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Past Questions — 2026
Nonlinear systems do not satisfy:
A)
Superposition principle
B)
Ohm’s law
C)
Kirchhoff’s law
D)
Faraday’s law
In control systems and network theory, a system is defined as 'Linear' if it satisfies two fundamental properties: Homogeneity (scaling) and Additivity. Together, these two properties constitute the 'Superposition Principle'. The Superposition Principle states that the response of a system to a sum of inputs is equal to the sum of the responses to each input individually. Nonlinear systems, by definition, violate one or both of these properties; therefore, they do not satisfy the superposition principle.
Regarding the other options:
- Ohm's Law (b) describes a specific linear relationship between voltage and current for certain materials, but a system can be nonlinear without violating the fundamental laws of physics.
- Kirchhoff's Laws (c) (KCL and KVL) are based on the conservation of charge and energy; they apply to all electrical circuits regardless of whether the components are linear or nonlinear.
- Faraday's Law (d) is a fundamental law of electromagnetism that governs how magnetic fields induce electromotive force; it remains valid for both linear and nonlinear systems.
When a single phase supply is connected across a single-phase winding, the nature of the magnetic field produced is:
A)
pulsating in nature
B)
rotating in nature
C)
constant in magnitude but rotating at synchronous speed
D)
constant in magnitude and direction.
Step-by-step reasoning: 1. A single-phase AC supply is a sinusoidal current that changes magnitude and direction periodically over time. 2. According to Ampere's Law, the magnetic field (flux) produced by a winding is proportional to the current flowing through it. 3. Since the current is sinusoidal (alternating), the resulting magnetic field will also be sinusoidal. 4. This means the magnetic field grows to a maximum in one direction, decreases to zero, and then grows to a maximum in the opposite direction. 5. This type of field is called a 'pulsating' or 'alternating' magnetic field because it oscillates in magnitude and reverses polarity, but it does not rotate spatially.
Why other options are incorrect:
- Option (b) and (c) are incorrect because a rotating magnetic field (RMF) requires at least two phases (e.g., 3-phase supply or 1-phase with a capacitor start) displaced by a spatial angle (usually 120° or 90°) to create a vector sum that rotates.
- Option (d) is incorrect because a constant magnitude and direction are characteristics of a DC supply, not a single-phase AC supply.
Two alternators A and B operate in parallel and supply a load of 8 MW at 0.8 pf lagging. The power output of A is adjusted to 5000 kW by changing its steam supply and its pf is adjusted to 0.9 lagging by changing its excitation. Find the pf of alternator B.
The induced emf in the armature of a lap-wound four-pole dc machine having 100 armature conductors rotating at 600 rpm and with 1 Wb flux per pole is:
A)
1000 V
B)
100 V
C)
600 V
D)
10,000 V
Option B is correct: 100 V.
In rotating electrical machines, torque is produced due to interaction of:
A)
Magnetic field and electric current
B)
Voltage and resistance
C)
Power and current
D)
Voltage and frequency
Option A is correct: Magnetic field and electric current.
A dc shunt machine, connected to 250 mains, has an armature resistance of 0.12 Ω, and the resistance of the field circuit is 100 Ω. Calculate the ratio of the speed as a generator to the speed as a motor, the line current in each case being 80 A.
Explain the operating principle of protective relays and circuit breakers used in power system protection.
If phase at gain crossover frequency is -150°, the phase margin is:
A)
20°
B)
60°
C)
45°
D)
30°
Option D is correct: 30°.
For a second order system, if ζ = 0.5, the percent overshoot is approximately:
A)
5%
B)
16%
C)
25%
D)
40%
For a standard second-order system, the percentage overshoot (%OS) is calculated using the formula: %OS = 100 * exp[(-ζπ) / sqrt(1 - ζ²)], where ζ (zeta) is the damping ratio.
Given: ζ = 0.5
Step 1: Calculate the exponent term.
Numerator = -0.5 * π ≈ -0.5 * 3.14159 = -1.5708
Denominator = sqrt(1 - 0.5²) = sqrt(1 - 0.25) = sqrt(0.75) ≈ 0.866
Step 2: Divide the numerator by the denominator.
