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UPRVUNL AE practice questions

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Question 1Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a three-phase, 50 Hz, 4-pole squirrel-cage induction motor, the rotor runs at 1440 rpm at full load. What is the percentage slip?

  1. 6%
  2. 5%
  3. 2%
  4. 4% Correct answer.

Explanation

Synchronous speed is Ns = 120f/P = 120 × 50/4 = 1500 rpm. Slip s = (Ns − N)/Ns = (1500 − 1440)/1500 = 0.04, i.e. 4%. Slip is always expressed relative to synchronous speed, not rotor speed.

Question 2Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 200 kVA transformer has a full-load copper loss of 4 kW and a core loss of 1.6 kW. At what fraction of full load does maximum efficiency occur?

  1. 0.4
  2. 0.63 Correct answer.
  3. 0.8
  4. 1.0

Explanation

Maximum efficiency occurs when variable copper loss equals constant core loss, i.e. x²·Pcu = Pi, so x = √(Pi/Pcu) = √(1.6/4) = 0.63. This gives maximum efficiency at about 63% of rated load.

Question 3Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a thermal power plant Rankine cycle, reheating the steam after partial expansion in the high-pressure turbine primarily achieves which of the following?

  1. It raises the boiler feedwater temperature
  2. It increases the mean temperature of heat addition and reduces exhaust wetness Correct answer.
  3. It lowers the boiler drum pressure
  4. It reduces the condenser cooling-water requirement

Explanation

Reheat raises the average temperature at which heat is supplied to the cycle, improving thermal efficiency, and it dries the steam before the low-pressure stages, limiting blade erosion. It does not directly change condenser duty or drum pressure.

Question 4Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 100 Ω resistor carries a current expressed as i(t) = 2 + 3sin(ωt) A. What is the total power dissipated in the resistor?

  1. 250 W
  2. 650 W Correct answer.
  3. 850 W
  4. 1300 W

Explanation

RMS current is √(2² + 3²/2) = √(4 + 4.5) = √8.5 A, so power is I²R = 8.5 × 100 = 850 W. Alternatively, DC component contributes 400 W and the sinusoidal component contributes 450 W, summing to 850 W.

Question 5Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a simply supported beam of span L carrying a central point load W, the maximum bending moment is:

  1. WL/8
  2. WL²/8
  3. WL/2
  4. WL/4 Correct answer.

Explanation

For a simply supported beam with a central point load, reactions are W/2 each and the maximum bending moment occurs at mid-span, equal to (W/2)(L/2) = WL/4. The WL/8 value applies to a uniformly distributed load, not a point load.

Question 6Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a first-order RC low-pass filter with R = 10 kΩ and C = 10 nF, what is the cutoff frequency?

  1. 159 Hz
  2. 1.59 kHz Correct answer.
  3. 15.9 kHz
  4. 10 kHz

Explanation

The cutoff frequency is fc = 1/(2πRC) = 1/(2π × 10⁴ × 10⁻⁸) ≈ 1591 Hz, i.e. about 1.59 kHz. This is the frequency at which output falls to 70.7% of the input magnitude.

Question 7Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 4-bit successive approximation ADC has a full-scale input of 5 V. What is the resolution (smallest resolvable step) of this converter?

  1. 1.25 V
  2. 0.3125 V Correct answer.
  3. 0.156 V
  4. 0.625 V

Explanation

Resolution = VFS/(2ⁿ − 1) = 5/(16 − 1) = 5/15 ≈ 0.333 V for step size definition, but using VFS/2ⁿ = 5/16 = 0.3125 V for LSB size. The standard LSB definition uses 2ⁿ, giving 0.3125 V.

Question 8Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a Pelton wheel turbine, the maximum hydraulic efficiency is obtained when the bucket speed is:

  1. Equal to the jet velocity
  2. One-fourth of the jet velocity
  3. Half the jet velocity Correct answer.
  4. Twice the jet velocity

Explanation

For a Pelton wheel, hydraulic efficiency is maximum when the peripheral velocity of the buckets u equals V/2, where V is jet velocity. This condition maximises the energy extracted from the jet.

Question 9Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 3-phase, 400 V, 50 Hz star-connected load draws a line current of 10 A at 0.8 power factor lagging. What is the total active power drawn?

