Question 1

AC voltage control of a 3-phase induction motor using a 3-phase AC regulator For which load torque characteristic does stator-voltage control produce the largest speed variation?

Accepted Answer

Introduction / Context: Three-phase AC regulators vary the RMS stator voltage of induction motors, thereby modifying breakdown and rated torque approximately with V^2. The resulting operating speed depends on the intersection of the motor torque–slip curve and the load torque characteristic. Given Data / Assumptions: Standard squirrel-cage induction motor. Stator voltage control (not frequency control). Torque capability scales roughly as V^2 for a given slip region. Concept / Approach: When voltage is reduced, available motor torque drops quickly (∝ V^2). For a constant-torque load, maintaining the same torque requires substantially higher slip, which means a larger reduction in speed. For loads where torque rises with speed (e.g., positive viscous damping), the operating point tends to stabilize at a higher speed for a given voltage; for fan-type loads where torque decreases with speed, the required torque falls, so speed drop is smaller. Step-by-Step Solution: Reduce voltage → motor torque curve scales down with V^2.Constant-torque demand → intersection shifts to much higher slip → larger speed reduction.For torque ∝ speed or torque ∝ speed^2, the required torque reduces at lower speed → less shift needed → smaller variation. Verification / Alternative check: Plot approximate torque–slip curves under different voltages and superimpose constant versus speed-dependent load torques; the constant-torque case shows the greatest speed change. Why Other Options Are Wrong: (b) and (c): speed-dependent torques moderate the drop in speed when voltage is reduced. (d): only (a) gives the largest variation. Common Pitfalls: Assuming voltage control is an efficient speed control method for constant-torque loads—it is not. Final Answer: Load torque is constant (independent of speed)

Question 2

Cycloconverter commutation types Assertion (A): A cycloconverter may be line-commutated or forced-commutated. Reason (R): A step-up cycloconverter requires forced commutation.

Accepted Answer

Introduction / Context: Cycloconverters synthesize low-frequency AC directly from line AC using phase-controlled devices. Their commutation method (line versus forced) depends on the required output frequency and power factor demands. Given Data / Assumptions: Line-commutated (natural) commutation is standard for step-down frequency conversion. Forced commutation is possible using auxiliary circuits/transistorized switches. Step-up cycloconversion (f_out > f_in) cannot be realized with simple line commutation. Concept / Approach: Line commutation relies on natural current zeroes of the grid voltage and is suited to step-down operation. To achieve step-up or to control at times when the line does not naturally commutate, external commutation (forced) is required. Thus, cycloconverters may be built in either mode, and specifically the step-up type requires forced commutation. Step-by-Step Solution: Validate A: Both line-commutated and forced-commutated cycloconverters are used → A is true.Validate R: Step-up operation needs device turn-off independent of line zeros → forced commutation → R is true.Causality: R explains why one class (step-up) must be forced-commutated → adequately supports A. Verification / Alternative check: Drive textbooks distinguish step-down (line-commutated) vs step-up (forced-commutated) cycloconverters explicitly. Why Other Options Are Wrong: Saying R is not the explanation ignores the direct need for forced commutation in step-up conversion. Claiming R or A is wrong conflicts with established practice. Common Pitfalls: Confusing cycloconverters with matrix converters; the latter can synthesize wider frequency ranges with bidirectional switches. Final Answer: Both A and R are correct and R is correct explanation of A

Question 3

Modern HVDC converter pulse numbers Present-day line-commutated HVDC terminals most commonly use which converter configuration?