Exponent = -1.5708 / 0.866 ≈ -1.8138
Step 3: Calculate the exponential value.
exp(-1.8138) ≈ 0.163
Step 4: Convert to percentage.
%OS = 0.163 * 100 = 16.3%
Comparing this result to the given options, 16% is the closest approximation.
Analysis of other options:
- 5% would require a much higher damping ratio (ζ ≈ 0.7).
- 25% would require a lower damping ratio (ζ ≈ 0.4).
- 40% would require an even lower damping ratio (ζ ≈ 0.3).
Therefore, option (b) is correct.
The main objective of optimal power system operation is to:
A)
Minimize fuel cost
B)
Maximize system losses
C)
Reduce voltage
D)
Increase short-circuit current
Option A is correct: Minimize fuel cost.
Nichols chart is used in:
A)
Time domain analysis
B)
Frequency domain analysis
C)
State space analysis
D)
Nonlinear analysis
The Nichols chart is a specialized plotting tool used in control systems engineering to analyze the stability and performance of a system. It plots the open-loop gain (in decibels, dB) against the phase shift (in degrees) of the system's transfer function. Since both gain and phase are functions of frequency (ω), this method is fundamentally a part of frequency domain analysis. It is particularly useful for determining the gain margin and phase margin of a system without needing to plot separate Bode diagrams.
Why other options are incorrect:
- a. Time domain analysis: This involves analyzing system responses over time (e.g., step response, impulse response) using tools like differential equations or Laplace transforms, not gain-phase plots.
- c. State space analysis: This is a modern control approach that uses a set of first-order differential equations to represent the internal state of a system in the time domain.
- d. Nonlinear analysis: This involves analyzing systems where the output is not proportional to the input (e.g., using Lyapunov stability or Describing Functions). While Nichols charts can be used for some linearized versions of nonlinear systems, the chart itself is a linear frequency domain tool.
Gain margin indicates:
A)
Amount of gain increase before instability
B)
Frequency response
C)
Time delay
D)
Error constant
Option A is correct: Amount of gain increase before instability.
Z-Bus formulation is mainly used in:
A)
Fault analysis
B)
Steady-state analysis
C)
Economic dispatch
D)
Load shedding
The Z-bus (Bus Impedance Matrix) is a fundamental tool in power system analysis. Unlike the Y-bus (Admittance Matrix), which is sparse and ideal for load flow (steady-state) analysis, the Z-bus is the inverse of the Y-bus and is a full matrix.
1. Why Fault Analysis: In fault analysis, the goal is to determine the current and voltage at a specific bus when a fault occurs. The Z-bus provides a direct relationship between the current injections at all buses and the resulting bus voltages. Specifically, the diagonal element Zii represents the Thevenin impedance looking into the system from bus i, which is essential for calculating the short-circuit current during a fault at that bus.
2. Why not Steady-state analysis: Steady-state analysis (like Load Flow) typically uses the Y-bus matrix because it is sparse, making the computational effort significantly lower for large systems.
3. Why not Economic Dispatch: Economic dispatch is an optimization problem based on cost functions and power balance constraints; it does not rely on the Z-bus matrix.
4. Why not Load shedding: Load shedding is a control strategy used during under-frequency or over-load conditions to maintain system stability; it is not a matrix-based calculation method.
Explain the effect of distribution of winding and use of short-pitch coil on the magnitude and wave shape of the induced emf of an alternator.
Hunting in synchronous machines refers to:
A)
Rotor vibration around synchronous position
B)
Increase in voltage
C)
Current fluctuations
D)
Temperature rise
Option A is correct: Rotor vibration around synchronous position.
In a single-phase repulsion motor, torque is developed on the rotor when the brush axis is fixed:
A)
at 90° electrical with the stator field axis
B)
in alignment with the stator field axis
C)
at an acute angle with the stator field axis
D)
at 90° mechanical with the stator field axis
Option C is correct: at an acute angle with the stator field axis.
The presence of a zero in the first column of Routh array indicates:
A)
Stable system
B)
Imaginary axis roots or marginal stability
C)
Unstable system only
D)
Overdamped system
In Routh-Hurwitz stability criterion, the first column of the Routh array provides critical information about the stability of a linear time-invariant (LTI) system.
1. **Standard Stability**: For a system to be stable, all elements in the first column must have the same sign (usually positive) and no element can be zero.