  1. 10 kW
  2. 8 kW
  3. 3.2 kW
  4. 5.54 kW Correct answer.

Explanation

Total active power P = √3 × VL × IL × cos φ = 1.732 × 400 × 10 × 0.8 ≈ 5543 W, i.e. about 5.54 kW. This formula holds for balanced three-phase loads regardless of star or delta connection.

Question 10Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

The primary purpose of a surge tank in a hydroelectric power plant is to:

  1. Absorb pressure surges in the penstock during sudden load rejection Correct answer.
  2. Increase the head available at the turbine
  3. Store water for peak load generation
  4. Remove sediment from the water before it enters the penstock

Explanation

A surge tank is located between the reservoir and the turbine to absorb water-hammer pressure rises when load is suddenly rejected and to supply water during sudden load acceptance. It protects the penstock from excessive pressure fluctuations.

Question 11Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 50 Hz, 6-pole, 3-phase induction motor has a full-load slip of 3%. What is the frequency of the rotor-induced EMF at full load?

  1. 3 Hz
  2. 50 Hz
  3. 1.5 Hz Correct answer.
  4. 0.5 Hz

Explanation

Rotor frequency fr = s × f = 0.03 × 50 = 1.5 Hz. This low frequency is why rotor iron losses are negligible in normal operation.

Question 12Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a vapour compression refrigeration cycle, the function of the expansion valve is to:

  1. Increase the refrigerant pressure before the evaporator
  2. Compress the refrigerant before it enters the condenser
  3. Separate lubricating oil from the refrigerant
  4. Reduce refrigerant pressure and temperature before it enters the evaporator Correct answer.

Explanation

The expansion valve throttles the high-pressure liquid refrigerant to low pressure and temperature, enabling it to absorb heat in the evaporator. The process is essentially isenthalpic.

Question 13Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

For a given material, the modulus of rigidity G, Young's modulus E, and Poisson's ratio ν are related by which expression?

  1. G = 2E(1 + ν)
  2. G = E/(2(1 + ν)) Correct answer.
  3. G = E/(1 − 2ν)
  4. G = E(1 + ν)/2

Explanation

The standard relation between elastic constants is G = E/(2(1 + ν)). For steel with ν ≈ 0.3, this gives G ≈ E/2.6, consistent with typical values.

Question 14Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a 4-bit flash (parallel) ADC, how many comparators are required?

  1. 15 Correct answer.
  2. 16
  3. 4
  4. 8

Explanation

A flash ADC with n bits uses 2ⁿ − 1 comparators, so for 4 bits it needs 15 comparators. This exponential growth is why flash converters are practical only for low bit counts.

Question 15Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A DC shunt generator delivers 50 A at 220 V. The shunt field resistance is 110 Ω and the armature resistance is 0.1 Ω. What is the generated EMF?

  1. 220 V
  2. 228 V
  3. 220.5 V
  4. 224 V Correct answer.

Explanation

Field current If = 220/110 = 2 A, so armature current Ia = 50 + 2 = 52 A. Generated EMF Eg = V + Ia·Ra = 220 + 52 × 0.1 = 225.2 V, closest to 224 V among options; using standard values gives approximately 225 V.

Question 16Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a steam turbine, the degree of reaction is defined as the ratio of:

  1. Enthalpy drop in the rotor to the total enthalpy drop in the stage Correct answer.
  2. Stage work to stage heat supply
  3. Enthalpy drop in the nozzle to the total enthalpy drop in the stage
  4. Blade speed to steam velocity

Explanation

Degree of reaction R = enthalpy drop in rotor / total enthalpy drop in stage. For a 50% reaction turbine, the expansion is shared equally between stator and rotor.

Question 17Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a 3-phase transmission line, the effect of transposition of conductors is to:

  1. Increase the surge impedance of the line
  2. Increase the insulation level of the line
  3. Reduce the corona loss only
  4. Equalise the inductance and capacitance of the three phases Correct answer.

Explanation

Transposition swaps conductor positions at regular intervals so that each phase occupies each position for an equal distance. This equalises the flux linkages and hence the inductance and capacitance of the three phases, balancing voltage drops.

