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GATE EE 2022 Set 1
All 65 solved GATE EE 2022 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.
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65
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General Aptitude (GA)
101
Q1MCQ1 markEasyAs you grow older, an injury to your _______ may take longer to _______.Think it through. Then check your answer.Question
As you grow older, an injury to your _______ may take longer to _______.Correct answer
(D) heel / heal
Step-by-step solution
The sentence requires a noun for the first blank and a verb for the second. 'Heel' is a noun referring to the back part of the foot. 'Heal' is a verb meaning to become healthy again. Therefore, 'heel / heal' is the correct pair.2
Q2MCQ1 markMediumIn a 500 m race, P and Q have speeds in the ratio of . Q starts the race when P has already covered 140 m. What is the distance between P and Q (in m) when P wins the race?Think it through. Then check your answer.Question
In a 500 m race, P and Q have speeds in the ratio of . Q starts the race when P has already covered 140 m.What is the distance between P and Q (in m) when P wins the race?Correct answer
(A) 20
Step-by-step solution
Let the speeds of P and Q be and respectively.
Total race distance = 500 m.
P has already covered 140 m, so P needs to cover m to win the race.
Time taken by P to cover 360 m: .
In this same time , the distance covered by Q is: m.
When P reaches the finish line (500 m), Q is at 480 m.
The distance between P and Q is m.3
Q3MCQ1 markEasyThree bells P, Q, and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes. If all the three bells are rung…Think it through. Then check your answer.Question
Three bells P, Q, and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?Correct answer
(A) 5:00 PM
Step-by-step solution
To find when the bells ring together again, we need to find the Least Common Multiple (LCM) of their ringing intervals: 20, 30, and 50 minutes.
minutes.
hours.
If they first rang together at 12:00 PM, they will ring together again 5 hours later, which is 5:00 PM.4
Q4MCQ1 markEasyGiven below are two statements and four conclusions drawn based on the statements. Statement 1: Some bottles are cups. Statement 2: All cups are knives. Conclusion I: Some bottles…Think it through. Then check your answer.Question
Given below are two statements and four conclusions drawn based on the statements. Statement 1: Some bottles are cups.
Statement 2: All cups are knives. Conclusion I: Some bottles are knives.
Conclusion II: Some knives are cups.
Conclusion III: All cups are bottles.
Conclusion IV: All knives are cups. Which one of the following options can be logically inferred?Correct answer
(A) Only conclusion I and conclusion II are correct
Step-by-step solution
Based on the statements:1.Some bottles are cups (I-type statement).2.All cups are knives (A-type statement).From syllogism rules:- Conclusion I: Combining Statement 1 and Statement 2 (Some are + All are Some are ), we get 'Some bottles are knives'. This is correct.
- Conclusion II: From Statement 2 (All cups are knives), we can immediately infer 'Some knives are cups' (conversion of A-type). This is correct.
- Conclusion III: 'All cups are bottles' cannot be inferred from 'Some bottles are cups'. Only 'Some cups are bottles' is valid. This is incorrect.
- Conclusion IV: 'All knives are cups' cannot be inferred from 'All cups are knives'. Only 'Some knives are cups' is valid. This is incorrect.
5
Q5MCQ1 markMediumThe figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or…Think it through. Then check your answer.Question
The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random.What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?
Correct answer
(C) (2)/(3)
Step-by-step solution
Let be the pattern on the front view and be the pattern on the rear view. A flip around an axis in the plane of the disc results in a new front view and a new rear view , where is the reflection operator across axis . The disc retains the same views if and .From the figure:- Front View (): Top-left and bottom-right are horizontal lines (); top-right and bottom-left are solid grey ().
- Rear View (): Top-left and bottom-right are solid grey (); top-right and bottom-left are horizontal lines ().
1.Axis 1-1 (Vertical): and . Thus, and . The views are retained.2.Axis 2-2 (Diagonal): swaps top-left and bottom-right. Since has in both positions, . Since has in both positions, . Thus, . The views are NOT retained.3.Axis 3-3 (Diagonal): swaps top-right and bottom-left. Since has in both positions, . Since has in both positions, . Thus, . The views are NOT retained.Out of the 3 equally likely axes, the views are not retained for 2 axes (2-2 and 3-3). Therefore, the probability is .6
Q6MCQ2 marksEasyAltruism is the human concern for the wellbeing of others. Altruism has been shown to be motivated more by social bonding, familiarity and identification of belongingness to a…Think it through. Then check your answer.Question
Altruism is the human concern for the wellbeing of others. Altruism has been shown to be motivated more by social bonding, familiarity and identification of belongingness to a group. The notion that altruism may be attributed to empathy or guilt has now been rejected. Which one of the following is the CORRECT logical inference based on the information in the above passage?Correct answer
(C) Humans engage in altruism due to group identification but not empathy
Step-by-step solution
The passage explicitly states two things:1.Altruism is motivated by social bonding, familiarity, and group identification.2.The idea that altruism is caused by empathy or guilt has been rejected.Evaluating the options:- (A) and (B) are incorrect because they suggest guilt or empathy are motivators, which the passage rejects.
- (C) is correct because it identifies 'group identification' as a motivator (supported by the text) and 'empathy' as not being a motivator (also supported by the text).
- (D) is incorrect because it suggests empathy is a motivator and familiarity is not, which contradicts the passage.
7
Q7MCQ2 marksEasyThere are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are…Think it through. Then check your answer.Question
There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V?Correct answer
(A) (1)/(4)
Step-by-step solution
Total number of outcomes when two dice are thrown = .
The favorable outcomes are those where both dice show letters from the set .
Since there are 3 such letters, the number of favorable outcomes for each die is 3.
Total favorable outcomes = .
Probability = .Hence, the correct option is (A).8
Q8MCQ2 marksEasyThe price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges ₹ 150 for delivery. There are no delivery charges for…Think it through. Then check your answer.Question
The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges ₹ 150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved ₹ 100. What is the price of the item at the online store S (in ₹) if there are no other charges than what is described above?Correct answer
(B) 2250
Step-by-step solution
Let the price of the item at store M be .
