Question 1

In a three-phase system, a Y-connected (wye) source feeds a Δ-connected (delta) load. For each delta phase element, what voltage appears across it relative to the source line voltage?

Accepted Answer

Introduction / Context: Delta–wye interconnections are common in power systems and laboratory setups. This question checks your understanding of how line and phase voltages map across a Δ-connected load when the source is Y-connected. Getting this right is essential for rating load components and predicting current and power in three-phase networks. Given Data / Assumptions: Balanced, sinusoidal three-phase system. Source side is Y (wye) connected; load side is Δ (delta) connected. We compare the voltage across each delta phase element to the source line voltage. Concept / Approach: In a Y source, the line-to-line voltage V_LL equals √3 times the phase (line-to-neutral) voltage. A delta load connects each phase element directly between two lines, so each delta branch sees the line-to-line voltage. Therefore, the voltage across each delta phase equals the source V_LL, not a fraction of it. Step-by-Step Solution: Let the source line-to-neutral voltages be V_an, V_bn, V_cn.Line-to-line voltages are V_ab = V_an − V_bn, etc., with |V_LL| = √3 * |V_phase|.Each Δ branch is connected across a pair of lines → branch voltage = corresponding V_LL. Verification / Alternative check: Measure with a meter: place probes across any one delta element; the reading is the same as the source line-to-line voltage because those two terminals are the same line conductors feeding the element. Why Other Options Are Wrong: One-third / two-thirds: There is no 1/3 or 2/3 factor in Δ branch voltage relative to V_LL. Difference involving neutral voltage: The delta element is not connected to neutral; it is strictly line-to-line. Common Pitfalls: Confusing Y relations (V_LL = √3 V_phase) with Δ branch conditions (branch = V_LL). Thinking a neutral affects the delta branch voltage—delta branches do not reference neutral. Final Answer: each phase of the load has the full line voltage across it

Question 2

Rotating vs stationary parts – What is the stator? Statement: “The stator is the rotating assembly in a generator or motor.” Determine whether this statement is correct.

Accepted Answer

Introduction / Context: Terminology in electric machines is foundational. Confusing stator and rotor leads to errors in analyzing windings, losses, and maintenance procedures. This question checks the correct identification of stationary versus rotating assemblies in motors and generators. Given Data / Assumptions: Applies to AC motors/generators (induction, synchronous) and DC machines. Standard construction: one stationary component and one rotating component. Focus is purely on definitions, not special configurations. Concept / Approach: Stator = stationary part that carries field or armature windings depending on machine type. Rotor = rotating part coupled to mechanical shaft. Therefore, the statement claiming the stator is the rotating assembly is false. Step-by-Step Solution: Identify parts: stator (static), rotor (rotating).In induction motors: stator has 3-phase windings; rotor may be squirrel-cage or wound.In synchronous machines: stator typically carries the armature; rotor carries DC field (via slip-rings) or permanent magnets.In DC machines: field/armature placements differ, but stator remains stationary. Verification / Alternative check: Maintenance and mounting evidence: stator frames are bolted to enclosures; rotors turn within bearings and are balanced to minimize vibration. Why Other Options Are Wrong: Any option asserting “True” (with or without qualifiers) contradicts basic machine nomenclature. Common Pitfalls: Assuming “stator” relates to “state of motion” ambiguously; remembering: “stator stays,” “rotor rotates.” Final Answer: False.

Question 3

Measuring three-phase power – Which instrument(s) are used? Statement: “Power is measured in a three-phase load by using an ammeter.” Choose the correct evaluation.

Accepted Answer

Introduction / Context: Accurate measurement of real power in three-phase circuits is critical for energy audits, motor testing, and tariffs. Knowing the correct instruments and methods prevents large errors that would arise from current-only measurements. Given Data / Assumptions: Three-phase, possibly unbalanced load, with sinusoidal voltages. Conventional measurement techniques apply (one-, two-, or three-wattmeter method). Goal: real power (not just current). Concept / Approach: Real power depends on voltage, current, and phase angle: P = √3 * VL * IL * cos(phi) for balanced three-phase systems. An ammeter measures only current magnitude. Real power requires wattmeters that sense both voltage and current with proper phase relation. Step-by-Step Solution: Balanced systems: use two-wattmeter method (or one wattmeter with appropriate switching for symmetrical loads).Unbalanced systems: use three-wattmeter method to capture each phase power and sum.Ammeter-only approach cannot account for voltage level or power factor, so it cannot yield true power. Verification / Alternative check: Compare computed power using only current against true wattmeter readings in a lagging power-factor load; discrepancies prove that current alone is insufficient. Why Other Options Are Wrong: Any qualified “True” still fails because even with known voltage, unknown power factor makes ammeter-only insufficient for real power. Common Pitfalls: Confusing apparent power (kVA) with real power (kW); overlooking unbalance and harmonic effects requiring appropriate instruments. Final Answer: False.