Question 18Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a 3-phase induction motor, the starting torque is maximum when the rotor resistance per phase equals:

  1. Zero
  2. The stator resistance per phase
  3. The standstill rotor reactance per phase Correct answer.
  4. Twice the standstill rotor reactance

Explanation

Maximum torque occurs when rotor resistance per phase equals standstill rotor reactance per phase. This is exploited in slip-ring motors by inserting external rotor resistance to achieve high starting torque.

Question 19Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 500 kVA, 11 kV/415 V transformer has a per-unit impedance of 0.05. What is the actual impedance referred to the 415 V side?

  1. 0.000172 Ω
  2. 0.344 Ω
  3. 0.0172 Ω Correct answer.
  4. 0.05 Ω

Explanation

Base impedance on LV side = V²/S = 415²/500000 = 0.344 Ω. Actual impedance = 0.05 × 0.344 ≈ 0.0172 Ω. Per-unit values must be multiplied by the base impedance on the chosen side.

Question 20Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

The maximum shear stress in a solid circular shaft of diameter d transmitting torque T is given by:

  1. 16T/(πd³) Correct answer.
  2. 32T/(πd³)
  3. T/(πd³)
  4. 8T/(πd³)

Explanation

For a solid circular shaft, polar moment J = πd⁴/32, and τ = T·r/J with r = d/2 gives τ = 16T/(πd³). The 32T/(πd³) form applies to bending stress, not torsion.

Question 21Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a bipolar junction transistor biased in the active region, the base-emitter junction and base-collector junction are respectively:

  1. Both reverse biased
  2. Reverse biased and forward biased
  3. Both forward biased
  4. Forward biased and reverse biased Correct answer.

Explanation

Active-region operation requires the base-emitter junction to be forward biased (for carrier injection) and the base-collector junction to be reverse biased (to collect carriers). This is the standard amplifier bias condition.

Question 22Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a 132 kV transmission line, the surge impedance is 400 Ω and the line is terminated by its surge impedance. What is the reflection coefficient at the receiving end?

  1. 0 Correct answer.
  2. −1
  3. 1
  4. 0.5

Explanation

Reflection coefficient Γ = (ZL − Z0)/(ZL + Z0). When ZL = Z0, Γ = 0, meaning no reflection occurs and the line is matched. This is the ideal condition for surge-free power transfer.

Question 23Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a centrifugal pump, if the impeller diameter is doubled while speed is held constant, the head developed changes by a factor of approximately:

  1. 8
  2. 16
  3. 2
  4. 4 Correct answer.

Explanation

By the affinity laws, head scales as D² at constant speed, so doubling the impeller diameter increases head by a factor of 4. Flow scales as D and power as D³.

Question 24Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A single-phase full-bridge inverter uses four thyristors with a purely resistive load and produces a square wave output. The fundamental RMS output voltage as a fraction of the total RMS square-wave voltage is approximately:

  1. 0.71
  2. 0.45
  3. 0.50
  4. 0.90 Correct answer.

Explanation

For a square wave, the fundamental RMS value is (2√2/π) × Vdc ≈ 0.90 × Vdc, while the total RMS is Vdc. Thus the fundamental is about 90% of the total RMS.

Question 25Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a CANDU-type nuclear reactor, heavy water is used primarily as a:

  1. Moderator and coolant Correct answer.
  2. Shielding material
  3. Control rod material
  4. Fuel

Explanation

CANDU reactors use heavy water (D₂O) as both moderator and primary coolant, allowing the use of natural uranium fuel. Its low neutron absorption enables a positive neutron economy.

Question 26Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 6-pole, 50 Hz, 3-phase induction motor runs at a rotor speed of 960 rpm. What is the slip of the motor?

  1. 5%
  2. 4% Correct answer.
  3. 3%
  4. 6%

Explanation

Synchronous speed is Ns = 120f/P = 120×50/6 = 1000 rpm. Slip s = (Ns − N)/Ns = (1000 − 960)/1000 = 0.04, i.e. 4%. Slip expresses the fractional shortfall of rotor speed below synchronous speed.

Question 27Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a thermal power plant, the function of the economiser is to:

  1. Remove dissolved oxygen from the condensate
  2. Condense the exhaust steam after the turbine
  3. Heat the boiler feed water using flue gases before it enters the drum Correct answer.
  4. Superheat the steam leaving the boiler drum

Explanation

An economiser is a heat exchanger placed in the flue-gas path that recovers waste heat to raise the feed-water temperature before it enters the boiler. This reduces fuel consumption for the same steam output. Superheating and deaeration are performed by the superheater and deaerator respectively.

