinduism, Christianity, Zoroastrianism, etc.
• This religious path was later referred to as the Din-i-illahi or Divine Monotheism.
• Historian Vinset Smith called Akbar's Din-i-ilahi as a monument of his folly not of wisdom.

The correct answer is (A) - (4), (B) - (3), (C) - (2), (D) - (1).

• The highest Peak of Tamil Nadu is Doda Betta.
• The highest peak of Tamil Nadu is Doddabetta and is a part of the Nilgiri Hills at the junction of the Western Ghats as well as the Eastern Ghats.
• ​The highest peak of Rajasthan is Guru Shikhar.
• ​Guru Shikhar, a peak in the Arbuda Mountains of Rajasthan, is the highest point of the Aravalli Range. The peak is named Guru Shikhar or “peak of the guru” after Dattatreya, an incarnation of Vishnu.
• ​The highest Peak of Nagaland is Saramati.
• ​Standing at an altitude of 3841 m, Saramati is the highest peak in the state of Nagaland and occupies a place of pride in the heart of its residents.
• ​The highest peak of Madhya Pradesh is Dhoopgarh.
• The Dhupgarh Peak (1,350 metres), near Pachmarhi in south-central Madhya Pradesh, is the state's highest point.

The correct answer is KC Niyogi.

Key Points

• KC Niyogi was appointed the Minister of 'Ministry of Rehabilitation' set up on 6 September 1947.
• Kshitish Chandra Neogy (1888–1970), also known as KC Neogi, was an Indian politician from West Bengal.
• He was a member of the Constituent Assembly of India, a member of the first Cabinet of independent India, and the chairman of the first Finance Commission of India.
• Neogy was elected as a member of the Constituent Assembly of India and after independence became a member of the First Cabinet of Independent India under Jawaharlal Nehru as the Minister of Relief and Rehabilitation and later as Minister for Commerce.

The correct answer is Environmental Impact Assessment Method.

• 'Leopold Matrix’ is associated with Environmental Impact Assessment Method.
• It is a procedure for the evaluation of the effect or impact of a proposed development on the environment.​

Important Points

• Environmental Impact Assessment (EIA) is a process of evaluating the likely environmental impacts of a proposed project or development, taking into account inter-related socio-economic, cultural and human-health impacts, both beneficial and adverse.
• It is statutorily backed by the Environment Protection Act, 1986 which contains various provisions on EIA methodology and process.
• UNEP defines Environmental Impact Assessment (EIA) as a tool used to identify the environmental, social and economic impacts of a project prior to decision-making.
• It aims to predict environmental impacts at an early stage in project planning and design, find ways and means to reduce adverse impacts, shape projects to suit the local environment and present the predictions and options to decision-makers.

The correct answer is The speaker of the Lok Sabha.

Key Points

• The joint sitting of the Indian Parliament for transacting a legislative business is presided over by The speaker of the Lok sabha.
• The joint sitting is called by the President.
• In his absence of the speaker of the Lok sabha, the sitting is presided over by the Deputy Chairman of the Rajya Sabha.
• The quorum to constitute a joint sitting: 1/10^th of the total number of members of the House.
• A joint sitting of both Houses of Parliament of the Indian Constitution given in Article 108.

Additional Information

Speaker of Lok Sabha

• The speaker of Lok Sabha is a member who elected from amongst the members of the house. He chairs the house and no proceedings in the house take place in his absence.
• 1^st Lok Sabha Speaker – Ganesh Vasudev Mavalankar
• 17^th Lok Sabha elections (2019 General Elections), Om Birla is the speaker of Lok Sabha.

The correct answer is the Constitution.

Key Points

• The term 'Office of profit' has not been directly defined by the Constitution.
• But The Constitution of India, apart from enlisting certain qualifications for Members of Parliament and Legislative Assembly, also enumerates certain disqualifications. One of these disqualifications is holding an “office of profit”.
• Under the provisions of Article 102 (1) and Article 191 (1) of the Constitution, an MP or an MLA (or an MLC) is barred from holding any office of profit under the central or state government.
• The articles clarify that “a person shall not be deemed to hold an office of profit under the government of India or the government of any state by reason only that he is a minister”.
• A person will be disqualified if he holds any office of profit under the central or state government, other than an office declared not to disqualify its holder by a law passed by Parliament or state legislature.

 Principles for including ‘office of profit’ as a criterion for disqualification are:

• Makers of the Constitution wanted that legislators should not feel obligated to the Executive in any way, which could influence them while discharging legislative functions.
• In other words, an MP or MLA should be free to carry out her duties without any kind of governmental pressure. The intent is that there should be no conflict between the duties and interests of an elected member.
• The office of profit law simply seeks to enforce a basic feature of the Constitution- the principle of separation of power between the legislature and the executive.

The correct answer is Election Commission.

• While deciding any question relating to the disqualification of a Member of Parliament, the President shall obtain the opinion of the Election Commission.
• Election Commission of India is a permanent Constitutional Body.
• The Constitution provides for an independent election commission to ensure free and fair election to the Parliament, the State legislature,and the offices of President and Vice-President.
• Consists of Chief Election Commissioner +2 Election Commissioners.
• The Chief Election Commissioner is appointed by the President and the other Election Commissioners are appointed by the President after consultation with the Chief Election Commissioner, Article 324 also provides for the appointment of Regional Commissioners at the time of General Elections after consultation with the Election Commission.
• Election Commissioners are appointed for a term of 6 years.
• They are not eligible for re-appointment. Also, they cannot hold any office of profit after their retirement.
• In article 324 of the Indian constitution, it envisages the Election Commission of India (ECI).

Additional Information

The correct answer is 40% protein and 20% oil.

Key Points

• Soybean seeds contain 40% of crude protein and about 20% of fat.
• The soybean is one of the most economical and valuable agricultural commodities because of its unique chemical composition.
• Since time immemorial, Soyabean has served as meat, milk, cheese, bread as well as oil for people across the globe.
• Soyabean is India’s one of the fastest-growing crops and a significant foreign exchange earner.

The correct answer is Lucknow​.

Key Points

• As announced by the Ministry of Housing and Urban Affairs, Lucknow is the cleanest city in Uttar Pradesh.
• Swachh Survekshan 2020 report was released by the Union Housing and Urban Affairs Ministry.
• Swachh Survekshan 2020 covered 4,242 cities, 62 cantonment boards and 92 Ganga towns.
• This survey was carried out in 28 days.

Additional Information

Swachh Survekshan 2020

• Indore was ranked the cleanest city in the overall category this year followed by Surat and Navi Mumbai.
• Chhattisgarh is the cleanest state in the category of states with more than 100 urban local bodies.
• Ahmedabad is India’s cleanest Megacity.
• New Delhi is the cleanest capital city.
• Chhattisgarh’s Ambikapur is the cleanest smallest city.
• Cleanest Cantonment: Jalandhar Cantt, Punjab.

The correct answer is Three.

Key Points

• Three teachers from Uttar Pradesh were selected for the 'National Award' on teacher day.
• The three from UP are — Mohammed Ishrat Ali, head teacher in a primary school, Rajwana in Mainpuri; Snehil Pandey, head teacher in a primary school Soharamau, Nawabganj in Unnao; and Vikas Kumar, principal, SD Inter College Meerapur, in Muzaffarnagar
• Union Education Ministry inferred the National Award to Teachers as a way of recognizing their achievements in the field of education.
• The awards were conferred by President Ram Nath Kovind on the occasion of Teacher's Day on September 5, 2020.
• 47 teachers have been selected by the government for 'National Awards to Teachers 2020.