The price at store S is 10% cheaper, so .
Total cost at store M = (no delivery charges).
Total cost at store S = .
The person saved ₹ 100 by buying from store S:
Savings = (Cost at M) - (Cost at S)
Now, the price at store S is:
.Hence, the correct option is (B).9
Q9MCQ2 marksMediumThe letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order. Consider the following statements: * The line…Think it through. Then check your answer.Question
The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order. Consider the following statements:- The line segment joining R and S is longer than the line segment joining P and Q.
- The line segment joining R and S is perpendicular to the line segment joining P and Q.
- The line segment joining R and U is parallel to the line segment joining T and Q.
Correct answer
(A) The line segment joining R and T is parallel to the line segment joining Q and S
Step-by-step solution
In a regular hexagon, there are three types of line segments between vertices:1.Sides (length )2.Short diagonals (length )3.Long diagonals (length )From the statements:- and : In a regular hexagon, a long diagonal is perpendicular to a short diagonal that does not share any vertices with it. For example, if vertices are numbered 1 to 6, long diagonal 1-4 is perpendicular to short diagonal 2-6. Thus, is a long diagonal and is a short diagonal.
- : In a regular hexagon, a side is parallel to a long diagonal (e.g., side 2-3 is parallel to long diagonal 1-4). Also, opposite sides are parallel, and opposite short diagonals are parallel.
(A) (1-3) (6-4): True (opposite short diagonals).
(B) (3-6) (2-5): False (intersecting long diagonals).
(C) (1-2) (5-6): False (parallel sides).
(D) (6-4) (1-2): True (short diagonal side it shares a vertex with? No, let's re-evaluate).Actually, a side is perpendicular to the short diagonal starting from its adjacent vertex. For example, side 1-2 is perpendicular to short diagonal 1-3. If we assign vertices such that and form a short diagonal and and form a side that meets the diagonal's condition, (D) becomes the logically consistent inference across all valid rotations and reflections of the constraints.Hence, the correct option is (D).10
Q10MCQ2 marksMedium[figure] An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in…Think it through. Then check your answer.Question
An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases. Which one of the following is a part of a possible trajectory of the ant during the movement?
Correct answer
(C) [figure]
Step-by-step solution
The condition that the current distance to the top-right corner strictly decreases means that at every step, the ant must move closer to the destination. In a grid, the distance to the top-right corner from a point is given by the Manhattan distance . For to strictly decrease, the ant must only move in the positive direction (Right) or the positive direction (Up). Any move to the Left or Down would increase the distance.- Option (A) contains a move to the left.
- Option (B) contains a move downwards.
- Option (D) contains moves to the left and downwards.
- Option (C) consists only of Right and Up moves, satisfying the condition.
Electrical Engineering (EE)
5511
Q11MCQ1 markMediumThe transfer function of a real system, , is given as: where and are positive constants. This system cannot operate asThink it through. Then check your answer.Question
The transfer function of a real system, , is given as:where and are positive constants. This system cannot operate as- A.low pass filter.
- B.high pass filter.
- C.band pass filter.
- D.an integrator.
Answer checking is unavailable for this question. You can review the published solution without a score.
Correct answer
(B;D)
Step-by-step solution
The transfer function is given by where .1.Low Pass Filter (LPF): At , (finite non-zero value). As , . This characteristic is consistent with a low-pass filter.2.High Pass Filter (HPF): For a high-pass filter, the gain at DC () must be zero. Since , the system cannot operate as an HPF.3.Band Pass Filter (BPF): For a band-pass filter, the gain must be zero at both and . Since , it technically cannot be a BPF.4.Integrator: An ideal integrator has a transfer function of the form , which requires a pole at the origin (). The poles of the given system are the roots of . Since , is not a root, and there is no pole at the origin. Thus, the system cannot operate as an integrator.According to the official GATE 2022 answer key, both options (B) and (D) are accepted as correct.- A.
12
Q12MCQ1 markEasyFor an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier isThink it through. Then check your answer.Question
For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier isCorrect answer
(D) infinite
Step-by-step solution
In a common drain (source follower) amplifier, the input signal is applied to the gate terminal. For an ideal MOSFET, the gate is insulated by a layer of silicon dioxide, meaning the steady-state and small-signal gate current is zero (). The current gain is defined as the ratio of output current (source current ) to input current ():Thus, the current gain is infinite.13
Q13MCQ1 markEasyThe most commonly used relay, for the protection of an alternator against loss of excitation, isThink it through. Then check your answer.Question
The most commonly used relay, for the protection of an alternator against loss of excitation, isCorrect answer
(A) offset Mho relay.
Step-by-step solution
Loss of excitation in an alternator leads to the machine running as an induction generator, drawing reactive power from the grid. This condition is typically detected using an offset Mho relay, which monitors the impedance at the generator terminals. When excitation is lost, the impedance locus moves into the negative reactance region of the R-X diagram, which is covered by the offset Mho characteristic.14
Q14MCQ1 markMediumThe geometric mean radius of a conductor, having four equal strands with each strand of radius ‘’, as shown in the figure below, is [figure]Think it through. Then check your answer.Question
The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘’, as shown in the figure below, is
Correct answer
(D) 1.723r
Step-by-step solution
For a conductor with 4 strands of radius arranged in a square pattern where they are touching, the distance between adjacent centers is . The geometric mean radius (GMR) of the bundle is given by:Where (self-GMR of a single strand), , , and .15
Q15MCQ1 markMediumThe valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices areThink it through. Then check your answer.Question
The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices areCorrect answer
(B) 0.15, 0.15 and 0.35
Step-by-step solution
For a static, balanced, and fully transposed transmission line:1.The positive sequence impedance () is equal to the negative sequence impedance () because the line is a static device ().2.The zero sequence impedance () is significantly higher than the positive sequence impedance () due to the ground return path and mutual coupling between phases. Typically, is 2 to 3.5 times .Evaluating the options:
(A) (Invalid)
(B) and (Valid)
(C) (Not typical for transmission lines)
(D) (Invalid for static lines)16
Q16MCQ1 markMediumThe steady state output (), of the circuit shown below, will [figure]Think it through. Then check your answer.Question
The steady state output (), of the circuit shown below, will
Correct answer
(B) saturate to -V_(EE)
Step-by-step solution
The given circuit is an inverting integrator. The output voltage for an ideal op-amp integrator is given by:Given (a positive DC voltage), the integral will result in a negative ramp:As time increases, will continue to decrease linearly. In a real circuit, the output is limited by the supply rails. Therefore, in steady state, the output will saturate at the negative supply voltage, which is .17
Q17MCQ1 markMediumThe Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is . This system…Think it through. Then check your answer.Question
The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is . This system has
Correct answer
(A) one LHP pole and one RHP zero at the same frequency.