Question 28Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

The threshold voltage of a silicon diode is approximately:

  1. 0.05 V
  2. 0.3 V
  3. 0.7 V Correct answer.
  4. 1.2 V

Explanation

For a forward-biased silicon pn-junction diode, conduction begins appreciably at about 0.7 V, which corresponds to the barrier potential of silicon. Germanium diodes conduct at roughly 0.3 V. This value is used in constant-voltage-drop models of diode circuits.

Question 29Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In limit state design of a reinforced concrete beam as per IS 456, the partial safety factor for the yield strength of steel is taken as:

  1. 1.50
  2. 0.87
  3. 1.00
  4. 1.15 Correct answer.

Explanation

IS 456 assigns a partial safety factor of 1.15 to the characteristic yield strength of reinforcement, giving the design strength fy/1.15. Concrete receives 1.5, giving 0.67fck/1.5. The 0.87 factor commonly seen is the ratio of design strength to characteristic strength for Fe415 steel.

Question 30Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A strain gauge with a gauge factor of 2 is bonded to a steel member and experiences a strain of 500 microstrain. What is the fractional change in resistance of the gauge?

  1. 0.002
  2. 0.001 Correct answer.
  3. 0.01
  4. 0.0005

Explanation

Gauge factor is defined as GF = (ΔR/R)/ε. Hence ΔR/R = GF × ε = 2 × 500×10⁻⁶ = 0.001. This small fractional change is why bridge circuits with high gain are used to read strain gauges.

Question 31Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

The Rankine cycle is the standard ideal cycle used for analysing:

  1. Vapour compression refrigerators
  2. Petrol engines
  3. Gas turbine plants
  4. Steam power plants Correct answer.

Explanation

The Rankine cycle models a steam power plant, with isentropic pumping, constant-pressure heat addition in the boiler, isentropic expansion in the turbine and constant-pressure condensation. Gas turbines use the Brayton cycle and petrol engines the Otto cycle.

Question 32Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A single-phase transformer has 500 primary turns and 100 secondary turns. If the primary is connected to 220 V, what is the secondary voltage on open circuit?

  1. 1100 V
  2. 22 V
  3. 44 V Correct answer.
  4. 88 V

Explanation

The voltage ratio equals the turns ratio: V2/V1 = N2/N1. Thus V2 = 220 × 100/500 = 44 V. This is a step-down transformer with a 5:1 ratio.

Question 33Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a cantilever beam of length L carrying a point load W at its free end, the maximum bending moment occurs at:

  1. The free end and equals WL
  2. Mid-span and equals WL/4
  3. Mid-span and equals WL/2
  4. The fixed support and equals WL Correct answer.

Explanation

For a cantilever with an end load, the bending moment diagram is triangular, zero at the free end and maximum at the fixed support where it equals W×L. The support must resist this moment to keep the beam in equilibrium.

Question 34Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 3-phase, 400 V, 50 Hz star-connected induction motor has a per-phase stator resistance of 0.5 Ω and draws a line current of 20 A at 0.85 power factor. What is the total stator copper loss?

  1. 1800 W
  2. 1020 W
  3. 600 W Correct answer.
  4. 200 W

Explanation

In star connection the phase current equals the line current, 20 A. Stator copper loss = 3 × Iph² × Rph = 3 × 400 × 0.5 = 600 W. Power factor does not enter a copper-loss calculation, only current and resistance.

Question 35Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a DC series motor, the field winding is connected in series with the armature. If the load torque is increased while the supply voltage is constant, the motor speed:

  1. Decreases, because flux rises with armature current Correct answer.
  2. Remains constant regardless of load
  3. Increases, because flux falls with armature current
  4. Increases, because back EMF rises

Explanation

In a series motor the flux is proportional to armature current up to saturation. Higher load torque demands more current, which strengthens the flux and lowers speed, since N ∝ (V − IaRa)/φ. This is why series motors must never be started unloaded.

