Q. 1
Electrical Engineering
Difficulty: Easy
(1 Mark)
The synchronous speed (Ns) of a 3-phase, 4-pole induction motor connected to a 50 Hz AC supply is:
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Step-by-Step Explanation & Concept Rationale
Synchronous speed Ns = 120 * f / P = (120 * 50) / 4 = 6000 / 4 = 1500 RPM. The actual rotor speed N will be slightly less (e.g., 1440 RPM) due to slip.
Q. 2
Electrical Engineering
Difficulty: Easy
(1 Mark)
The slip (s) of a 3-phase induction motor operating at standstill (rotor locked) is:
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Step-by-Step Explanation & Concept Rationale
Slip is defined as s = (Ns - N) / Ns. At standstill, rotor speed N = 0, so s = (Ns - 0) / Ns = 1.0 (or 100%). At synchronous speed (N = Ns), slip is zero.
Q. 3
Electrical Engineering
Difficulty: Easy
(1 Mark)
The frequency of rotor induced currents (f_r) in an induction motor running at slip s with stator supply frequency f is:
💡
Step-by-Step Explanation & Concept Rationale
Rotor EMF is induced by relative motion between the rotating stator field (Ns) and rotor (N). Since relative speed is s * Ns, rotor frequency is f_r = s * (P * Ns / 120) = s * f. At full load (s ≈ 0.03-0.05 on 50 Hz), f_r is only 1.5 to 2.5 Hz.
Q. 4
Electrical Engineering
Difficulty: Medium
(1 Mark)
In a 3-phase induction motor, maximum torque (breakdown torque) occurs at a slip s_max equal to:
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Step-by-Step Explanation & Concept Rationale
From maximum power transfer principles applied to the rotor equivalent circuit, maximum developed torque occurs when rotor resistance equals stand-still rotor leakage reactance: R2 = s * X2, giving s_max = R2 / X2.
Q. 5
Electrical Engineering
Difficulty: Medium
(1 Mark)
The magnitude of maximum developed torque in a 3-phase induction motor is:
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Step-by-Step Explanation & Concept Rationale
Substituting s_max = R2/X2 into the torque equation reveals that T_max = (3 / (2 * omega_s)) * (V1^2 / (2 * X2)). Thus, T_max depends on V1^2 and X2, but is completely independent of rotor resistance R2 (R2 only shifts the slip at which T_max occurs).
Q. 6
Electrical Engineering
Difficulty: Medium
(1 Mark)
Rotor skewing in squirrel-cage induction motors is employed to:
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Step-by-Step Explanation & Concept Rationale
Skewing rotor conductor bars slightly along the shaft axis prevents stator and rotor tooth harmonics from locking together (cogging) during startup, suppresses harmonic synchronous torques causing crawling at 1/7th speed, and lowers electromagnetic humming noise.
Q. 7
Electrical Engineering
Difficulty: Hard
(1 Mark)
Crawling in a 3-phase squirrel cage induction motor is primarily caused by:
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Step-by-Step Explanation & Concept Rationale
Stator space harmonics produce parasitic rotating fields. The 7th space harmonic rotates forward at Ns/7. Superimposing this on the fundamental torque-speed curve creates a stable dip where the motor can 'crawl' stably at slightly below 1/7th synchronous speed.
Q. 8
Electrical Engineering
Difficulty: Medium
(1 Mark)
Cogging (magnetic locking) in an induction motor occurs when:
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Step-by-Step Explanation & Concept Rationale
When stator slot count S1 equals rotor slot count S2 (or an integer ratio), the stator and rotor teeth align perfectly at standstill, creating minimum reluctance paths that magnetically lock the rotor, preventing it from starting.