Question 4

Three-phase generator basics – Coil displacement Statement: “A simple three-phase generator consists of three conductive loops separated by 120°.” Is this correct?

Accepted Answer

Introduction / Context: Three-phase generation produces three sinusoidal voltages of equal magnitude and frequency, phase-displaced by 120°. Understanding physical coil placement illuminates why the phase displacement is 120° and underpins vector relationships of line and phase quantities in Y and Δ connections. Given Data / Assumptions: Three coils (or coil groups) placed in stator slots of an AC generator. Air-gap flux is approximately sinusoidally distributed. Mechanical arrangement achieves electrical displacement of 120° between phases. Concept / Approach: When three identical coils are placed 120° apart (electrical) and the rotor field sweeps past them, each coil experiences a sinusoidal EMF phase-shifted by 120°. This yields a balanced three-phase set, the foundation for efficient power generation and transmission. Step-by-Step Solution: Position phase-A, phase-B, phase-C coils with 120° electrical spacing.As the rotor field rotates, each coil's flux linkage shifts in time by 120°.Induced EMFs: Va = Vp∠0°, Vb = Vp∠−120°, Vc = Vp∠+120° (balanced set).Result: three-phase output suitable for Y or Δ connection. Verification / Alternative check: Phasor diagrams of a balanced generator show equal magnitudes separated by 120°. Slot/pole combinations in practical machines are chosen to approximate this geometry closely. Why Other Options Are Wrong: “False” or “60° separation” contradicts standard three-phase architecture. Δ versus Y affects terminal relationships, not internal coil spacing that sets phase displacement. Common Pitfalls: Confusing mechanical degrees with electrical degrees in fractional-slot designs; the fundamental remains a 120° electrical phase separation for three-phase sets. Final Answer: True.

Question 5

Two-phase generation – Orthogonal coil placement Statement: “A simple two-phase generator consists of two conductive loops separated by 90°, rotating in a magnetic field.” Evaluate this statement.

Accepted Answer

Introduction / Context: Before three-phase became dominant, two-phase systems (quadrature-phase) were used in early power and control applications. Understanding their geometry helps with quadrature signal generation used today in communications and motor control (e.g., rotating fields from orthogonal windings). Given Data / Assumptions: Two identical coils placed with electrical angle separation. Uniform rotating magnetic field provided by a rotor (field winding or permanent magnet). Goal: produce two sinusoidal voltages in time quadrature (90° apart). Concept / Approach: Two coils displaced by 90° electrical experience flux linkages that peak at times differing by a quarter cycle. The induced EMFs are equal in magnitude (ideally) and shifted by ±90°, forming a two-phase system suitable for certain motors and signal-processing tasks. Step-by-Step Solution: Place coil A and coil B with 90° electrical separation on the stator.Rotate the magnetic field past both coils; apply Faraday's law to each coil.Obtain Va = Vp∠0°, Vb = Vp∠−90° (or +90°).Result: orthogonal voltage set enabling a revolving magnetic field. Verification / Alternative check: Phasor representation shows perfect quadrature. In vector control of AC machines, similar orthogonal components (d–q axes) are synthesized electronically. Why Other Options Are Wrong: Requiring 120° is a three-phase property, not two-phase. Rotor type is irrelevant to the quadrature requirement; the electrical separation defines the phase relationship. Common Pitfalls: Mixing mechanical with electrical degrees in multi-pole machines; overlooking amplitude balance due to winding factors. Final Answer: True.

Question 6

Definition check – Polyphase systems Statement: “Polyphase is characterized by two or more sinusoidal voltages, each having a different phase angle.” Is this definition accurate?

Accepted Answer

Introduction / Context: Polyphase systems underpin modern power transmission and many rotating machines. A clear definition helps discriminate single-phase, two-phase, three-phase, and multiphase systems used in power and signal-processing contexts. Given Data / Assumptions: Sinusoidal voltages of the same frequency but with phase displacement. Amplitudes may be equal (balanced) or unequal (unbalanced). Two or more phases qualify as polyphase. Concept / Approach: Polyphase literally means “many phases.” Any system with two or more sinusoids of the same frequency that are phase-shifted relative to each other satisfies the definition. Common examples include two-phase (90°) and three-phase (120°) systems. Balance is desirable but not required by definition. Step-by-Step Solution: Identify number of phase voltages ≥ 2.Confirm same frequency and defined phase displacements.Conclude that such a set is polyphase whether balanced or not. Verification / Alternative check: Practical grids predominantly use three-phase due to constant power transfer and machine efficiency, but vector-control drives often synthesize multiphase sets (e.g., two-phase for control axes) that are still polyphase. Why Other Options Are Wrong: Requiring three phases only is too restrictive. Amplitude equality is not part of the definition; it pertains to “balanced” operation, not to being polyphase. Common Pitfalls: Confusing “polyphase” with “three-phase only,” or assuming unequal magnitudes disqualify a system from being polyphase. Final Answer: True.