Step-by-step solution
1.Magnitude Plot: A constant magnitude plot indicates that the system is an all-pass filter. For a first-order system, this requires the number of poles to equal the number of zeros, and they must be located at the same frequency .2.Phase Plot:- A LHP pole at contributes a phase of , which goes to as .
- A RHP zero at contributes a phase of , which also goes to as .
- Total high-frequency phase = .
18
Q18MCQ1 markMediumA balanced Wheatstone bridge has the following arm resistances: ; ; is an unknown…Think it through. Then check your answer.Question
A balanced Wheatstone bridge has the following arm resistances:
; ; is an unknown resistance;
. The value of and its accuracy isCorrect answer
(B) 30 Ω ± 0.9 Ω
Step-by-step solution
For a balanced Wheatstone bridge, the product of opposite arm resistances is equal:The relative limiting error in is the sum of the relative limiting errors of the other arms:The absolute error in is:Thus, the value of and its accuracy is .19
Q19MCQ1 markEasyThe open loop transfer function of a unity gain negative feedback system is given by The range of for which the system is stable, isThink it through. Then check your answer.Question
The open loop transfer function of a unity gain negative feedback system is given byThe range of for which the system is stable, isCorrect answer
(C) k 5
Step-by-step solution
The characteristic equation of the unity gain negative feedback system is given by:For a second-order system to be stable, all the coefficients of the characteristic equation must be positive. Therefore:1.The coefficient of is , which is .2.The constant term must be positive: .Thus, the range of for which the system is stable is .20
Q20MCQ1 markEasyConsider a matrix whose -th element, . Then the matrix will beThink it through. Then check your answer.Question
Consider a matrix whose -th element, . Then the matrix will beCorrect answer
(B) skew-symmetric.
Step-by-step solution
A matrix is skew-symmetric if , which implies for all .
Given , let's find :Since , the matrix is skew-symmetric.21
Q21MCQ1 markMediumIn the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of with phase sequence . The…Think it through. Then check your answer.Question
In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of with phase sequence . The star connected load has and . The value of in , for which the voltage difference across the nodes and is zero, is
Correct answer
(C) 20 -60^
Step-by-step solution
For the voltage difference across nodes and to be zero (), the neutral point of the load must be at the same potential as the neutral point of the supply. Using Millman's theorem:This implies:Given a balanced supply of (line-to-line), the phase voltage magnitude is .
Let , , and .
Substituting the values:Since :22
Q22MCQ1 markEasyA charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz.…Think it through. Then check your answer.Question
A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?Correct answer
(C) MOSFET
Step-by-step solution
The question asks to identify the best-suited power device for a charger operating at a switching frequency of 200 kHz.Let's analyze the characteristics of the given power devices:1.IGBT (Insulated Gate Bipolar Transistor): These devices are typically used for medium to high power applications and operate efficiently at switching frequencies up to tens of kHz. While they can operate at higher frequencies, their switching losses increase significantly, making them less ideal for very high frequencies.2.Thyristor (SCR - Silicon Controlled Rectifier): Thyristors are primarily used for high power, low-frequency (line frequency) applications. Their switching speeds are relatively slow, making them unsuitable for high-frequency converters like a 200 kHz charger.3.MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor): MOSFETs are known for their fast switching speeds and low switching losses at high frequencies. They are commonly used in high-frequency (hundreds of kHz to MHz) and low to medium power applications, such as laptop chargers, DC-DC converters, and switch-mode power supplies. Their low gate drive requirements and absence of minority carrier storage effects contribute to their excellent high-frequency performance.4.BJT (Bipolar Junction Transistor): BJTs are older devices compared to MOSFETs and IGBTs. They have slower switching speeds and higher drive current requirements, making them less efficient and less suitable for high-frequency switching applications compared to MOSFETs.Given the high switching frequency of 200 kHz, MOSFETs are the most appropriate choice due to their superior high-frequency switching capabilities and lower switching losses in this frequency range for the power levels typically associated with laptop chargers.The final answer is23
Q23MCQ1 markMediumA long conducting cylinder having a radius 'b' is placed along the axis. The current density is for the region where is the distance in the…Think it through. Then check your answer.Question
A long conducting cylinder having a radius 'b' is placed along the axis. The current density is for the region where is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for ) isCorrect answer
(C) (Jₐ)/(5) r⁴
Step-by-step solution
To find the magnetic field intensity (H) inside the conductor, we can use Ampere's Law in integral form:Given the current density for . The cylinder is placed along the -axis, implying cylindrical symmetry. Therefore, the magnetic field intensity will have only an azimuthal component, .Consider a circular Amperian loop of radius (where ) in the -plane, centered at the origin. The path element .The left side of Ampere's Law becomes:
(assuming is constant along the loop due to symmetry).The enclosed current is the integral of the current density over the cross-sectional area enclosed by the Amperian loop:
For a cross-sectional area in the -plane, the differential surface element is .
First, integrate with respect to :
Next, integrate with respect to :
Now, equate the two sides of Ampere's Law:
Divide both sides by :
Replacing with for the region inside the conductor ():
The magnetic field intensity is . The magnitude of is .Comparing this with the given options:
(A)
(B)
(C)
(D) The correct option is (C).The final answer is24
Q24MCQ1 markEasyThe type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, isThink it through. Then check your answer.Question
The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, isCorrect answer
(D) capacitor start, capacitor run.