Accepted Answer

Introduction / Context: HVDC systems convert AC to DC (and back) using phase-controlled bridges. Pulse number determines characteristic harmonics and filtering requirements. Modern practice favors configurations that minimize AC and DC harmonics. Given Data / Assumptions: Line-commutated converter technology (thyristor LCC). Standard utility practice for harmonic mitigation. Concept / Approach: A 12-pulse converter is realized by series or parallel connection of two 6-pulse bridges fed by transformers with 30° phase shift. This cancels the lowest characteristic harmonics (5th and 7th on AC side), reducing filter size and improving power quality compared with a single 6-pulse bridge. Step-by-Step Solution: Assess harmonic content: 6-pulse → strong 5th/7th harmonics.Use phase-shifted pair → 12-pulse → cancels 5th/7th, leaving 11th/13th as lowest.Industry standardize on 12-pulse for bulk power HVDC terminals. Verification / Alternative check: Most classic HVDC schemes (e.g., monopole/bipole LCC) specify 12-pulse converter groups at each pole. Why Other Options Are Wrong: 3-pulse is obsolete. 6-pulse only has higher harmonic burden. “Either 6 or 12” is too broad; modern practice predominantly uses 12-pulse. 18-pulse is uncommon and complex at HVDC ratings. Common Pitfalls: Confusing with VSC-HVDC, which uses PWM converters rather than line-commutated bridges. Final Answer: 12-pulse converters

Question 4

Single-phase phase-controlled heater with firing angle α = 90° What fraction of maximum heating (power) is obtained at α = 90° for a purely resistive load?

Accepted Answer

Introduction / Context: Single-phase AC regulators control RMS voltage by delaying conduction each half-cycle. For a resistive heater, average power is proportional to the square of the RMS output voltage delivered to the element. Given Data / Assumptions: Purely resistive heater load. Firing angle α = 90° (π/2 radians). Supply is sinusoidal with RMS value V_rms. Concept / Approach: The RMS output voltage of a single-phase controller with R load is given by a standard expression involving α. The normalized power P/P_max equals (V_out,rms/V_rms)^2. Step-by-Step Solution: For R load, V_out,rms^2/V_rms^2 = (1/π) * (π − α) + (1/2π) * sin(2α).Insert α = π/2 → V_out,rms^2/V_rms^2 = (1/π)*(π − π/2) + (1/2π)*sin(π) = 1/2 + 0 = 0.5.Therefore power fraction P/P_max = 0.5 → 50% of maximum heating. Verification / Alternative check: At α = 0°, P/P_max = 1; at α = 90°, symmetry implies equal on/off areas → 50% power; at α → 180°, power tends to 0. Why Other Options Are Wrong: 25% and 75% contradict the analytical result 0.5. “None of the above” is incorrect because 50% is exact. Common Pitfalls: Confusing voltage fraction (≈0.707) with power fraction (square → 0.5). Final Answer: 50% of maximum

Question 5

Single-phase full bridge controlled rectifier (B-2) with resistive DC load For input v(t) = V_m sin(ωt), the average DC output voltage V_dc equals:

Accepted Answer

Introduction / Context: The single-phase full bridge controlled rectifier produces a controllable average DC voltage by delaying the firing of each thyristor pair by angle α. With a resistive DC load, conduction occurs over each half-cycle after firing, and the average can be computed by integrating the instantaneous output. Given Data / Assumptions: Full bridge (B-2) controlled rectifier. Input v(t) = V_m sin(ωt). Resistive DC load; commutation at natural current zeros. Concept / Approach: The instantaneous output is the line-to-line rectified segment selected by the fired devices. For symmetric firing at α in each half-cycle, the average over 0 to π for a resistive load yields the familiar expression V_dc = (2 V_m / π) cos α (valid for 0 ≤ α ≤ 90°; for larger α the average reduces accordingly and reaches zero at α = 90° for discontinuous conduction assumptions). Step-by-Step Solution: Compute average over a half-cycle: V_dc = (1/π) ∫{α}^{π} V_m sin(θ) dθ − (1/π) ∫{π+α}^{2π} V_m sin(θ) dθ.Symmetry results in V_dc = (2 V_m / π) cos α.Thus the mean DC output decreases with α and is maximum at α = 0°. Verification / Alternative check: For α = 0°, V_dc = 2 V_m / π (same as uncontrolled bridge). For α = 90°, V_dc ≈ 0, matching the integral. Why Other Options Are Wrong: (V_m/π)(1 + cos α) corresponds to a semi-converter, not a full bridge. “Independent of α” is incorrect for a controlled bridge. Zero for all α contradicts observed control. (2 V_m/π) is only for α = 0°. Common Pitfalls: Mixing semi-converter and full bridge formulas. Confusing RMS and average values. Final Answer: (2 V_m / π) cos α

Question 6

Thyristorized on-load tap changer (OLTC) capability “On-load tap changers using thyristors can have a maximum of only two taps.” Is this statement correct?