Q. 9
Electrical Engineering
Difficulty: Medium
(1 Mark)
A Star-Delta starter reduces the starting current of a 3-phase induction motor compared to Direct-On-Line (DOL) starting by a factor of:
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Step-by-Step Explanation & Concept Rationale
In star connection, phase voltage is V_line / sqrt(3). Since current per phase is proportional to voltage, phase current is reduced by 1/sqrt(3). The line current in star is equal to phase current, so line starting current is reduced to (1/sqrt(3)) * (1/sqrt(3)) = 1/3 (33.3%) of DOL delta starting current.
Q. 10
Electrical Engineering
Difficulty: Easy
(1 Mark)
A wound-rotor (slip ring) induction motor allows inserting external resistance into the rotor circuit during startup to:
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Step-by-Step Explanation & Concept Rationale
Adding external rotor resistance shifts the maximum torque peak toward standstill (s_max = R2/X2 = 1.0), achieving maximum possible starting torque (T_start = T_max) while increasing rotor impedance to choke starting current.
Q. 11
Electrical Engineering
Difficulty: Medium
(1 Mark)
In a single-phase induction motor, why is an auxiliary winding and capacitor required for starting?
💡
Step-by-Step Explanation & Concept Rationale
According to Double Revolving Field Theory, a pulsating 1-phase field decomposes into two fields rotating in opposite directions at synchronous speed. At standstill, both produce equal forward and backward torques, yielding zero net starting torque. The capacitor creates a 90-degree phase shift to produce a net rotating field.
Q. 12
Electrical Engineering
Difficulty: Easy
(1 Mark)
Which single-phase motor has the highest starting torque?
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Step-by-Step Explanation & Concept Rationale
Capacitor-start capacitor-run motors utilize a high electrolytic capacitor for starting (giving nearly 90-degree phase split and 300-400% starting torque) and a smaller run capacitor for optimal running efficiency and power factor.
Q. 13
Electrical Engineering
Difficulty: Medium
(1 Mark)
A synchronous generator (alternator) operating at lagging power factor has an armature reaction that is:
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Step-by-Step Explanation & Concept Rationale
At lagging power factor, the current lags induced EMF. Resolving armature MMF shows that the in-phase component is cross-magnetizing (distorting field) while the lagging reactive component directly opposes the main field (demagnetizing), reducing terminal voltage.
Q. 14
Electrical Engineering
Difficulty: Medium
(1 Mark)
In a synchronous generator operating at leading power factor, the armature reaction is:
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Step-by-Step Explanation & Concept Rationale
At leading power factor, armature current leads induced EMF. The reactive leading current produces an MMF that directly aids and reinforces the main rotor pole flux (magnetizing effect), causing terminal voltage to rise with load.
Q. 15
Electrical Engineering
Difficulty: Medium
(1 Mark)
The pitch factor (or chording factor) Kp of a fractional-pitch armature winding short-pitched by an angle alpha is:
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Step-by-Step Explanation & Concept Rationale
Pitch factor is the ratio of phasor sum to arithmetic sum of coil-side voltages: Kp = 2*E*cos(alpha/2) / (2*E) = cos(alpha / 2). Chording eliminates specific unwanted harmonics (e.g., short-pitching by 60 deg eliminates the 3rd harmonic since cos(3 * 60/2) = cos(90) = 0).
Q. 16
Electrical Engineering
Difficulty: Hard
(1 Mark)
The distribution factor (or breadth factor) Kd for a distributed armature winding with m slots per pole per phase and slot pitch gamma is:
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Step-by-Step Explanation & Concept Rationale
Distributing winding coils into multiple slots per pole per phase produces EMFs that are out of phase by slot angle gamma. Their phasor sum yields Kd = sin(m * gamma / 2) / [m * sin(gamma / 2)], which effectively suppresses harmonic voltages to generate a clean sinusoidal output.
Q. 17
Electrical Engineering
Difficulty: Medium
(1 Mark)
The Short Circuit Ratio (SCR) of a synchronous generator is defined as:
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Step-by-Step Explanation & Concept Rationale
SCR = If_oc / If_sc = 1 / Xd_sat(pu). A high SCR indicates a larger air gap, lower synchronous reactance Xd, better steady-state stability, superior voltage regulation, and higher short-circuit capacity, but requires a physically larger and more expensive machine.