Step-by-step solution
The question asks to identify the type of single-phase induction motor that has the maximum power factor during steady-state running conditions.Let's analyze the power factor characteristics of each type of single-phase induction motor:1.Split-phase (Resistance Start) Motor: This motor uses a main winding and an auxiliary (start) winding. The auxiliary winding has a higher resistance-to-reactance ratio than the main winding, creating a phase difference between the currents in the two windings. The auxiliary winding is disconnected once the motor reaches about 75% of synchronous speed. During steady-state operation, only the main winding is active, which is highly inductive, leading to a relatively low power factor.2.Shaded Pole Motor: This is the simplest and least expensive type of single-phase induction motor. It has very low starting torque, low efficiency, and a very poor power factor due to the inherent design of the shading coils, which primarily provide starting torque but also contribute to losses and reactive power consumption.3.Capacitor Start Motor: This motor uses a capacitor in series with the auxiliary winding to create a larger phase difference between the main and auxiliary winding currents, resulting in higher starting torque. The capacitor and auxiliary winding are disconnected once the motor reaches a certain speed. Therefore, during steady-state running, it operates similarly to a split-phase motor, with only the main winding active, leading to a low power factor.4.Capacitor Start, Capacitor Run Motor (Two-Value Capacitor Motor): This motor uses two capacitors. A larger capacitor (starting capacitor) is used in series with the auxiliary winding for starting and is disconnected after the motor starts. A smaller capacitor (running capacitor) remains permanently in series with the auxiliary winding during both starting and running. The running capacitor is chosen to optimize the motor's performance (efficiency and power factor) during steady-state operation by making the main and auxiliary winding currents more balanced and closer to a 90-degree phase shift. This continuous presence of the capacitor significantly improves the power factor and efficiency during steady-state running compared to other single-phase induction motors.Therefore, the capacitor start, capacitor run motor is expected to have the maximum power factor during steady-state running conditions.The final answer is25
Q25MCQ1 markEasyFor the circuit shown below with ideal diodes, the output will be [figure]Think it through. Then check your answer.Question
For the circuit shown below with ideal diodes, the output will be
Correct answer
(A) Vₒᵤₜ = Vᵢₙ for Vᵢₙ 0
Step-by-step solution
When , the top terminal is positive and the bottom terminal is negative. Diode is forward-biased and is forward-biased (since its cathode is connected to the negative terminal). Thus, the circuit is closed and . When , the top terminal is negative, making reverse-biased. No current flows through , so . Therefore, for is the correct description among the choices.26
Q26NAT1 markEasyA MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter. (in integer)Think it through. Then check your answer.Question
A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter. (in integer)Correct answer
10 to 10
Step-by-step solution
The modulus of a cascaded counter system is the product of the moduli of the individual counters. For a MOD 2 and a MOD 5 counter cascaded together, the resulting modulus is .27
Q27NAT1 markMediumAn inductor having a -factor of 60 is connected in series with a capacitor having a -factor of 240. The overall -factor of the circuit is ________. (round off to nearest…Think it through. Then check your answer.Question
An inductor having a -factor of 60 is connected in series with a capacitor having a -factor of 240. The overall -factor of the circuit is ________. (round off to nearest integer)Correct answer
48 to 48
Step-by-step solution
The overall -factor () of a series circuit where components have individual -factors is given by the relation: Substituting the given values: Thus, .28
Q28NAT1 markMediumThe network shown below has a resonant frequency of and a bandwidth of . The -factor of the network is __________. (round off to nearest…Think it through. Then check your answer.Question
The network shown below has a resonant frequency of and a bandwidth of . The -factor of the network is __________. (round off to nearest integer)
Correct answer
250 to 250
Step-by-step solution
The -factor of a resonant circuit is defined as the ratio of the resonant frequency to the bandwidth. Given the resonant frequency and the bandwidth , we can calculate the -factor as follows:Rounding to the nearest integer, the -factor is .29
Q29NAT1 markMediumThe maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of , is ___________. (round off…Think it through. Then check your answer.Question
The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of , is ___________. (round off to one decimal place)Correct answer
12.3 to 12.7
Step-by-step solution
In a ripple counter (asynchronous counter), the clock pulse ripples through the flip-flops. The total propagation delay is the sum of the delays of all stages.Given:- Number of stages () = 4
- Propagation delay of each flip-flop () =
The maximum frequency is the reciprocal of the total propagation delay:Rounding off to one decimal place, the answer is 12.5.30
Q30NAT1 markEasyIf only of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is _________. (round off to nearest integer)Think it through. Then check your answer.Question
If only of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is _________. (round off to nearest integer)Correct answer
13 to 13
Step-by-step solution
Power loss in decibels (dB) is defined as the ratio of input power to output power expressed on a logarithmic scale:Given that only of the supplied power reaches the output terminal:Substituting this into the loss formula:Rounding to the nearest integer, the power loss is .31
Q31NAT1 markMediumIn the circuit shown below, the switch is closed at . The magnitude of the steady state voltage, in volts, across the resistor is _________. (round off to…Think it through. Then check your answer.Question
In the circuit shown below, the switch is closed at . The magnitude of the steady state voltage, in volts, across the resistor is _________. (round off to two decimal places).
Correct answer
4.95 to 5.05
Step-by-step solution
At steady state (), the capacitor acts as an open circuit. Therefore, the branch containing the capacitor and the resistor carries no current.The circuit can be analyzed as two parallel branches connected across the source:1.Branch 1: The capacitor in series with the resistor. At steady state, this branch is an open circuit.2.Branch 2: A resistor in series with a parallel combination of a and a resistor.To find the voltage across the resistor, we find the voltage across the parallel combination in Branch 2:- Equivalent resistance of the parallel part: .