Question 36Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A Zener diode with a rated voltage of 12 V is used to regulate a load. If the input voltage rises while the load current stays constant, the current through the Zener diode:

  1. Increases, absorbing the extra current through the series resistor Correct answer.
  2. Decreases, because the Zener voltage rises sharply
  3. Becomes zero because the Zener turns off
  4. Remains unchanged, since the load current is constant

Explanation

The series resistor carries the sum of load current and Zener current. With the Zener holding the load voltage nearly constant, an increase in input voltage raises the resistor drop and hence the total current, and the excess flows through the Zener. The Zener therefore absorbs the difference.

Question 37Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

In a short 3-phase transmission line, the voltage regulation is defined as:

  1. (No-load receiving-end voltage − full-load receiving-end voltage)/full-load receiving-end voltage Correct answer.
  2. The per-unit voltage drop across the line reactance only
  3. The ratio of line resistance to line reactance
  4. (Sending-end voltage − receiving-end voltage)/sending-end voltage

Explanation

Regulation compares the receiving-end voltage at no load with that at full load for the same sending-end voltage, expressed as a fraction of the full-load value. For a short line the no-load receiving voltage equals the sending voltage. Regulation is a measure of how much the terminal voltage rises when load is removed.

Question 38Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 100 kVA transformer has an iron loss of 1 kW and a full-load copper loss of 2 kW. At what fraction of full load does maximum efficiency occur?

  1. 0.707 Correct answer.
  2. 1.000
  3. 0.500
  4. 0.250

Explanation

Maximum efficiency occurs when variable copper loss equals constant iron loss. Since copper loss varies with the square of load fraction x, x² × 2 kW = 1 kW, giving x = √0.5 ≈ 0.707. Thus the transformer is most efficient at about 70.7% of rated kVA.

Question 39Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A simply supported beam of span 4 m carries a uniformly distributed load of 10 kN/m over its entire length. What is the maximum bending moment?

  1. 40 kN·m
  2. 80 kN·m
  3. 10 kN·m
  4. 20 kN·m Correct answer.

Explanation

For a simply supported beam with a UDL, the maximum moment is wL²/8 at mid-span. Here 10 × 4²/8 = 160/8 = 20 kN·m. The reaction at each support is wL/2 = 20 kN.

Question 40Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A cylindrical pressure vessel has an internal diameter of 1 m and a wall thickness of 10 mm. If the internal pressure is 2 MPa, what is the hoop (circumferential) stress in the wall?

  1. 20 MPa
  2. 200 MPa
  3. 50 MPa
  4. 100 MPa Correct answer.

Explanation

For a thin cylinder, hoop stress σh = pD/(2t) = 2×1000/(2×10) = 100 MPa. The longitudinal stress would be half of this, pD/(4t) = 50 MPa. Thin-cylinder theory is valid here since the wall is much thinner than the diameter.

Question 41Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A simply supported steel column of effective length 3 m has both ends pinned. If the cross-section has a least radius of gyration of 25 mm, what is the slenderness ratio?

  1. 75
  2. 150
  3. 120 Correct answer.
  4. 60

Explanation

Slenderness ratio is λ = Le/r, where Le is the effective length and r the least radius of gyration. Here λ = 3000/25 = 120. A high slenderness ratio indicates a column prone to buckling rather than yielding.

Question 42Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 4-bit R-2R ladder digital-to-analog converter has a reference voltage of 8 V. What is the output voltage for the digital input 1010 (MSB first)?

  1. 5.0 V Correct answer.
  2. 2.5 V
  3. 4.0 V
  4. 6.0 V

Explanation

For an R-2R ladder, each bit contributes Vref/2ⁿ scaled by its binary weight. With Vref = 8 V and 4 bits, the LSB step is 8/16 = 0.5 V. The code 1010 equals decimal 10, so Vout = 10 × 0.5 = 5.0 V.

Question 43Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A common-emitter amplifier has a voltage gain of −100 and an input signal of 10 mV peak. If the supply is ±12 V, the output signal is:

  1. 0.1 V peak, inverted relative to the input
  2. 10 V peak, inverted relative to the input
  3. 1 V peak, in phase with the input
  4. 1 V peak, inverted relative to the input Correct answer.

Explanation

Output magnitude equals gain magnitude times input, 100 × 10 mV = 1 V peak. The negative sign of the gain shows the common-emitter stage inverts the signal, so the output is 180° out of phase with the input. The 1 V peak fits comfortably within the ±12 V supply.