2. **Zero in the First Column (Special Case 1)**: If only one element in the first column is zero, but the rest of the row is not all zeros, the system is typically unstable because it indicates a sign change occurs immediately after the zero or the system is marginally stable. However, in the context of standard competitive exam questions, a zero in the first column is the primary indicator that the system is not 'absolutely stable'.
3. **Row of Zeros (Special Case 2)**: If an entire row becomes zero, it indicates the presence of 'symmetrically located roots' about the origin. These roots can be:
- Pairs of purely imaginary roots (e.g., s = ±jω), which leads to marginal stability (sustained oscillations).
- Pairs of real roots with opposite signs (e.g., s = ±σ), which leads to instability.
- Complex conjugate pairs forming a rectangle in the s-plane, which leads to instability.
Since the presence of a zero in the first column (specifically when it leads to a row of zeros or a sign change) is the necessary condition for the existence of roots on the imaginary axis (marginal stability) or roots in the right-half plane (instability), and given the options provided, option (b) is the most technically accurate description of the 'critical' state the system enters. While a zero can lead to instability, it specifically signals the boundary condition of marginal stability (imaginary axis roots) before the system becomes fully unstable.
A first order system has transfer function G(s) = 2 / (s + 2). For a unit step input, the steady-state value of the output is:
A)
0.5
B)
1
C)
2
D)
4
Option B is correct: 1.
Transmission lines are usually represented in analysis by:
A)
Lumped parameters
B)
Distributed parameters
C)
Both (a) and (b)
D)
None
Option C is correct: Both (a) and (b).
Starting torque of a DC series motor is:
A)
Very low
B)
Moderate
C)
Very high
D)
Zero
Option C is correct: Very high.
The equal area criterion is used to determine:
A)
Voltage stability
B)
Transient stability
C)
Steady-state voltage
D)
Fault current
Option B is correct: Transient stability.
The step response of a first order system reaches 63.2% of its final value at:
A)
t=2τ
B)
t=τ
C)
t=3τ
D)
t=0.5τ
Option B is correct: t=τ.
A system has the following sequence reactances: X1 = X2 = 0.3 pu, X0 = 0.6 pu. Prefault voltage = 1 pu. For a single line-to-ground fault, the fault current is:
A)
0.83 pu
B)
1.25 pu
C)
2.5 pu
D)
3 pu
Option C is correct: 2.5 pu.
Slip in an induction motor is defined as:
A)
Difference between rotor and synchronous speed
B)
Difference between rotor and stator voltage
C)
Difference between current and voltage
D)
Difference between torque and speed
In an induction motor, the stator creates a rotating magnetic field that rotates at a constant speed known as the synchronous speed (Ns). The rotor rotates at a speed (Nr) which is always slightly less than the synchronous speed to maintain the relative motion necessary to induce current in the rotor bars. The difference between these two speeds (Ns - Nr) is defined as the 'slip'. Mathematically, slip (s) is often expressed as a fraction or percentage: s = (Ns - Nr) / Ns.
Why other options are incorrect:
- Option b: The difference between rotor and stator voltage is not 'slip'; it relates to voltage drops or transformation ratios.
- Option c: The difference (or phase shift) between current and voltage is known as the 'power factor' or 'phase angle'.
- Option d: Torque and speed are related via the torque-speed characteristic curve, but their difference is not defined as slip.
The circle diagram of an induction motor is used to determine:
A)
Efficiency and power factor
B)
Voltage regulation
C)
Transformer ratio
D)
Frequency
The circle diagram of a three-phase induction motor is a graphical representation used to determine the performance characteristics of the motor from a few simple tests (specifically the No-Load test and the Blocked-Rotor test). By plotting these results on a graph, the diagram forms a circle. From this circle, one can determine the output power, torque, slip, efficiency, and power factor for any given load.
- Option (a) is correct because efficiency and power factor are primary parameters derived from the circle diagram.
- Option (b) is incorrect because voltage regulation is typically associated with synchronous machines or transformers, not the primary purpose of the induction motor circle diagram.
- Option (c) is incorrect because the transformer ratio is a property of transformers, not induction motors.
- Option (d) is incorrect because frequency is a constant input parameter of the power supply, not a value determined by the motor's performance diagram.