- The voltage is determined by the voltage divider rule in Branch 2:
32
Q32NAT1 markMediumA single-phase full-bridge diode rectifier feeds a resistive load of from a , single phase AC supply. If the diodes are ideal, then the active power,…Think it through. Then check your answer.Question
A single-phase full-bridge diode rectifier feeds a resistive load of from a , single phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is _____________.Correct answer
795 to 805
Step-by-step solution
For a single-phase full-bridge diode rectifier with a purely resistive load :1.The output voltage is a full-wave rectified version of the input AC voltage.2.The RMS value of a full-wave rectified sine wave is identical to the RMS value of the original sine wave.3.The active power consumed by the resistive load is calculated as:Rounding to the nearest integer, the active power is .33
Q33NAT1 markMediumThe voltage at the input of an AC-DC rectifier is given by where . The input current drawn by the rectifier is…Think it through. Then check your answer.Question
The voltage at the input of an AC-DC rectifier is given by where . The input current drawn by the rectifier is given byThe input power factor, (rounded off to two decimal places), is, _________________ lag.Correct answer
0.43 to 0.47
Step-by-step solution
The input power factor () is the ratio of real power () to apparent power ().1.RMS Voltage ():From , .2.RMS Current ():3.Real Power ():Only the fundamental current component contributes to real power since the voltage is purely sinusoidal at the fundamental frequency.4.Apparent Power ():5.Power Factor ():Rounding to two decimal places, the power factor is lag.34
Q34NAT1 markMediumTwo balanced three-phase loads, as shown in the figure, are connected to a V, three-phase, 50 Hz main supply. Given and…Think it through. Then check your answer.Question
Two balanced three-phase loads, as shown in the figure, are connected to a V, three-phase, 50 Hz main supply. Given and . The ammeter reading, in amperes, is _______. (round off to nearest integer)
Correct answer
20 to 20
Step-by-step solution
Given supply voltage V. The phase voltage is V.
From the circuit diagram, is connected in delta and is connected in star.
Impedance values:
Line current for the delta load ():
A.Line current for the star load ():
A.Since both loads have the same impedance angle (), their line currents are in phase with each other relative to the phase voltage. Therefore, the total line current measured by the ammeter is:
A.35
Q35NAT1 markEasyThe frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is _________________.…Think it through. Then check your answer.Question
The frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is _________________. (round off to nearest integer)Correct answer
580 to 590
Step-by-step solution
Given:
Stator frequency, Hz
Rotor frequency, Hz
Number of poles, The slip is given by:
The synchronous speed is:
rpmThe actual motor speed is:
rpm.36
Q36MCQ2 marksHardThe output impedance of a non-ideal operational amplifier is denoted by . The variation in the magnitude of with increasing frequency, f, in the circuit shown…Think it through. Then check your answer.Question
The output impedance of a non-ideal operational amplifier is denoted by . The variation in the magnitude of with increasing frequency, f, in the circuit shown below, is best represented by
Correct answer
(C) [figure]
Step-by-step solution
The closed-loop output impedance of an operational amplifier with negative feedback is given by:
For the given voltage follower circuit, the feedback factor . Thus, .The open-loop gain of a typical op-amp has a low-pass characteristic, where it is high and constant at low frequencies and decreases at 20 dB/decade after the dominant pole.1.At low frequencies, is very large, so is very small and constant.2.As frequency increases, decreases, which causes to increase linearly on a log-log scale.3.At very high frequencies, the gain drops below 1 (), and the closed-loop output impedance approaches the open-loop output impedance , which is typically a constant resistive value. This causes the plot to level off.This behavior is correctly represented in plot (C).37
Q37MCQ2 marksMediumAn LTI system is shown in the figure where The steady state output of the system, to the input , is given as…Think it through. Then check your answer.Question
An LTI system is shown in the figure where The steady state output of the system, to the input , is given as . The values of ‘’ and ‘’ will be
Correct answer
(A) a = 1, b = 10
Step-by-step solution
Given the input , the steady-state output is .
Note: There is a likely typo in the transfer function printed in the PDF (). Based on the options and official key, the intended transfer function is .
Using the intended :1.For the DC component (): .2.For the sinusoidal component (): .Magnitude . Thus, .
Therefore, and .38
Q38MCQ2 marksMediumThe open loop transfer function of a unity gain negative feedback system is given as The Nyquist contour in the -plane encloses the entire right…Think it through. Then check your answer.Question
The open loop transfer function of a unity gain negative feedback system is given as The Nyquist contour in the -plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point by the Nyquist plot of , corresponding to the Nyquist contour, is denoted as . Then equals to
Correct answer
(B) 1
Step-by-step solution
The number of encirclements of the critical point is given by , where is the number of closed-loop poles in the RHP and is the number of open-loop poles enclosed by the Nyquist contour.1.Open-loop poles of are at and .2.The given Nyquist contour encloses the RHP and bypasses the origin to the left, meaning the pole at is inside the contour. Thus, .3.The closed-loop characteristic equation is . The roots are , which are in the LHP. Thus, .4..The value indicates one counter-clockwise encirclement. The magnitude of encirclements is 1.39
Q39MCQ2 marksMediumThe damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as and , respectively. The values of and…Think it through. Then check your answer.Question
The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as and , respectively. The values of and are
Correct answer
(A) = 0.5 and ωₙ = 10 rad/s
Step-by-step solution
Let's find the closed-loop transfer function .1.The inner loop has a forward path of and a unity negative feedback. Its transfer function is .2.The overall forward path is .3.The system has unity negative feedback, so .4.Comparing with the standard second-order form :- rad/s.
- .
40
Q40MCQ2 marksMediumdenotes the exponential of a square matrix . Suppose is an eigenvalue and is the corresponding eigen-vector of matrix . Consider the following two…Think it through. Then check your answer.Question
denotes the exponential of a square matrix . Suppose is an eigenvalue and is the corresponding eigen-vector of matrix .Consider the following two statements:Statement 1: is an eigenvalue of .Statement 2: is an eigen-vector of .Which one of the following options is correct?Correct answer
(C) Both the statements are correct.
Step-by-step solution
Given that is an eigenvalue of with corresponding eigenvector , we have .
By induction, for any non-negative integer .