Question 7

Y-connected generator phasors – Line vs phase voltage angles Statement: “In a Y-connected generator, there is a 120° difference between each line voltage and the nearest phase voltage.” Determine the correctness of this statement.

Accepted Answer

Introduction / Context: Understanding the phasor relationships between phase and line quantities in Y (wye) systems is essential for measurements and design. The phase angle between line and phase voltages is a common exam point that tests phasor geometry, not just magnitudes. Given Data / Assumptions: Balanced, three-phase, Y-connected generator. Phase voltages VaN, VbN, VcN are 120° apart and equal in magnitude. Line voltages Vab, Vbc, Vca are differences between phase voltages. Concept / Approach: In a balanced Y system, line voltage leads its corresponding phase voltage by 30° (not 120°). Magnitude relationship: |V_line| = √3 * |V_phase|. Angle relationship: each line-to-line voltage is the vector difference of two phase voltages and is shifted by ±30° relative to a phase voltage. Step-by-Step Solution: Let VaN = V∠0°, VbN = V∠−120°, VcN = V∠+120°.Compute Vab = VaN − VbN = √3V ∠+30°.Thus Vab leads VaN by 30°; similar results hold cyclically for Vbc and Vca.Therefore, the stated 120° difference is incorrect. Verification / Alternative check: Draw the phasor diagram to visualize the 30° lead/lag and the √3 magnitude factor. Measurements on a balanced Y-connected alternator corroborate this geometry. Why Other Options Are Wrong: Conditions like unbalance or power factor do not change the inherent phase relation between instantaneous line and phase voltages in the source; the 30° relation is geometric. Common Pitfalls: Confusing the 120° separation between phase voltages with the line-to-phase angle. Remember: 120° is between phases; 30° is between a line voltage and its nearest phase voltage. Final Answer: False.

Question 8

Machine types – What does “squirrel-cage” describe? Statement: “The term squirrel-cage applies to a type of three-phase AC generator.” Choose the best answer.

Accepted Answer

Introduction / Context: Machine nomenclature can be confusing across motors and generators. “Squirrel-cage” is a widely used term in industry and examinations. Correctly identifying where it applies helps avoid misinterpretations in specifications and maintenance manuals. Given Data / Assumptions: Standard AC machines: induction motors, synchronous machines, and alternators. “Squirrel-cage” refers to a specific rotor construction. Focus on whether it describes a generator type. Concept / Approach: “Squirrel-cage” describes the rotor of an induction motor: aluminum or copper bars shorted at both ends by end rings, resembling a cage. It is not a descriptor for alternators (AC generators). Alternators typically have a wound or permanent-magnet rotor and a three-phase stator; the term “squirrel-cage generator” is not standard terminology. Step-by-Step Solution: Identify that induction machines are predominantly motors with cage rotors.Alternators (synchronous generators) use DC-excited or PM rotors, not cage rotors as a classification.Therefore, the statement is false. Verification / Alternative check: Catalogs and datasheets label “squirrel-cage induction motors,” while generators are labeled “alternators” or “synchronous generators,” confirming standard usage. Why Other Options Are Wrong: Qualifiers about permanent magnets or single-phase do not transform the term into a generator descriptor. Common Pitfalls: Assuming any rotating electrical machine could be termed “squirrel-cage.” Keep the association strictly with induction motor rotor construction. Final Answer: False.

Question 9

Terminology check – What is an alternator? Statement: “An alternator is an electromechanical AC generator.” Indicate whether the statement is correct.