Additional Information

• Teacher’s Day is celebrated across India today to honour Dr. Sarvepalli Radhakrishnan.
• It is observed annually on September 5, as Dr. Radhakrishnan was born on September 5, 1888.
• Dr. Sarvepalli Radhakrishnan was India's first Vice President and second President.
• Teachers' Day was first celebrated in 1962, the year he became the second President of India.
• Since then, the day has been celebrated every year. Dr. Radhakrishnan highly believed that teachers should be the best minds in the country.

The correct answer is September.

Key Points

• Rashtriya Poshan Maah was celebrated in September 2020.
• It was celebrated to promote nutrition among Women and Children.
• Poshan Maah is celebrated every year to encourage Jan Bhagidaari in order to ensure health and nutrition for everyone.
• Every year Poshan Maah is celebrated all over the country under POSHAN Abhiyaan, launched in 2018.
• The importance of Nutrition in our lives was emphasized by Prime Minister Shri Narendra Modi in his popular programme “Mann ki Baat” on 30^th August 2020.

The correct answer is (A) - (3), (B) - (1), (C) - (4), (D) - (2)​.

Key Points

• Kiratarjuniyam- It is a Sanskrit epic written in the 6^th century by Bharavi.
• It is his only recognized work.
• It is an epic poem with eighteen cantos in which Lord Shiva tests the power of Arjuna, one of the Pandavas in the Mahabharata.
• Dashakumar Charitam-  It is authored by renowned Sanskrit poet Dandi.
• It relates the adventures of ten princes in their pursuit of love and royal power.
• Buddha Charitam-  It is an epic poem in the Sanskrit maha kavya style on the life of Gautam Budha by Ashvagosha, composed in the early second century.
• Vikramorvashiya-  It is a five-act Sanskrit play by ancient Indian poet Kalidasa who flourished in the 4^th Century CE, on the Vedic love story of king Pururavas and an Apsara, a celestial nymph named Urvashi.

The correct answer is Rahil. 

• A large tank near Mahoba, temples at Ajaygarh and Mahoba and the city of Rajavsini were built by Chandella King Rahil.
• The town Rahilya which is three km southwest of Mohaba was named after Rahil.
• The Chandela or Chandel is a Rajput clan in Central India.
• An area of the Chandelas which was otherwise called Chandela Dynasty led a great part of the Bundelkhand district of central India for a long period of time between the 10^th and the thirteenth century AD.
• Chandel Dynasty is known in Indian history for Maharaja Rao Vidyadhara, who spurned the assaults of Mahmud of Ghazni.

The correct answer is Right to mortgage and gift.

• Cultivators during the Mughal period enjoyed the Right to mortgage and gift their land.
• The Mughal dynasty was founded by Babur.
• He was a Chagatai Turkic prince and was descended from the Turkic conqueror Timur (Tamerlane) on his father’s side and Genghis Khan, on his mother’s side.
• The Mughal period was between 1526-1857.
• Mughal Empire controlled almost the entire Indian subcontinent.
• It stretched from the edges of the Indus river basin, northern Afghanistan and Kashmir in the north west to the now-Assam and Bangladesh highlands in the east, and down to the uplands of Deccan plateau in the south.

The correct answer is option 4.

Key Points

• Gond is a tribe of Madhya Pradesh.
• Gond tribe is one of the largest Adivasi communities.
• The Gond called themselves Koi or Koiture.
• They inhabited the dense forests of the Vindhyas, Satpura and Mandla in the Narmada region of the Amarkantak range for centuries.
• Tharus is a tribe of Uttarakhand.
• They are live in Khatima and Sitarganj tehsil of UdhamSingh Nagar district (Uttarakhand).
• Todas is a tribe of Tamil Nadu.
• Todas is a tribal group in the higher altitudes of the Nilgiris.
• Santhal is a tribe of Jharkhand.
• They are also called Manjhi.
• The third-largest tribes of India are the Santhal Tribe.
• This tribe habitation is mainly in the states of West Bengal, Bihar, Odisha, Jharkhand and Assam.

Additional Information

Important tribes of :

The correct answer is (A) - (4), (B) - (3), (C) - (1), (D) - (2).

Key Points

 In the given table, Biosphere reserves are given.  These are biosphere reserve of states:

• Nokrek is a biosphere reserve in Meghalaya.

• The Nokrek Biosphere Reserve is located in the northeast of India on the Tura Range, which forms part of the Meghalaya Plateau.

• ​Agasthyamalai is a biosphere reserve in Kerala.

• ​The Agasthyamala Biosphere Reserve (ABR) has got its name into UNESCO’s World Network of Biosphere Reserves (BR).

• It was established in 2001 and straddles the border of Kollam and Thiruvananthapuram Districts in Kerala and Tirunelveli and Kanyakumari Districts in Tamil Nadu, South India at the southern end of the Western Ghats.

• Nandadevi is a biosphere reserve in Uttarakhand.

• Nanda Devi Biosphere Reserve, located in the Himalayan Mountains in the northern part of the country.

• It includes core areas of the Nanda Devi and Valley of Flowers National Parks, which are one World Heritage site.

• ​​​Dehang Debang is a biosphere reserve in Arunachal Pradesh.

• Dihang-Dibang or Dehang-Debang is a biosphere reserve constituted in 1998.

• It is in the Indian state of Arunachal Pradesh.

• Biosphere reserves are areas of terrestrial and coastal ecosystems promoting solutions to reconcile the conservation of biodiversity with its sustainable use.

• They are internationally recognized, nominated by national governments, and remain under the sovereign jurisdiction of the states where they are located.

• They often include one or more National Parks and/or preserves, along with buffer zones that are open to some economic uses. Protection is granted not only to the flora and fauna of the protected region, but also to the human communities who inhabit these regions, and their ways of life.

The correct answer is Excise tax.

Key Points

• The state gets a share of the revenue from the Excise tax.
• Excise tax is a form of indirect tax that is levied by the Central Government of India for the production, sale, or license of certain goods.
• It is also collected by state governments for alcohol and narcotics.
• GST has now subsumed a number of indirect taxes including excise tax.
• This means excise tax, does not exist in India except on a few items such as **liquor and petroleum. **​

Additional Information

The correct answer is Article 253.

• Article 253 of the Indian Constitution empowers Parliament to make laws for implementing international agreements.
• Article 253- empowers Parliament to make any law for the whole or any part of the territory of India for implementing treaties, international agreements, and conventions.
• It enables the Government of India to implement all international obligations and commitments.

Additional Information

• Article 249- empowers the parliament to legislate with respect to a matter in the State List in the national interest.
• Article 250- According to this parliament is empowered to make laws on any item that is included in the State List for the whole or part of India, while a Proclamation of emergency is in operation.
• Article 252- It is about the Power of Parliament to legislate for two or more States by consent and adoption of such legislation by any other State.

The correct answer is the President of India.

Key Points

• The appointment of acting Chief Justice is to be made by the President under Article 126 of the Constitution.
• Vacancy in the office of the Chief Justice must be filled whatever the period of vacancy.
• Article 126 – Appointment of acting Chief justice.
• Justice D Y Chandrachud is the current and 50^th CJI.

Additional Information

Role of Chief Justice of India

• The Chief Justice is responsible for the allocation of work to other judges.
• The Chief Justice administers the oath of office to the President In the absence of the President and the Vice-President, the Chief Justice sits as the Acting President of India
• The Chief Justice is the ex-officio Chancellor to most autonomous law schools in India.

Eligiblity

• The individual must be a citizen of India.
• The person must not exceed 65 years of age.
• In order to be eligible to be Chief Justice of India, the person must serve as a judge at High Court for at least five years or the person should be an advocate in the High court or the Supreme court for at least 10 years or a distinguished jurist.