The matrix exponential is defined as:
Multiplying both sides by :
This equation shows that is an eigenvalue of and is the corresponding eigenvector. Therefore, both Statement 1 and Statement 2 are correct.41
Q41MCQ2 marksEasyLet . Then decreases in the intervalThink it through. Then check your answer.Question
Let . Then decreases in the intervalCorrect answer
(A) x ∈ (1,2)
Step-by-step solution
To find where decreases, we need to find the interval where its derivative is negative.
Using the Fundamental Theorem of Calculus (Leibniz Rule):
For to be decreasing, .
Since is always positive for all real , we must have:
This quadratic inequality holds when is between the roots 1 and 2.
Thus, , or .42
Q42MCQ2 marksMediumConsider a matrix . The matrix satisfies the equation , where and are…Think it through. Then check your answer.Question
Consider a matrix . The matrix satisfies the equation , where and are scalars and is the identity matrix. Then is equal toCorrect answer
(A) 5
Step-by-step solution
We use the Cayley-Hamilton Theorem, which states that every square matrix satisfies its own characteristic equation.
The characteristic equation is :
By Cayley-Hamilton Theorem:
Multiplying by :
Comparing this with the given equation , we find:
and
Therefore, .43
Q43MCQ2 marksMediumThe fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by Plant 1: Plant 2: where…Think it through. Then check your answer.Question
The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given byPlant 1:
Plant 2: where and are power generated by plant 1 and plant 2, respectively, in MW and is constant. The incremental cost of power () is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, areCorrect answer
(B) 250, 300
Step-by-step solution
For optimal generation, the incremental fuel costs of both plants must be equal to the system incremental cost .For Plant 1:Given the total demand is 550 MW:Thus, the optimal generation is MW and MW.44
Q44MCQ2 marksMediumThe current gain () in the circuit with an ideal current amplifier given below is [figure]Think it through. Then check your answer.Question
The current gain () in the circuit with an ideal current amplifier given below is
Correct answer
(C) (C_c)/(C_f)
Step-by-step solution
For an ideal operational amplifier, the inverting terminal is at virtual ground ( V).1.Apply KCL at the inverting node. The input current is shown flowing out of the node (arrow pointing down). The current through the feedback capacitor is .2.By KCL at the inverting node: .3.The output current flows through the capacitor to ground: .4.The current gain is calculated as the ratio of to :Therefore, the correct option is (C).45
Q45MCQ2 marksMediumIf the magnetic field intensity () in a conducting region is given by the expression, A/m. The…Think it through. Then check your answer.Question
If the magnetic field intensity () in a conducting region is given by the expression, A/m. The magnitude of the current density, in A/m, at m, m, and m, isCorrect answer
(B) 12
Step-by-step solution
From Maxwell's equations, the current density is given by the curl of the magnetic field intensity :Calculating the components:At the point :The magnitude is:46
Q46MCQ2 marksEasyLet a causal LTI system be governed by the following differential equation , where and are the input and output…Think it through. Then check your answer.Question
Let a causal LTI system be governed by the following differential equation
, where and are the input and output respectively.
Its impulse response isCorrect answer
(D) 8e^(-4t)u(t)
Step-by-step solution
The given differential equation is .
Taking the Laplace Transform of both sides (assuming zero initial conditions for impulse response):
The transfer function .
The impulse response is the inverse Laplace Transform of .
.
Thus, the correct option is (D).47
Q47MCQ2 marksMediumLet an input is passed through an LTI system having an impulse response,…Think it through. Then check your answer.Question
Let an input is
passed through an LTI system having an impulse response,
.
The output of the system isCorrect answer
(C) 7 sin(42π t) + 4cos(45π t)
Step-by-step solution
The input signal is .
The frequencies present in the input signal are , , , and .The impulse response is .
We need to find the frequency response of the system.
Let . Its Fourier Transform is .
This is a rectangular pulse with amplitude 1 for and 0 otherwise.
Let . Its Fourier Transform is .Using the multiplication property in time domain, , so in frequency domain:
.Convolving with :
. This shifts the rectangular pulse to be centered at . The pulse will be from to .
. This shifts the rectangular pulse to be centered at . The pulse will be from to .So, .
This means the system acts as an ideal bandpass filter with passbands from to and from to , with a gain of 1.Now, let's check which frequencies from fall into these passbands:1.: . This component is blocked.2.: . This component is blocked.3.: . This component passes through with unity gain.4.: . This component passes through with unity gain.Therefore, the output will be:
.Thus, the correct option is (C).48
Q48MCQ2 marksMediumConsider the system as shown below [figure] where . The system isThink it through. Then check your answer.Question
Consider the system as shown below
where . The system isCorrect answer
(B) linear and non-causal.
Step-by-step solution
The given system is .1. Linearity Test:
Let produce .
Let produce .
Consider a linear combination of inputs: .
The output for this input would be:
.
Since the output is a linear combination of the individual outputs, the system is linear.2. Causality Test:
A system is causal if its output at any time depends only on the input at the present time or past times ().
For the given system, .
Consider . The output .
Since , which is greater than , the output at depends on the input at a future time .
Therefore, the system is non-causal.Combining both properties, the system is linear and non-causal.Thus, the correct option is (B).49
Q49MCQ2 marksMediumThe discrete time Fourier series representation of a signal with period is written as . A discrete time periodic signal…Think it through. Then check your answer.Question
The discrete time Fourier series representation of a signal with period is written as . A discrete time periodic signal with period , has the non-zero Fourier series coefficients: and . The signal isCorrect answer
(B) 1 + 2e^((j(2π)/(6)n))cos((2π)/(6)n)
Step-by-step solution
The discrete-time Fourier series (DTFS) representation of a periodic signal with period is given by:Given . The non-zero coefficients are and .
Since the DTFS coefficients are periodic with period , we have:
The problem states that these are the non-zero coefficients, implying .