Accepted Answer

Introduction / Context: “Alternator” is a foundational term in power engineering and automotive systems. Knowing precisely what an alternator is—and is not—ensures clarity when discussing generation, rectification, and system integration. Given Data / Assumptions: An electromechanical device converts mechanical power to electrical power. Alternators produce alternating current at their terminals. External rectifiers may convert AC to DC for specific applications (e.g., vehicles). Concept / Approach: An alternator is a synchronous AC generator: a rotating field (DC-excited or permanent magnet) induces AC in stationary stator windings. While automotive alternators include rectifier bridges to supply DC to the battery, the machine itself generates AC, confirming the definition in the statement. Step-by-Step Solution: Rotor field rotates at synchronous speed.Stator windings intercept time-varying flux → AC EMF is induced.Terminal AC may be directly used or rectified for DC loads. Verification / Alternative check: Textbook classifications: DC generator vs. AC generator (alternator). Manufacturer datasheets refer to synchronous generators as alternators for AC output. Why Other Options Are Wrong: Claiming it produces DC conflates the machine with downstream rectification. Limiting to single-phase is wrong; alternators are commonly three-phase for power quality and efficiency. Common Pitfalls: Equating the electrical output after rectification (DC) with the machine type; always differentiate machine output from system-level conditioning. Final Answer: True.

Question 10

Three-Phase Circuits (Δ Connection): Line Current vs. Phase Current  In a delta-connected (Δ-connected) three-phase generator, it is claimed that there is a 120° phase difference between each line current and the nearest phase current. Decide whethe…

Accepted Answer

Introduction / Context: Understanding the phasor relationship between line and phase quantities in three-phase systems is essential for power calculations and fault analysis. In a delta (Δ) connection, the line current is related to the difference of two phase currents; this produces a characteristic magnitude scaling and a specific phase shift, not 120° as sometimes misconceived. Given Data / Assumptions: Balanced, sinusoidal three-phase source. Ideal Δ connection (line connected directly across each phase winding). Negligible line impedance for fundamental relationships. Concept / Approach: In Δ connection, each line is connected to the junction of two phase windings. The line current equals the phasor difference of the two phase currents meeting at that junction. This leads to a magnitude factor of √3 between line and phase currents and a phase displacement of 30°, not 120°. Step-by-Step Solution: Let I_phase be the current in a Δ branch; the three branch currents are separated by 120°.The line current I_line is the vector difference of two adjacent branch currents: I_line = I_phase(θ) − I_phase(θ − 120°).Phasor subtraction of two equal-magnitude vectors separated by 120° yields |I_line| = √3 * |I_phase|.The resulting I_line leads (or lags) the corresponding branch current by 30°, not 120°. Verification / Alternative check: Using standard three-phase relations: in Δ, V_line = V_phase; I_line = √3 * I_phase at a ±30° shift. Draw the phasor diagram for the three branch currents and compute their vector differences to confirm the 30° shift. Why Other Options Are Wrong: “True” contradicts the Δ phasor geometry. “True only for unbalanced loads” is incorrect; unbalance complicates angles but does not create a systematic 120° difference. “True only when power factor is zero” confuses load angle with the inherent topology. “Indeterminate without line impedance” is unnecessary for the ideal relationship. Common Pitfalls: Mixing Y and Δ results (in Y, line voltage is √3 times phase voltage with a 30° shift). Also, assuming the 120° phase separation of phase quantities carries to the line–phase relationship directly; it does not. Final Answer: False

Question 11

Definition Check: What Constitutes a Balanced Load?  Evaluate the statement: “A balanced load is one in which all the impedances are equal.”

Accepted Answer

Introduction / Context: Balance in three-phase systems simplifies analysis and maximizes efficiency. Recognizing the definition of a balanced load is foundational for applying per-phase equivalents and for predicting neutral currents and phase voltages accurately. Given Data / Assumptions: Three-phase system (Y or Δ), sinusoidal steady state. Per-phase impedances considered at the same frequency. Line impedances are neglected for the core definition. Concept / Approach: A load is balanced if the three impedances are equal in magnitude and phase angle (i.e., identical complex impedances). This ensures equal phase currents (for Y) or equal branch currents (for Δ) separated by 120° and results in symmetrical voltages and currents across phases. Step-by-Step Solution: Balanced condition: Z_A = Z_B = Z_C as complex quantities.For a Y load on a symmetrical source, equal impedances produce equal phase currents 120° apart.For a Δ load, equal branch impedances yield equal branch currents 120° apart; line currents are then √3 times branch currents with a ±30° shift.Neutral current in a Y system with equal impedances becomes zero due to phasor sum cancellation. Verification / Alternative check: Measure phase currents in a practical setup; equal magnitudes and 120° spacing confirm balance. Network analyzers or phasor calculations reaffirm that equal complex impedances create symmetrical currents. Why Other Options Are Wrong: Limiting balance to Δ or Y only is incorrect; balance applies in either connection. Power factor does not need to be unity; the impedances may be inductive or capacitive as long as all three are identical. Common Pitfalls: Assuming “equal magnitude only” is enough; the phase angle must also match. Different angles yield unbalanced reactive power even if magnitudes are equal. Final Answer: True

Three-Phase Systems in Power Applications Questions