Q. 18
Electrical Engineering
Difficulty: Easy
(1 Mark)
The 'V-curves' of a synchronous motor illustrate the relationship between:
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Step-by-Step Explanation & Concept Rationale
V-curves plot armature current Ia versus field current If. For a given mechanical load, under-excitation causes lagging power factor and high Ia. Increasing If brings Ia to a minimum at unity power factor. Over-excitation causes leading power factor and high Ia, tracing a characteristic V-shape.
Q. 19
Electrical Engineering
Difficulty: Easy
(1 Mark)
An over-excited synchronous motor operating on no-load acts as a:
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Step-by-Step Explanation & Concept Rationale
When over-excited (Eb > V), a synchronous motor draws current that leads the terminal voltage by almost 90 degrees, acting as a variable capacitor bank known as a Synchronous Condenser to support grid voltage and correct lagging power factor.
Q. 20
Electrical Engineering
Difficulty: Easy
(1 Mark)
Hunting (phase swinging) in synchronous machines is suppressed by installing:
💡
Step-by-Step Explanation & Concept Rationale
Damper windings are heavy copper bars embedded in the rotor pole faces short-circuited by end rings. During load oscillations (hunting), relative speed between the rotor and stator field induces currents in the damper bars, producing damping torque by Lenz's Law that quenches oscillations.
Q. 21
Electrical Engineering
Difficulty: Easy
(1 Mark)
Damper windings also serve which crucial auxiliary function in synchronous motors?
💡
Step-by-Step Explanation & Concept Rationale
Because pure synchronous motors have zero net starting torque at standstill, the damper windings act as a squirrel-cage induction rotor. The motor accelerates to near synchronous speed on induction torque, whereupon DC field excitation is applied to pull into synchronism.
Q. 22
Electrical Engineering
Difficulty: Medium
(1 Mark)
In a salient-pole synchronous machine, the direct-axis synchronous reactance (Xd) is:
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Step-by-Step Explanation & Concept Rationale
The direct axis aligns with the magnetic pole core where the air gap is minimum (reluctance is lowest, permeance highest), yielding maximum flux and high inductance Xd. The quadrature axis lies in the interpolar gap with maximum air gap, yielding higher reluctance and lower inductance Xq. Thus, Xd > Xq.
Q. 23
Electrical Engineering
Difficulty: Easy
(1 Mark)
Salient-pole rotors are preferred over cylindrical (smooth round) rotors for:
💡
Step-by-Step Explanation & Concept Rationale
Salient pole rotors have projecting poles with large diameter and short axial length, ideal for low-speed hydro plants with many poles (P = 120*f / N). High-speed steam turbine sets (3000 RPM, 2-pole) require cylindrical rotors to withstand immense centrifugal forces.
Q. 24
Electrical Engineering
Difficulty: Medium
(1 Mark)
Reluctance torque in a salient-pole synchronous motor arises due to:
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Step-by-Step Explanation & Concept Rationale
Reluctance power is given by P_rel = (V^2 / 2) * (1/Xq - 1/Xd) * sin(2*delta). Because Xd != Xq, torque is developed as the rotor naturally aligns with minimum reluctance paths. Reluctance motors operate entirely on this torque without DC excitation.
Q. 25
Electrical Engineering
Difficulty: Hard
(1 Mark)
The Potier Reactance method (Zero Power Factor characteristic method) is widely regarded as the most accurate method for calculating alternator voltage regulation because:
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Step-by-Step Explanation & Concept Rationale
Unlike the Synchronous Impedance (EMF) method (which overestimates regulation) and MMF method (which underestimates regulation), the Potier Triangle method accurately distinguishes leakage reactance voltage drop from armature reaction ampere-turns under realistic saturation.
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