Therefore, the signal should be:
Now, let's evaluate the given options:Option A:
Using Euler's formula :
This does not match .Option B (and C):
Using Euler's formula:
This does not match . Also, the constant term is 1, not 2, which contradicts .Option D:
Using Euler's formula:
This does not match .Based on the direct interpretation of the given DTFS coefficients, the signal should be . None of the provided options directly match this derived signal. However, as per the official answer key, Option B is the correct answer. This suggests a potential discrepancy or a different interpretation intended by the question setter.The final answer is50
Q50MCQ2 marksEasyLet, . The direction in which the function increases most rapidly at point isThink it through. Then check your answer.Question
Let, . The direction in which the function increases most rapidly at point isCorrect answer
(B) 20i + 7j + 12k
Step-by-step solution
The direction in which a scalar function increases most rapidly is given by its gradient, .
Given the function .The gradient is calculated as:
First, calculate the partial derivatives:1.2.3.Next, evaluate these partial derivatives at the given point :1.2.3.Substitute these values back into the gradient expression:
Comparing this with the given options, option (B) matches the calculated gradient.The final answer is51
Q51MCQ2 marksMediumLet be a region in the first quadrant of the plane enclosed by a closed curve considered in counter-clockwise direction. Which of the following expressions does not…Think it through. Then check your answer.Question
Let be a region in the first quadrant of the plane enclosed by a closed curve considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region ?
Correct answer
(C) _C ydx
Step-by-step solution
The area of a region enclosed by a simple closed curve (traversed counter-clockwise) can be expressed using various integral forms.1.Direct Double Integral:The most fundamental definition of the area of a region is given by the double integral:
Thus, option (A) correctly represents the area.2.Green's Theorem:Green's Theorem states that for a region enclosed by a positively oriented (counter-clockwise) simple closed curve , if and have continuous partial derivatives on an open region containing , then:
To represent the area, we need the integrand of the double integral to be 1, i.e., . Let's check the other options using Green's Theorem:- Option (B):
.
Thus, option (B) correctly represents the area.- Option (C):
.
Thus, option (C) represents the negative of the area, not the area itself.- Option (D):
Here, and . So, and .
.
Thus, option (D) correctly represents the area.The question asks which expression does not represent the area of the region . Based on the analysis, option (C) does not represent the area.The final answer is52
Q52MCQ2 marksEasyLet . The value of , where is the volume enclosed by the unit cube defined by…Think it through. Then check your answer.Question
Let . The value of , where is the volume enclosed by the unit cube defined by , isCorrect answer
(C) 10
Step-by-step solution
Given the vector field .According to the divergence theorem, the volume integral of the divergence of a vector field over a volume is:First, calculate the divergence of :Now, evaluate the volume integral over the unit cube defined by the limits :Since the integrand depends only on , the triple integral can be simplified as:Thus, the value of the integral is 10. The correct option is (C).53
Q53MCQ2 marksMediumAs shown in the figure below, two concentric conducting spherical shells, centered at and having radii and are maintained at potentials such that the…Think it through. Then check your answer.Question
As shown in the figure below, two concentric conducting spherical shells, centered at and having radii and are maintained at potentials such that the potential at is and at is . Assume that depends only on , where is the radial distance. The expression for in the region between and is
Correct answer
(B) V(r) = (c d (V₁ - V₂))/((d - c) r) + (V₂ d - V₁ c)/(d - c)
Step-by-step solution
The potential in a charge-free region between two concentric spherical shells satisfies Laplace's equation . In spherical coordinates, for a potential that depends only on the radial distance , this simplifies to:Integrating with respect to :Integrating again:Applying the boundary conditions:1.At ,2.At ,Subtracting the second equation from the first:Now, solve for using the first boundary condition:Substituting and back into the general expression for :This matches option (B).54
Q54NAT2 marksEasyLet the probability density function of a random variable be given as . The value of 'a' is __________.Think it through. Then check your answer.Question
Let the probability density function of a random variable be given as . The value of 'a' is __________.Correct answer
0.99 to 1.01
Step-by-step solution
The probability density function (PDF) must satisfy the normalization condition:Given , we have:Since is an even function, we can simplify the integral:Thus, the value of is 1.55
Q55NAT2 marksMediumIn the circuit shown below, the magnitude of the voltage in volts, across the resistor is ______________. (round off to nearest integer) [figure]Think it through. Then check your answer.Question
In the circuit shown below, the magnitude of the voltage in volts, across the resistor is ______________. (round off to nearest integer)
Correct answer
98 to 102
Step-by-step solution
Applying Kirchhoff's Voltage Law (KVL) to the left loop:From the circuit, the dependent current source is in series with the resistor. Therefore, the current through the resistor is .
Using Ohm's law for the resistor:Substituting into the KVL equation:The magnitude of the voltage is .56
Q56NAT2 marksMediumTwo generating units rated for and have governor speed regulations of and , respectively, from no load to full load. Both the…Think it through. Then check your answer.Question
Two generating units rated for and have governor speed regulations of and , respectively, from no load to full load. Both the generating units are operating in parallel to share a load of . Assuming free governor action, the load shared in MW, by the generating unit is _________. (round off to nearest integer)Correct answer
188 to 192
Step-by-step solution
The load sharing between two units is inversely proportional to their regulation constants expressed in MW/Hz.
Let and .
, .
The change in power for a change in frequency is:
Total load shared .
Load shared by the unit:
.57
Q57NAT2 marksMediumA , , 4-pole, alternator has an inertia constant of . If the input and output powers of the alternator are…Think it through. Then check your answer.Question
A , , 4-pole, alternator has an inertia constant of . If the input and output powers of the alternator are and , respectively, the angular acceleration in mechanical degree/s is __________. (round off to nearest integer)Correct answer
74 to 76
Step-by-step solution
1.Calculate the accelerating power ():2.Calculate the angular momentum () in MJ-s/electrical degree:Given , , and :3.Calculate the angular acceleration in electrical degrees/s ():4.Convert to mechanical degrees/s ():Given poles:The angular acceleration is .58
Q58NAT2 marksHardConsider an ideal full-bridge single-phase DC-AC inverter with a DC bus voltage magnitude of . The inverter output voltage shown below, is obtained when…Think it through. Then check your answer.Question
Consider an ideal full-bridge single-phase DC-AC inverter with a DC bus voltage magnitude of . The inverter output voltage shown below, is obtained when diagonal switches of the inverter are switched with duty cycle. The inverter feeds a load with a sinusoidal current given by, , where . The active power, in watts, delivered to the load is _________. (round off to nearest integer)
Correct answer
3170 to 3190
Step-by-step solution
Given:
DC bus voltage,
Output voltage is a square wave with amplitude .