Karnaugh map (K-map):

• The Karnaugh map (K-map) is a method of simplifying Boolean algebra expressions.
• The Karnaugh map reduces the need for extensive calculations.
• Karnaugh map can be explained as An array that contains 2^k number of cells, where k is the number of variables in the Boolean expression that is to be reduced or optimized.

Number of cells in 2 variable k-map = 2² = 4

Number of cells in 3 variable k-map = 2³ = 8

Number of cells in 4 variable k-map = 2⁴ = 16

2 variable K-maps:

There are 4 cells in the 2-variable k-map as shown,

3 variable K-maps:

• For a 3-variable Boolean function, there is a possibility of 8 output minterms.
• The general representation of all the minterms using 3-variables is shown below.

Explanation:

From the given K-map, the simplified Boolean expression is

F = C A̅ B̅ + C̅ A̅ B + CAB + C̅ A B̅ 

= C̅ (A̅ B + A B̅) + C (A̅ B̅ + AB)

= A ⊕ B ⊕ C

Dual slope ADC:

• These reduce design complexity and improves measurement quality.

• Dual-Slope integration type ADC is the most accurate type of ADC because of non-dependency on variation in components values caused by noise.

• It is quite slow in nature and used in application as digital voltmeter, multimeters etc.

• In dual slope and single slope ADCs instead of using a DAC with a ramped output, we use an op-amp circuit called integrator to generate a sawtooth wave.

• These are used in the precision application.

• Counter type ADC and successive approximate ADC uses DAC

• Counter type ADC uses linear search and successive approximation type ADC uses binary search

• A ring counter is used in successive approximation type ADC

• Flash type ADC is fastest ADC

• Flash type ADC requires no counter

• For an n-bit ADC, flash type ADC requires (2n – 1) comparators

• Dual slope ADC is most accurate

Concept:

• The EX-OR gate is used extensively in digital data processing circuits and is known as Exclusive-OR-gate.
• The E XOR gate has a high output only when an odd number of inputs are high.
• For the two input E XOR gates, the output will be high when the set of input is either 01 or 10.
• The E XOR gate is used in the adder, subtractor, and controlled inverter circuit. It is also used in computers for implementing binary addition.
• Therefore, the gate can be used as a Comparator where it gives high output if both the inputs are not equal.

NAND Gate:

The NAND or “Not AND” function is a combination of the two separate logical functions, the AND function and the NOT function in series. The logic NAND function can be expressed by the Boolean expression of, A.B.

Explanation:

The XOR Gate can be constructed with NAND gates in the following manner:

Y = A̅.B + A.B̅ 

Hence a minimum of 4 NAND gates is required to construct an EX-OR gate.

Important Points

Concept:

Low-Pass RC filter:

• One simple low-pass filter circuit consists of a resistor in series with a load and a capacitor in parallel with the load.
• The capacitor exhibits reactance, and blocks low-frequency signals, forcing them through the load instead.
• At higher frequencies, the reactance drops, and the capacitor effectively functions as a short circuit.

The cut-off frequency is also known as the break frequency, turnover frequency, corner frequency and it is given by

${f_c} = \dfrac{1}{{2\pi RC}}$

Calculation:

Given that, R = 8.2 Ω and C = 0.0033 μF

${f_c} = \dfrac{1}{{2\pi \times 8.2 \times 0.0033 \times {{10}^{ - 6}}}}$

= 5.88 MHz

The main difference between synchronous and asynchronous transmission is that the clocking is derived from the data in synchronous transmission and it is absent in asynchronous transmission.

Synchronous transmission is more preferred because it has no start and stop bit

Some basic differences between synchronous & asynchronous transmission are given below

Concept:

The total transmitted power for an AM system is given by:

${P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)$

Pc = Carrier Power

μ = Modulation Index

Calculation:

Given:

Pc = 400 W, μ = 0.75

${P_t} = 400\left( {1 + \frac{{{{0.75}^2}}}{2}} \right)$

= 512.5 W

Concept:

The wave impedance of the waveguide is given by:

\({η } = \frac{{{η 0}}}{{\sqrt {1 - \frac{{f_c^2}}{{f;^2}}} }}\)  ---(1)

Where,

f_c = cutoff frequency

f = operating frequency

The cutoff frequency can be calculated by:

$f_c=\frac{c}{2}\sqrt{{(\frac{m}{a}})^2 \ + \ (\frac{n}{b})^2}$  ----(2)

Where,

c = 3 × 10¹⁰ cm/s

a and b are dimensions of rectangular waveguide

m and n determines the mode number

For a > b, TE10 is the dominant mode for the waveguide.

Calculation:

Given:

a = 3 cm

b = 2 cm

The cutoff frequency for TE₂₀ can be calculated using equation (2):

$f_c=\frac{3\times10^{10}}{2}\sqrt{{(\frac{2}{3}})^2 \ + \ (\frac{0}{2})^2}$

f_c = 10 GHz

Now the wave impedance can be calculated using equation (1)

${η } = \frac{{{377}}}{{\sqrt {1 - \frac{{{(10 \ GHz})^2}}{{(30 \ GHz)}^2}} }}$

η = 400 Ω 

**Hence option (3) is the correct answer.**​

Explanation:

Noise temperature

1. It is one way of expressing the level of available noise power introduced by a component or source. The power spectral density of the noise is expressed in terms of the temperature (in kelvins) that would produce that level of Johnson–Nyquist noise.

2. It is useful in dealing with UHF.

The Sun is a strong variable noise source with a noise temperature of about 10⁶ K at 50 to 200 MHz and at least 10⁴ K at 10 GHz under quiet Sun conditions.

Large increases occur when the Sun is disturbed. Hence option (3) is the correct answer.

Important Points

Thermal noise:

• It is also called Johnson-Nyquist noise
• It arises due to thermal agitation of electrons in a conductor material when the temperature is increased above absolute zero and it is also called thermal agitation noise
• It is distributed across the entire frequency spectrum range so it is also called white noise
• Thermal noise is generally observed in the passive component like R, L & C due to the random movement of charge carriers electrons.
• Random noise power is

Pn = KTB

Where,

K = Boltz man's constant

T = temperature

B = Bandwidth over which noise is measured

The cavity magnetron is acts like a microwave oscillator and generates microwaves and it uses strapping to prevent mode jumping.

Cavity Magnetron:

• The cavity magnetron is a high-power vacuum tube that generates microwaves using the interaction of a stream of electrons with a magnetic field while moving past a series of cavity resonators which are small, open cavities in a metal block.

• Electrons pass by the cavities and cause microwaves to oscillate within, similar to the functioning of a whistle producing a tone when excited by an air stream blown past its opening.

• The resonant frequency of the arrangement is determined by the cavities' physical dimensions.

• Advance magnetron is the resonant cavity magnetron or electron-resonance magnetron

• The cavity magnetron consists of a large, solid cylinder of metal with a hole drilled through the center of the circular face.

• A wire acting as the cathode is run down the center of this hole, and the metal block itself forms the anode.

• Around this hole, known as the "interaction space", are a number of similar holes ("resonators") drilled parallel to the interaction space, connected to the interaction space by a short channel.

• An AC circuit the electrons travel along the surface, not the core, of the conductor, the parallel sides of the slot acts as a capacitor while the round holes form an inductor: an LC circuit made of solid copper, with the resonant frequency defined entirely by its dimensions.

• The oscillating currents flowing around the cavities, and their effect on the electron flow within the tube, causes large amounts of microwave radiofrequency energy to be generated in the cavities.

• The cavities are open on one end, so the entire mechanism forms a single, larger, microwave oscillator.

• A "tap", normally a wire formed into a loop, extracts microwave energy from one of the cavities.

• In some systems the tap wire is replaced by an open hole, which allows the microwaves to flow into a waveguide.