Question 44Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 3-phase, 50 Hz, 4-pole squirrel-cage motor has a rotor resistance of 0.2 Ω per phase and standstill rotor reactance of 1.0 Ω per phase. At what slip is the torque maximum?

  1. 0.50
  2. 0.20 Correct answer.
  3. 0.10
  4. 0.02

Explanation

Maximum torque in an induction motor occurs at the slip where rotor resistance equals slip times standstill rotor reactance, i.e. s = R2/X2. Here s = 0.2/1.0 = 0.20. Inserting external rotor resistance shifts this slip higher, which is how slip-ring motors raise starting torque.

Question 45Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A centrifugal pump delivers 20 L/s against a head of 25 m. Assuming water density of 1000 kg/m³ and g = 9.81 m/s², what is the hydraulic power output?

  1. 2.45 kW
  2. 4.91 kW Correct answer.
  3. 0.49 kW
  4. 9.81 kW

Explanation

Hydraulic power is P = ρgQH = 1000 × 9.81 × 0.020 × 25 = 4905 W ≈ 4.91 kW. Shaft power would be higher, divided by the pump efficiency. The 20 L/s must first be converted to 0.020 m³/s.

Question 46Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 3-phase, 11 kV transmission line delivers 5 MW at 0.8 power factor lagging. What is the approximate line current?

  1. 328 A Correct answer.
  2. 164 A
  3. 568 A
  4. 262 A

Explanation

Line current is I = P/(√3 × VL × cosφ) = 5×10⁶/(1.732 × 11000 × 0.8) ≈ 328 A. The √3 factor is needed because the given voltage is line-to-line in a three-phase system. Ignoring power factor would understate the current.

Question 47Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 3-phase fully controlled bridge converter is supplied from a 400 V, 50 Hz source and feeds a highly inductive load, so the load current is continuous and ripple-free. If the firing angle is 60°, the average DC output voltage is approximately:

  1. 270 V Correct answer.
  2. 360 V
  3. 540 V
  4. 180 V

Explanation

For a 3-phase fully controlled bridge with continuous current, Vdc = (3√2/π) × VL × cosα. With VL = 400 V and α = 60°, Vdc = (1.35)(400)(0.5) ≈ 270 V. The 1.35 factor is the ideal no-control average of a 3-phase bridge.

Question 48Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 50 Hz alternator has 4 poles and 48 slots with a 3-phase, double-layer winding having 4 slots per pole per phase. What is the distribution factor for the fundamental?

  1. 0.827
  2. 0.966
  3. 0.958 Correct answer.
  4. 1.000

Explanation

Slots per pole per phase m = 48/(4×3) = 4, and slot angle β = 180°/12 = 15°. Distribution factor kd = sin(mβ/2)/(m sin(β/2)) = sin 30°/(4 sin 7.5°) = 0.5/(4×0.1305) ≈ 0.958. Concentrated windings would give unity, so distribution slightly reduces the EMF.

Question 49Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A steel shaft transmits 100 kW at 300 rpm. If the allowable shear stress is 40 MPa, the minimum shaft diameter is closest to:

  1. 80 mm Correct answer.
  2. 160 mm
  3. 40 mm
  4. 100 mm

Explanation

Torque T = P/ω = 100000/(2π×300/60) ≈ 3183 N·m. From τ = 16T/(πd³), d³ = 16×3183/(π×40×10⁶) ≈ 4.05×10⁻⁴ m³, so d ≈ 0.080 m or 80 mm. This is a strength-based design; a rigidity check may govern in practice.

Question 50Engineering Discipline (Electrical / Mechanical / Electronics / Civil / Instrumentation, as per post)

A 132 kV, 50 Hz, 3-phase transmission line has a surge impedance of 400 Ω and is 300 km long. Taking the velocity of propagation as 3×10⁵ km/s, the surge impedance loading and the electrical length in degrees are approximately:

  1. 43.6 MW and 18° Correct answer.
  2. 87.1 MW and 18°
  3. 43.6 MW and 36°
  4. 21.8 MW and 9°

Explanation

SIL = VL²/Zc = (132)²/400 ≈ 43.6 MW. The wavelength is λ = v/f = 3×10⁵/50 = 6000 km, so 300 km corresponds to 300/6000 of a wavelength, i.e. 0.05 × 360° = 18°. This shows a 300 km line is a small fraction of a wavelength at 50 Hz.