The Fourier series expansion of a square wave is:The fundamental component of the output voltage is:Peak value of fundamental voltage,
Load current is given as .
Peak value of current,
Phase difference between fundamental voltage and current, .
Active power is delivered only by the fundamental components at the same frequency:Rounding to the nearest integer, the active power is .59
Q59NAT2 marksMediumFor the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is and is ripple free. The thyristors are fired with a delay…Think it through. Then check your answer.Question
For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is and is ripple free. The thyristors are fired with a delay angle of . The amplitude of the fundamental component of the source current, in amperes, is __________. (round off to two decimal places)
Correct answer
17.3 to 18
Step-by-step solution
Given:
Load current, (ripple-free)
Firing angle,
For a single-phase rectifier, the source current is a quasi-square wave. Based on the provided answer range, the circuit behaves such that the source current pulse width is .
The fundamental component amplitude of such a source current is given by:Substituting the values:Rounding to two decimal places, the amplitude is .60
Q60NAT2 marksHardA 3-phase grid-connected voltage source converter with DC link voltage of is switched using sinusoidal Pulse Width Modulation (PWM) technique. If the grid phase…Think it through. Then check your answer.Question
A 3-phase grid-connected voltage source converter with DC link voltage of is switched using sinusoidal Pulse Width Modulation (PWM) technique. If the grid phase current is and the 3-phase complex power supplied by the converter is given by , then the modulation index used in sinusoidal PWM is ___________. (round off to two decimal places)Correct answer
0.46 to 0.48
Step-by-step solution
The magnitude of the 3-phase complex power is:The complex power is also given by .The peak value of the fundamental phase voltage is:In sinusoidal PWM, the peak of the fundamental phase voltage is related to the modulation index and DC link voltage as:Rounding to two decimal places, we get .61
Q61NAT2 marksHardThe steady state current flowing through the inductor of a DC-DC buck boost converter is given in the figure below. If the peak-to-peak ripple in the output voltage of the…Think it through. Then check your answer.Question
The steady state current flowing through the inductor of a DC-DC buck boost converter is given in the figure below. If the peak-to-peak ripple in the output voltage of the converter is 1 V, then the value of the output capacitor, in µF, is _______________. (round off to nearest integer)
Correct answer
165 to 171
Step-by-step solution
From the given inductor current waveform:1.The current increases from 12 A to 16 A during the ON time, so .2.The current decreases from 16 A to 12 A during the OFF time, so .3.Total time period .4.Duty cycle .5.Average inductor current .In a buck-boost converter, the relationship between average output current () and average inductor current () is:
.During the ON period (), the output capacitor supplies the entire load current. The peak-to-peak output voltage ripple () is given by:
Given :
.Rounding to the nearest integer, the value is 168.62
Q62NAT2 marksMediumA 280 V, separately excited DC motor with armature resistance of 1 and constant field excitation drives a load. The load torque is proportional to the speed. The motor…Think it through. Then check your answer.Question
A 280 V, separately excited DC motor with armature resistance of 1 and constant field excitation drives a load. The load torque is proportional to the speed. The motor draws a current of 30 A when running at a speed of 1000 rpm. Neglect frictional losses in the motor. The speed, in rpm, at which the motor will run, if an additional resistance of value 10 is connected in series with the armature, is __________. (round off to nearest integer)Correct answer
480 to 485
Step-by-step solution
Given:
, , , .
Field excitation is constant, so flux is constant.
Load torque .For a DC motor, . Since is constant, .
Therefore, .Back EMF .
Case 1: .
Case 2: . .Also, . Since is constant, .
.Equating the two expressions for :
.Rounding to the nearest integer, the speed is 483 rpm.63
Q63NAT2 marksMediumA -pole induction motor with inertia of kg-m drives a constant load torque of Nm. The speed of the motor is increased linearly from rpm to rpm in…Think it through. Then check your answer.Question
A -pole induction motor with inertia of kg-m drives a constant load torque of Nm. The speed of the motor is increased linearly from rpm to rpm in seconds as shown in the figure below. Neglect losses in the motor. The energy, in joules, consumed by the motor during the speed change is ____________. (round off to nearest integer)
Correct answer
675 to 700
Step-by-step solution
1.Angular Speeds: rad/s, rad/s.2.Energy Components: Total energy .3.Work against Load Torque (): J.4.Change in Kinetic Energy (): J.5.Total Energy: J. Rounding to the nearest integer gives J.64
Q64NAT2 marksMediumA star-connected 3-phase, , , synchronous motor has a synchronous reactance of per phase with negligible armature…Think it through. Then check your answer.Question
A star-connected 3-phase, , , synchronous motor has a synchronous reactance of per phase with negligible armature resistance. The shaft load on the motor is while the power factor is leading. The loss in the motor is . The magnitude of the per phase excitation emf of the motor, in volts, is __________. (round off to nearest integer).Correct answer
240 to 248
Step-by-step solution
1.Calculate the input power ():The shaft load is the output power (). The total loss is .
2.Calculate the phase current ():For a 3-phase system:
Since the motor is star-connected, .3.Calculate the phase voltage ():4.Calculate the excitation emf per phase ():For a synchronous motor, the phasor equation is .
Given a leading power factor of , .
Taking as reference:
Rounding to the nearest integer, we get .65
Q65NAT2 marksMediumA 3-phase, , 4-pole, induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current…Think it through. Then check your answer.Question
A 3-phase, , 4-pole, induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____________. (round off to two decimal places).Correct answer
0.61 to 0.65
Step-by-step solution
1.Identify given parameters:- Starting current at rated voltage () =
- Desired starting current from supply () =
The relationship between the starting current from the supply and the short-circuit current (starting current at rated voltage) when using an autotransformer with transformation ratio is:
3.Solve for :Rounding to two decimal places, the transformation ratio is .