• The Crossed Field Amplifier (CFA) is a broadband microwave amplifier that can also be used as an oscillator.
• It is a microwave tube amplifier that uses an axial magnetic field and radial electric field
• Its operation is similar in operation to the magnetron and can provide relatively large amounts of power with high efficiency.

Travelling Wave Tube:

• A specialized vacuum tube that is used in electronics to amplify radio frequency (RF) signals in the microwave range.
• The TWT belongs to a category of "linear beam" tubes, such as the klystron, in which the radio wave is amplified by absorbing power from a beam of electrons as it passes down the tube.
• A major advantage of the TWT over some other microwave tubes is its ability to amplify a wide range of frequencies i.e. a large bandwidth.
• The bandwidth of the helix TWT can be as high as two octaves, while the cavity versions have bandwidths of 10% - 20%.
• Operating frequencies range from 300 MHz to 50 GHz.
• The power gain of the tube is on the order of 40 to 70 decibels, and output power ranges from a few watts to megawatts.

Explanation:

• A circular waveguide is a tubular, circular conductor. A plane wave propagating through circular waveguide results in transverse electric (TE) or transverse magnetic (TM) mode.
• Transverse electric (TE) and transverse magnetic (TM) waves are propagated in circular waveguides in almost the same manner as in rectangular waveguides.
• A plane wave propagating through circular waveguide results in TE and TM modes and one of these modes will be present depending upon the wave launcher.
• The field configuration in the circular waveguide closely follows a sine wave pattern.
• In a circular waveguide, TE11 mode has the lowest cut-off frequency and is, therefore, the dominant mode. Hence option (2) is the correct answer.
• If D is the diameter of the waveguide, then λc = 1.706 D for TE11 mode

1. The dominant mode in a rectangular waveguide is TE10, and in a circular waveguide is TE11

2. Cut-off frequency equation for circular waveguide given below is defined as:

${f_c} = \frac{{1.8412.c}}{{2\pi a}}$

a = Radius of the inner circular cross-section

c = Speed of light

3. The cutoff frequency for the dominant mode in the rectangular waveguide is given as:

$f_c=\frac{c}{2a}$

Where a = length of rectangular waveguide.

Explanation:

1. A waveguide is a special form of transmission line consisting of a hollow, metal tube. The tube wall provides distributed inductance, while the empty space between the tube walls provides distributed capacitance.

2. Waveguides are practical only for signals of extremely high frequency, where the wavelength approaches the cross-sectional dimensions of the waveguide. 

A hollow rectangular waveguide cannot propagate TEM wave because of the following reasons:

1. If a transmission line is made by perfect conductors then propagation of pure TEM wave will be not possible as in TEM wave propagation electron and magnetic field components are perpendicular to the guide axis and its cut-off frequency is zero and TEM wave propagate only along guide axis.

2. A transmission line such that rectangular waveguide and cylindrical waveguide are hollow waveguides in which center conductor (i.e. guide axis) does not exist. Therefore in this TEM wave can not propagate.

Hence option (1) is the correct answer.

Important Points

• A rectangular waveguide is a hollow metal tube with a rectangular cross-section.
• The conducting walls of the waveguide confine the electromagnetic fields and thereby guide the electromagnetic wave.
• Microwave energies propagate the length of the waveguide by the reflection of its sidewalls.

Differential relay:

• Differential relay operation depends on the phase difference of two or more electrical quantities.
• It works on the principle of comparison between the phase angle and the magnitude of the same electrical quantities.
• The differential relay is used for the protection of the feeder, large busbars, etc.

Differential protection for feeders consist of

1. Voltage balance differential relay

2. Current balance differential relay

Note:

Generally Translay relay is used for feeder protection

• The translay relay is a differential relay

• The arrangement is similar to overcurrent relay, but the secondary winding is not closed on itself

• These types of relays are used in the feeder protection and the scheme is called Translay scheme

• In this scheme, two such relays are employed at the two ends of feeder as shown in the Fig

• The secondaries of the two relays are connected to each other using pilot wires

• The connection is such that the voltages induced in the two secondaries oppose each other

• The copper coils are used to compensate the effect of pilot wire capacitance currents and unbalance between two currents transformers

• Under normal operating conditions, the current at the two ends of the feeder is same

• The primaries of the two relays carry the same currents inducing the same voltage in the secondaries

• As these two voltages are in opposition, no current flows through the two secondaries circuits and no torque is exerted on the discs of both the relays

• When the fault occurs, the currents at the two ends of the feeder are different, hence unequal voltages are induced in the secondaries

• Hence the circulating current flows in the secondary circuit causing torque to be exerted on the disc of each relay

• But as the secondaries are in opposition, hence torque in one relay operates to close the trip circuit while in other relay the torque just holds the movement in unoperated position

• The care is taken that at least one relay operates under the fault condition

Types of Protection:

• The fault occurs on any part of the electric power system, it must be cleared as soon as possible to avoid damage or interference with the rest of the system.
• The protection scheme divided into two-part that is primary protection and back-up protection.

Primary Protection:

• It is the protection scheme that is designed to protect the component parts of the power system.
• The fault occurs on any line, it will be cleared first by its relay and circuit breaker.
• This forms the primary or main protection and serves as the first line of defense.
• The service record of primary relaying is very high with well over ninety percent of all operations being correct.
• Sometimes faults are not cleared by the primary relay system because of trouble within the relay, wiring system, or breaker. Under such conditions, back-up protection used.

Back-up protection:

• It is the second line of defense in case of failure of the primary protection.
• It is designed to operate with sufficient time delay so that primary relaying will be given enough time hence it is slower than primary protection.
• Definite time delay is used in backup protection.

Substation Battery:

• In a Substation, DC power is supplied to the various equipment such as trip and Closing circuit of the circuit breaker, Protection Relay, isolator control circuit, indication lamp, alarm, PLC circuit, emergency lamps in the control room, indicating instrument, etc.
• Suppose the Transformer is failed due to any reason, in that case, supply should be available for the panels of line and Power Transformer protection or other equipment protection to monitor the type of failure.

Lightning arresters or Surge diverters:

• A lightning arrester or a surge diverter is a protective device that diverts the high voltage surges on the power system to the ground.
• It consists of a spark gap in series with a non-linear resistor.
• The property of the non-linear resistance is that its resistance decreases as the voltage (or current) increases and vice-versa.
• One end of the diverter is connected to the terminal of the equipment to be protected and the other end is effectively grounded.

**Impedance Relay:**​

• Its working depends on the distance between the impedance of the faulty section and the position of the relay.
• It measures the impedance of the faulty part, if the impedance is less than the impedance of the relay setting, it gives the tripping command to the circuit breaker for closing their contacts.
• In the normal operating condition, the value of voltage is more than the current and hence impedance is large.
• On the occurrence of a fault on the line, the magnitude of the fault current rises and the voltage becomes less and hence impedance is less.
• The fault occurs nearer to the location of the relay, the fault current will be minimum, and if the fault is farther, then the fault current will be maximum at constant fault impedance.

Speed of Protective Relay:

• A protective relay must operate at the required speed.
• It should neither be too slow which may result in damage to the equipment nor should it be too fast which may result in undesired operation during transient faults.
• A high-speed relay should be performed an operation from 2 cycles to 8 cycles.

Transient stability: Transient stability is the ability of the power system to maintain synchronism when subjected to a severe transient disturbance.

Transient stability of the system can be improved by

• Increasing the system voltage
• Increase in the X/R ratio
• ​Using high-speed governors on machines
• Series capacitance
• Excitation control
• High-speed circuit breakers help to clear the fault as quickly as possible
• By turbine fast valving
• High-speed excitation
• Use of auto re-closing breakers
• Some of the other ways to improve the transient stability are by employing lightning arresters, high neutral grounding impedance, single pole switching, quick Automatic Voltage Regulators (AVRs).

Important Points

Steady-state stability limit = $\frac{{{V_1};{V_2}}}{X}$

More steady-state stability represents more transient stability of the system.

Steady-state stability limit of the system can be increased by the following methods:

• Upgrading voltage on the existing transmission system or opting for higher voltages on the new transmission system.
• The use of an additional parallel transmission line reduces transfer reactance X, thereby increases it.
• The use of a transformer with lower leakage reactance improves a steady-state stability limit.
• Series capacitive compensation of transmission line reduces transfer reactance X and hence steady-state stability limit increases.
• The use of bundled phase conductors reduces the reactance thereby increasing the stability limit.

Explanation:

In a circuit breaker, the main contacts are usually made up of copper and conduct current in closed positions. Circuit breakers have low contact resistance and they are silver plated. The arcing contacts are solid, resistant to heat and are made up of copper tungsten alloy.

Important Points

Contact resistance is the resistance to current flow, due to surface conditions and other causes, when contacts are touching one another (in the closed condition of the device). This can occur between contacts of breakers.

The contact resistance is in the order of μΩ and it is approximately 20 μΩ.

Additional Information

**There are three types of circuit breaker contacts:**Tulip type contacts:

• It consists, of moving contact which moves inside the fixed contacts.
• During the separation of contact, the arc is established between the tips of the fixed contacts and the tip of the moving contact.
• The advantage of this type of contact is that arcing is confined to the regions which are not in contact in the fully engaged position.

Finger and wedge contacts: 

This type of contact is mainly used for low-voltage oil circuit breakers because of general unsuitability use with arc control devices.

Butt contacts:

• It made up of springs and the moving contact.
• Spring pressure is available to assist contact separation.
• It mainly used single-break oil circuit breakers and air-blast circuit breakers.

Concept:

We know that

$Q = \frac{{{V^2}}}{{{X_L}}} = \frac{{{V^2}}}{{2\pi fL}}$

$\frac{{{Q_2}}}{{{Q_1}}} = {\left( {\frac{{{V_2}}}{{{V_1}}}} \right)^2} \times \left( {\frac{{{f_1}}}{{{f_2}}}} \right)$

Calculation:

${Q_2} = 100;MVAR{\left[ {\frac{{0.98{V_1}}}{{{V_1}}}} \right]^2}\left[ {\frac{{{f_1}}}{{0.96{f_1}}}} \right]$

= 100.042 MVAR

Protective Relays:

• It is a sensing device.
• It senses the fault or given situation when the current attains a certain predetermined value.
• It knows its position and finally, it gives the tripping command to the circuit breaker.
• The protective relay gives the command to the circuit breaker to disconnect the faulted element.
• Relays can be designed to respond to changes in resistance, reactance, impedance, voltage, current, light intensity and temperature.

Additional InformationOverload relay:

An overload relay is an electrical device used to protect an electric motor from overheating. It is mainly three types.

Thermal relay: 

Thermal overload relay is a protective device, and that is mainly designed to cut the power whenever the motor uses too much current for an extended time period.

Once extreme current supplies throughout the motor circuit, then the relay gets open because of the improved temperature of the motor.

Magnetic relay: 

Magnetic overload relay can be operated by detecting the magnetic field strength which is generated by the flow of current towards the motor. This relay can be built with a variable magnetic core within a coil that holds the motor current.

Solid-state relay: 

Solid-state relays are semiconductor equivalents of the electromechanical relay and can be used to control the electrical loads without the use of moving parts.

Considering the Euler’s method,

Y_n+1 = y_n + h f(t_n, y_n)

Euler’s method is only conditionally stable, i.e., the step size has to be chosen sufficiently small to ensure stability.

Explanation:

Newton Raphson method has a second order of quadratic convergence.

According to Newton Raphson method:

\({{\rm{x}}{{\rm{n}} + 1}} = {{\rm{x}}{\rm{n}}} - \frac{{{\rm{f}}\left( {{{\rm{x}}{\rm{n}}}} \right)}}{{{\rm{f'}}\left( {{{\rm{x}}{\rm{n}}}} \right)}}\)

Suppose xn differs from the root α by a small quantity ϵn so that x0 = α + ϵn and xn+1 = α + ϵn+1  

Now the above equation will become

\(\begin{array}{l} \alpha + {{\rm{\varepsilon }}_{n + 1}} = ;\alpha + {{\rm{\varepsilon }}_n} - \frac{{f\left( {\alpha + {{\rm{\varepsilon }}_n}} \right)}}{{f'\left( {\alpha + {{\rm{\varepsilon }}n}} \right)}};\ {{\rm{\varepsilon }}{n + 1}} = {{\rm{\varepsilon }}_n} - \frac{{f\left( {\alpha + {{\rm{\varepsilon }}_n}} \right)}}{{f'\left( {\alpha + {{\rm{\varepsilon }}_n}} \right)}} \end{array}\)

By Taylor’s expansion

$\begin{array}{l} = {_n} - \frac{{f\left( \alpha \right) + {{\rm{\varepsilon }}_n}f'\left( \alpha \right) + \frac{1}{{2!}}{\rm{\varepsilon }}_n^2;f''\alpha + \ldots }}{{f'\left( \alpha \right) + ;{{\rm{\varepsilon }}_n}f'\left( \alpha \right) + \ldots }};\ f\left( \alpha \right) = 0,\ = {{\rm{\varepsilon }}_n} - \frac{{{{\rm{\varepsilon }}_n}f'\left( \alpha \right) + \frac{1}{{2!}}{\rm{\varepsilon }}_n^2;f''\alpha + \ldots }}{{f'\left( \alpha \right) + ;{{\rm{\varepsilon }}_n}f'\left( \alpha \right) + \ldots }} \end{array}$

 Neglecting third and higher powers of ϵn

$= \frac{{{\rm{\varepsilon }}_n^2f'\left( \alpha \right)}}{{2;[f'\left( \alpha \right) + ;{{\rm{\varepsilon }}_n}f'\left( \alpha \right)]}}; \approx \frac{{{\rm{\varepsilon }}_n^2}}{2}.;\frac{{f''\left( \alpha \right)}}{{f'\left( \alpha \right)}}$

This shows that the subsequent error at each step is proportional to the square of the previous error and as such the convergence is quadratic.

Important Points

Methods used for the solution of non-linear algebraic equations:

• Bisection method
• Regula falsi method
• Newton-Raphson method
• Secant method

Additional Information

Methods used for the solution of differential equations:

Single step methods:

• Euler’s method
• Heun’s method
• Runge’s method
• Runge-Kutta method
• Taylor’s series method

Multi step methods:

• Milne’s-predicator Simpson-corrector method
• Adam’s Bash forth Moulton method

Concept:

Miller Indices:

• Miler indices is a symbolic representation of vector for the orientation of an atomic plane in the crystal lattice.
• It is defined as the reciprocal of fractional intercept which the plane makes with the crystallographic axes.

Procedure to find Miller Indices:

1. Determine the intercept of the plane along each of three crystallographic directions.
2. Taking reciprocal of intercept.
3. Taking LCM of the fraction and multiply it by reciprocal of intercept.

Calculation:

Given,

Intercepts of plane = (a, 2b, $- \frac{{3c}}{2}$)

Intercept = (1, 2, $- \frac{{3}}{2}$)

Reciprocal of intercept = 1, $\frac{{1}}{2}$, $- \frac{{2}}{3}$)

LCM = 6

Miller indicates of the plane = LCM × Reciprocal of intercept

∴ Miller indicates of the plane = (6, 3, - 4)

Explanation:

The critical magnetic field of a superconductor is given by

${H_c} = {H_0}\left[ {1 - {{\left( {\frac{T}{{{T_c}}}} \right)}^2}} \right]$

Where,

Hc is a critical magnetic field at T°K

H0 is a critical magnetic field at 0°K

Tc is a critical temperature

The superconductivity can be destroyed with the applications of the magnetic field and it depends upon the temperature as 

From the above-given graph we may conclude that

• At absolute zero critical magnetic field Hc is maximum
• At temperature equal to critical temperature the critical magnetic field Hc is zero.
• Superconductors remain in the state of super conduction for T < Tc

Explanation:

The instruction for starting the computer are housed in ​Read Only Memory (ROM) Chip.

The difference between RAM and ROM is given below.

Control and Status Signals:

This group contains:

• Two control signals ($\overline {RD} ;and;\overline {WR} )$
• Three status signals (IO/M̅, S1 and S0) to identify the nature of the operation
• One special signal (ALE) to indicate the beginning of the operation.

ALE: (Address Latch Enable)

It indicates that the bits on AD7 - AD0 are address bits.

This signal is used to latch the lower order address from multiplexed bus and generate a separate set of eight address lines A7 – A0.

$\overline {{\bf{RD}}} - {\bf{Read}}:$

This is a Read control signal (active low).

This signal indicates that the selected I/O or memory device is to be read and data are available on the data bus.

$\overline {{\bf{WR}}} - {\bf{Write}}:$

This is a Write control signal (active low). This signal indicates that the data on the data bus are to be written into a selected memory or I/O location.

${\bf{IO}}/{\bf{\bar M}}:$

This is a status signal used to differentiate between I/O and memory operations.

When it is high, it indicates an I/O operation; when it is low, it indicates a memory operation.

This signal is combined with $\overline {{\rm{RD}}} \left( {{\rm{Read}}} \right);{\rm{and;}}\overline {{\rm{WR}}} {\rm{;}}\left( {{\rm{Write}}} \right)$ to generate I/O and memory control signals.

S1 and S0:

These status signals, similar to ${\rm{IO}}/{\rm{\bar M}}$, can identify various operations, but they are rarely used in small systems.

(All the operations and their associated status signals are listed in Table)

From the above table, when memory write or I/O read are active, data remains output of the processor.

The correct answer is option 3

Key Points

• A memory unit stores binary information in groups of bits called words.
• Data input lines provide the information to be stored in the memory, Data output lines carry the information out from the memory.
• While performing read operation, one must take care that much current should NOT be sourced or sinked from data lines while reading to avoid loading

​

Additional Information

• Data Acknowledge signal asserts that the data has been placed onto the memory bus, and is available to the processor for reading.

Concept:

Power flow in the Induction motor is as shown below.

Rotor input or air gap power \({{P}{in}}=\frac{3I{2}^{2}{{R}_{2}}}{s}\)

Rotor copper losses \({{P}{cu}}=s\times {{P}{in}}=3I_{2}^{2}{{R}_{2}}\)

Gross mechanical power output \({{P}{g}}={{P}{in}}-{{P}{cu}}=\frac{3I{2}^{2}{{R}{2}}}{s}-3I{2}^{2}{{R}{2}}=3I{2}^{2}{{R}_{2}}\left( \frac{1-s}{s} \right)\)

The relation between the rotor air gap power, rotor copper losses, and gross mechanical power output is,

\({{P}{in}}:{{P}{cu}}:{{P}{g}}=\frac{3I{2}^{2}{{R}{2}}}{s}:3I{2}^{2}{{R}{2}}:3I{2}^{2}{{R}_{2}}\left( \frac{1-s}{s} \right)\)

\(\Rightarrow {{P}{in}}:{{P}{cu}}:{{P}_{g}}=\frac{1}{s}:1:\left( \frac{1-s}{s} \right)=1:s:\left( 1-s \right)\)

Therefore, the electrical rotor losses are proportional to the slip.

Calculation:

Given that,

Shaft output = 16 kW

Constant losses = Mechanical losses = 1 kW

Rotor output = 16 + 1 = 17 kW

Slip (s) = 4%

Rotor copper losses ${P_{cu}} = \frac{s}{{\left( {1 - s} \right)}} \times {P_g}$

$= \frac{{0.04}}{{1 - 0.04}} \times 17 \times {10^3} = 708.33;W$

Concept:

Let N be the number of rotor poles (or teeth) and m is the number of stacks or phases. Then

Pole pitch = 360° / N

Step angle = 360° / (m × N)

Calculation:

In a three-stack 12/8 pole variable reluctance motor,

Number of rotor poles = 8

Pole pitch = 360/8 = 45°

 Mistake Points

Students usually get confused in pole pitch and step angle. Both are different terms with different meanings which are mentioned below.

Pole pitch: The distance measured in terms of armature slots or armature conductors between two adjacent pole centers.

Pole pitch = 360° / N

Step angle: The step angle of a stepper motor is defined as the angle by which the rotor of a stepper motor moves when one input pulse is applied to the stator of the motor.

The step angle for a stepper motor is given by:

$β = \frac{360°}{m × N_r}$

where, β = Step angle

m = No. of stator phases

Nr = No. of rotor teeth

Here in our question rotor pole pitch is to be calculated, so the calculations should be done accordingly.

Explanation:

The principle of operation of a 3-phase induction motor is most similar to that of the transformer with a shorted secondary. A transformer has primary and secondary windings, primary winding induces a voltage in secondary. In 3 phase induction motor, primary winding induces a voltage in secondary but secondary is shorted.

Important Points

Induction motor is also known as a generalized transformer. Both the machines are almost similar, but they have following differences.

• Transformer is a device in which two windings are magnetically coupled and when one winding is excited by AC supply of certain frequency, the emf gets induced in the second winding having same frequency as that of supply given to the first winding
• The winding to which supply is given is called primary winding while winding in which emf gets induced is called secondary winding, the induction motor can be regarded as the transformer
• The difference is that the normal transformer is an alternating flux transformer while induction motor is rotating flux transformer
• The normal transformer has no air gap as against this an induction motor has distinct air gap between its stator and rotor
• In an alternating flux transformer, the frequency of induced emf and current in primary and secondary is always same, however, in the induction motor frequency of emf and current on the stator side remains same but frequency of rotor emf and current depends on the slip
• In case of the alternating flux transformer the entire energy present in the secondary circuit, is in the electrical form
• In an induction motor part of its energy in the rotor circuit is in electrical form and the remaining part is converted into mechanical form

• The angle between the rotor poles and stator poles in a synchronous motor is known as the Torque angle.
• The term torque angle is used in the context of the asynchronous motor. It is the angle by which rotor trails behind the revolving field produced by armature currents.
• The term load angle (or power angle) is used in the context of a synchronous generator. It is the angle by which the rotor magnetic axis is ahead of the resultant air-gap flux. The resultant flux is the vectorial sum of the armature flux and rotor flux and rotates synchronously.

Explanation:

The presence of air-gap between the stator and rotor of an induction motor increases the reluctance of the magnetic circuit. Consequently, an induction motor draws a large magnetizing current (Im) to produce the required flux in the air-gap. That is why the small air-gap is preferred for the induction motor which helps to reduce the magnetizing current.

If the air gap of an induction motor is increased,

• The permeability of the magnetic circuit will decrease
• The magnetizing inductance of the motor will decrease
• Leakage reactance will increase
• Leakage flux will increase
• The magnetizing current will increase
• This will cause a poorer power factor at all loads

Concept:

Pulse per second is mathematically given as

PPS = (rpm/120) × (number of steps per minute)

Calculation:

The speed of motor = 2400 rpm

By converting into rps,

= 2400/60 = 40 revolutions per second

Resolution of motor = 300 steps/revolution

Steps per second = revolutions per second × number of steps/revolution

= 40 × 300 = 12000

Pulses per second = 6000

Concept:

In an induction motor,

• The stator is stationary and the stator field rotates with synchronous speed.
• The rotor field rotates with synchronous speed and the rotor rotates at a speed less than the synchronous speed.

Synchronous speed in rpm of a three-phase induction motor is given by,

${N_s} = \frac{{120f}}{P}$

Where f is the frequency in Hz

P is the number of poles

A rotor of a three-phase induction motor rotates at a speed close to the synchronous speed but not equal to the synchronous speed.

The difference between the synchronous speed and the rotor speed is known as slip speed. It is given by

Slip speed = Ns - Nr

Slip is defined as the ratio of slip speed to the rotor speed.

$s = \frac{{{N_s} - {N_r}}}{{{N_s}}}$

⇒ Nr = Ns (1 – s)

Calculation:

Given that,

Number of poles (P) = 6

Frequency (f) = 50 Hz

Synchronous speed, ${N_s} = \frac{{120 \times 50}}{6} = 1000;rpm$

Slip at no load, s = 5 %

Rotor speed N = Ns (1 – s) = 1000(1 – 0.05) = 950 rpm

The speed of stator magnetic field = speed of rotor magnetic field = 1000 rpm

The speed of the stator magnetic field with respect to the rotor magnetic field = 1000 – 1000 = 0

The speed of the rotor with respect to the stator magnetic field = 950 – 1000 = -50 rpm

Concept:

Thyristor commutation:

• Commutation is defined as the process of turning off a thyristor.
• Thyristor commutation is a necessary mechanism for obtaining the controlled output in many of the thyristor circuits
• A thyristor is a semi-controlled device, It cannot be turned off directly by the gate signal.
• So by the use of external commutation circuits, we can turn off the SCR.

Thyristor turnoff time (t_q):

• It is the time between the instant anode current becomes zero and the instant SCR regains forward blocking capability.
• During this time (t_q) all the excess carriers from four layers of SCR are removed.
• The turn off time is divided into two intervals of reverse recovery time (t_rr) and gate recovery time (t_gr)

t_q = t_rr  + t_gr

Circuit turnoff time (t_c):

It is defined as the time between the instant anode current becomes zero and the instant reverse voltage due to practical circuit reaches zero.

Note:

The circuit turn off time should be more than the device turnoff time for reliable turn off, otherwise, the device may turn on at an undesired instant, a process called Commutation failure.

TRIAC:

• A TRIAC is equivalent to two SCRs joined together in parallel; It has two main terminal and one gate
• In the TRIACs, there will be single gate control conduction in both the directions
• It is a bidirectional device and in both the directions it will conduct
• It is available in high voltage ratings
• TRIAC is a five-layer device

Turn on time: thyristor takes some transition time to go from forward blocking mode to forward conduction mode. This transition time is called turn on time of SCR

Turn off time: time during which a reverse voltage is applied across the thyristor during its commutation process.

Turn off time of a thyristor is greater than turn-on time.

Two thyristors of the same rating and same specifications may have equal or unequal turn-on and turn-off periods.

Fast Switching Thyristor: Fast Switching Thyristor is a fast turn-off semiconductor device, also called “Inverter Thyristor”.

Application of Fast Switching Thyristor: Inverters, Chopper, Inductive heating, Various types of forced converters, Electric welding, AC motor speed control.

The turn-off time of Thyristor:

• Once the thyristor is switched ON (the anode current is above the latching current), the gate loses control over it. That means the gate circuit cannot turn off the device.
• For turning off the SCR anode current must fall below the holding current. After the anode current falls to zero, we cannot apply a forward voltage across the device due to the presence of the carrier. So, we must sweep out or recombine these charges to properly turn off SCR.
• So, the turn-off time of SCR can be defined as the interval between anode current falls to zero and the device regains its forward blocking mode.
• Fast switching SCR has a low turn-off time.
• Low turn-off time enables fast switching.

Explanation:

• SCR is also known as thyristor and the turn-off time SCR is low.
• For switching operations in Inverter and Chopper, we used fast switching thyristor.

Hence, Both (A) and (R) are correct and (R) is the correct explanation of (A)

Explanation:

The expression for the source current is,

{I_{st}} = \mathop \sum \limits_{n = 1,3,5}^\infty \frac{{4;Io}}{{n\pi }}\sin \left( {n\omega t - n \alpha } \right)

R.M.S value of nth harmonic input current

$isn = \frac{{4Io}}{{\sqrt 2 ;n\pi }} = \frac{{2\sqrt 2 {I_0}}}{{n\pi }}$

R.M.S value of fundamental current

${I_{s1}} = \frac{{2\sqrt {2;} {I_0}}}{\pi }$

R.M.S value of input current = I0

Additional Information

In a three-phase full converter,

Peak current flows through the thyristor = load current = I0

RMS value of thyristor current $= {I_0}\sqrt {\frac{1}{3}}$

RMS value of source current $= {I_0}\sqrt {\frac{2}{3}}$

Electrical Drive:

The system employed for motion control (rotational or translational) by means of an electrical input parameter such as voltage, frequency, etc is called an electric drive.

Advantages of Electrical Drive:

• It is simple in construction and has less maintenance cost.
• Its speed control is easy and smooth.
• It is neat, clean, and free from any smoke or flue gases.
• It can be installed at any desired convenient place thus affording more flexibility in the layout, being compact, it requires less space.
• It can be started immediately without any loss of time.
• It has a comparatively longer life.

Disadvantages of Electrical Drive:

• It comes to stop as soon as there is a failure of the electric supply.
• It cannot be used at far-off places that are not served by electric supply.

Classification of Electrical Drive:

AC Drive:

• AC drives are used to step-less speed control of motors mostly used in process industries due to their ruggedness and maintenance-free long life.
• Speed control of AC drive mainly achieved by voltage-frequency speed control by means of a power semiconductor-based device.
• Squirrel cage induction motor is widely used in AC drive due to its simple and rugged construction.
• AC drive is available at various voltage levels and there is no limit on the operating voltage.
• For the same power rating, the weight of the AC motor drive is less than that of the DC motor drive.

DC Drive:

• The main reason for using a DC drive is that it has a wide range of speed control.
• It has high starting torque (DC Series motor) hence can be used in traction, steel rolling mills, etc.
• It gives a fast response with the input parameter and can provide smooth speed control.
• It has the ability to quick starting and stopping.
• The cost of a DC motor drive is more than that of an AC motor drive because of additional equipment required for DC supply such as converter, battery, etc.

Additional Information

Individual Drive:

• In the case of an individual drive, each machine is driven by its own separate motor with the help of gears, pulley, etc.
• It is most economical, with less maintenance.
• Application: Ceiling fan, drilling machine, etc

Group Drive:

• In group drive, a single motor drives a number of machines through belts from a common shaft.
• It is also called line shaft drive
• It is more economical as compared to Individual drive.
• Application: Several machine tools perform their option by using a single motor in a belt or rope drive.

Multi motor Drive:

• In multi-motor drives, separate motors are provided for actuating different parts of the driven mechanism.
• Application: Cranes

Important Points

Wide Speed control range Drive:

• The drive used for speed control over a wide range that is above or below the base speed then we have required various speed control method such as frequency changer method, Ward Leonard System, Armature control method, Flux control method, etc.
• The frequency changer method is used for AC motor drive speed control. But this method cause saturation of the core in the motor.
• Ward Leonard System, Armature control method, Flux control method is used for speed control of DC motor over a wide range and it operated motor satisfactory. Hence DC motor has a wide range of speed control.

High Starting Torque Drive:

• High starting torque drive is used in traction, Rolling mills, crane, etc.
• DC series motor has very high starting torque among all AC motor. Therefore, we preferred DC motor drive for high starting torque application.

Transient Stability of Electric Drive:

• The stability of a drive is caused by the inertia of the rotating masses and inductances of the motor, in the same manner as the transient behavior.
• In cases of sudden changes in input or output response causing the drive to change its equilibrium state, the effects of these components cannot be ignored.
• The stability behavior of the electric drive is due to the effects of change in param­eters is called Transient stability.
• Transient response in the case of DC drive is faster than the AC drive.

Concept:

The heating time constant is defined as the time taken by the machine to attain 0.623 of its final steady temperature rise.

The heating curve of an electric motor is given as below

The equation of the curve is given as

$Δ T=\frac{{P}}{{α A}}(1-e^{\frac{{-t}}{{τ}}})$

At time t = τ,

ΔT = T_max(1 - e^-1) = 0.623 T_max

Where,

T_max = P/αA

ΔT = Temperature raise

P = Power rating of the motor in Watts

τ = Time constant of the motor

t = Time for which motor is loaded.

A = Heating surface area in m²

α = Specific heat dissipation or emissivity in J/sec/m²

Calculation:

Given, P₁ = 20 kW for t₁ = τ = 60 min, t₂ = 15 min

Temperature raise for an electric motor must be constant, so

From equation (1)

$P \propto \frac{{1}}{{(1-e^{\frac{{-t}}{{τ}}})}}$

$\frac{{P_1}}{{P_2}}=\frac{{(1-e^{\frac{{-t_2}}{{τ}}})}}{{(1-e^{\frac{{-t_1}}{{τ}}})}}$

$\frac{{20}}{{P_2}}=\frac{{(1-e^{\frac{{-15}}{{60}}})}}{{(1-e^{\frac{{-60}}{{60}}})}}$

P₂ = 57 kW

Additional Information

Cooling curve:

The cooling time constant is defined as the time required to cool the machine down to 0.368 times the initial temperature rise above ambient temperature.

The cooling curve of an electric motor is given as below

The equation of the curve is given as

$Δ T=T_{max};e^{\frac{{-t}}{{τ}}}$

At t = τ, ΔT = 0.368 T_max

Concept:

For a step-down chopper,

$\frac{{{V_o}}}{{{V_s}}} = \delta = ;\frac{{{T_{on}}}}{T} = f{T_{on}}$

Ton is the ON time

T is time period

f is the chopping frequency

Vs is the input supply

V0 is the average output voltage

Calculation:

Case 1:

Voltage (V₁) = 220 V

Line current (I) = 20 A

Speed (N₁) = 1000 rpm

Armature resistance (R_a) = 1 Ω

Back emf (E_b1) = V₁ – IR_a = 220 – 20 (1) = 200 V

Case 2:

As the rated torque is the same, the current remains the same.

Line current (I) = 20 A

Speed (N₂) = 500 rpm

${E_{b2}} = {E_{b1}} \times \frac{{{N_2}}}{{{N_1}}}$

$= 200 \times \frac{{500}}{{1000}} = 100;V$

Armature resistance (R_a) = 1 Ω

Terminal voltage (V₂) = E_b2 + IR_a = 100 + 20(1) = 120 V

The output of the chopper (V₀) = 120 V

Input of the chopper (V_i) = 250 V

V₀ = δ V_i

⇒ 120 = δ × 250

⇒ δ = 0.48

Electrical Drive:

• The system employed for motion control (rotational or translational) by means of an electrical input parameter such as voltage, frequency, etc is called an electric drive.
• Parts of Electric Drive are, Power Modulator, Motor, Controlling Unit, Sensing Units.

Following are the consideration involved in the selection of the type of electric drive for a specific application:

• The limits of the speed range and its nature
• Motor efficiency
• Starting requirements
• Reliability of operation
• Environmental effects
• Availability of supply
• Effects of supply variations
• Economical aspects
• Power factor
• Load factor
• Braking

Additional Information

Classification of Electrical Drive:

AC Drive:

• AC drives are used to step-less speed control of motors mostly used in process industries due to their ruggedness and maintenance-free long life.
• Speed control of AC drive mainly achieved by voltage-frequency speed control by means of a power semiconductor-based device.
• Squirrel cage induction motor is widely used in AC drive due to its simple and rugged construction.
• AC drive is available at various voltage levels and there is no limit on the operating voltage.
• For the same power rating, the weight of the AC motor drive is less than that of the DC motor drive.

DC Drive:

• The main reason for using a DC drive is that it has a wide range of speed control.
• It has high starting torque (DC Series motor) hence can be used in traction, steel rolling mills, etc.
• It gives a fast response with the input parameter and can provide smooth speed control.
• It has the ability to quick starting and stopping.
• The cost of a DC motor drive is more than that of an AC motor drive because of additional equipment required for DC supply such as converter, battery, etc.

Individual Drive:

• In the case of an individual drive, each machine is driven by its own separate motor with the help of gears, pulley, etc.
• It is most economical, with less maintenance.
• Application: Ceiling fan, drilling machine, etc

Group Drive:

• In group drive, a single motor drives a number of machines through belts from a common shaft.
• It is also called line shaft drive
• It is more economical as compared to Individual drive.
• Application: Several machine tools perform their option by using a single motor in a belt or rope drive.

Multi motor Drive:

• In multi-motor drives, separate motors are provided for actuating different parts of the driven mechanism.
• Application: Cranes

Advantages of Electrical Drive:

• It is simple in construction and has less maintenance cost.
• Its speed control is easy and smooth.
• It is neat, clean, and free from any smoke or flue gases.
• It can be installed at any desired convenient place thus affording more flexibility in the layout, being compact, it requires less space.
• It can be started immediately without any loss of time.
• It has a comparatively longer life.

Disadvantages of Electrical Drive:

• It comes to stop as soon as there is a failure of the electric supply.
• It cannot be used at far-off places that are not served by electric supply.

Concept:

Freewheeling  Diode: 

A freewheeling diode is basically a diode connected across the inductive load terminals to prevent the development of high voltage across the switch. When the inductive circuit is switched off, this diode gives a short circuit path for the flow of inductor decay current and hence dissipation of stored energy in the inductor. Freewheeling diodes are also known as Flyback diode, kickback diode, clamp diodes, commutating diodes, suppression diodes, or snubber diode, etc.

Characteristics of an Ideal Freewheeling Diode:

• The diode must have very large forward current carrying capacity so that the freewheeling diode carry current without burning
• It should have a low forward voltage drop nearly 0.2 V
• It must undergo a quick reverse bias operation.

Purpose of using Freewheeling Diode:

• The Freewheeling Diode improves the waveform of the load current of Rectifier circuits, inverter circuits, and chopper circuits by making it continuous.
• The Freewheeling protect the SCRs from damage in the circuits with Inductive Load from the excessive reverse voltage creating by the Inductive Load.
• In the converter, freewheeling diode is used to conduct current during the off period of the thyristor
• The Freewheeling Diode improves the Input Power Factor of Phase controlled Rectifiers.
• It decreases the possibility of discontinuous conduction in the load.
• The Freewheeling diode sustains the average output voltage of the circuit with an Inductive Load.
• It also helps to reduce Ripple components in the output signal of the circuit with Inductive Load.

Explanation:

Freewheeling diode conducts when load consists of any inductive load. Therefore, the free-wheeling diode will conduct only if load is purely inductive or combination of R and L.

Current commutated chopper:

The power circuit diagram for current commutated chopper is shown in figure. In this diagram, T₁ is the main thyristor, T_A is the auxiliary thyristor, C is the capacitor, L is the inductor diodes D₁ and D₂ constitute commutation circuitry. FD is the freewheeling diode and R_c is the charging resistor.