Accepted Answer

Introduction / Context: On-load tap changers (OLTCs) adjust transformer turns ratio under load to regulate voltage. Solid-state (thyristorized) OLTCs replace mechanical contacts with controlled switches, enabling fast, arcless commutation between taps. Given Data / Assumptions: Multiple discrete taps on the transformer winding. Thyristor pairs or bidirectional devices connect selected taps via transition schemes. Concept / Approach: There is no inherent limit of “two taps” with thyristor implementations. Designs can realize many taps (e.g., ±10% in 1.25% steps) by arranging switch matrices or using per-tap valve modules and appropriate interlocks/timing to avoid short-circuits between taps during transitions. Step-by-Step Solution: Identify claim: “maximum two taps”.Counter-example: commercial solid-state OLTCs routinely provide numerous taps.Conclusion: Statement is false. Verification / Alternative check: Product literature and utility specifications list many-tap solid-state voltage regulators and OLTCs. Why Other Options Are Wrong: Any “True” variants contradict practical systems with multiple taps. Connectivity (delta/wye) does not impose a two-tap maximum. Common Pitfalls: Confusing a minimal demonstrator (two taps) with real-world multi-tap OLTC capability. Final Answer: False

Question 7

Role of thyristors in controlled heating circuits In industrial heating controllers, thyristors most commonly function as which type of power-conversion element?

Accepted Answer

Introduction / Context: Industrial electric heating often uses resistive elements powered from AC mains. Power is controlled either by phase-angle control within each half-cycle or by integral-cycle (burst) control. Thyristors are well suited for both modes due to their high current capability and simplicity. Given Data / Assumptions: AC mains supply to a resistive heater. Target is to vary RMS voltage or duty on whole cycles. Concept / Approach: As AC regulators, antiparallel SCRs vary the portion of each half-cycle delivered (phase control) or gate entire blocks of cycles (integral-cycle). This directly modulates the effective RMS voltage across the heater, thus controlling power P = V_rms^2 / R without intermediate conversion stages. Step-by-Step Solution: Select topology: back-to-back SCRs on AC line.Choose control method: phase control (vary α) or integral-cycle (burst firing).Result: effective heater power adjusted smoothly from near 0% to ~100%. Verification / Alternative check: Commercial “thyristor power controllers” are marketed explicitly as AC regulators for heaters, ovens, and furnaces. Why Other Options Are Wrong: Rectifier/inverter/chopper imply DC conversion stages not required for simple AC heaters. Cycloconverter is used for low-frequency AC drives, not basic heater control. Common Pitfalls: Confusing DC heater supplies (where rectifiers or choppers may be used) with the far more common AC heater control. Final Answer: AC regulator (phase or integral-cycle control)

Question 8

Single-phase fully controlled bridge converter (R load) At what firing angles does a single-phase full converter (full-controlled bridge) produce its maximum average output voltage and its minimum (most negative) average output voltage?

Accepted Answer

Introduction / Context: This question tests understanding of how the firing angle controls the average DC output of a single-phase fully controlled bridge (full converter) feeding a resistive load. Knowing the cosine control law is essential for rectifier design, motor control, and power supply engineering. Given Data / Assumptions: Single-phase full-controlled bridge converter. Ideal thyristors and purely resistive load for clarity. Firing angle denoted by α (degrees). Concept / Approach: The average output voltage of a full converter is controlled by the firing angle as: Vdc_avg = (2 * Vm / π) * cos(α) where Vm is the peak of the supply phase voltage. The cosine term directly sets sign and magnitude of the average DC output. Step-by-Step Solution: For α = 0° → cos(0°) = 1 → Vdc_avg = maximum positive = 2Vm/π.For α = 180° → cos(180°) = −1 → Vdc_avg = minimum (most negative) = −2Vm/π.Between these limits, Vdc_avg varies smoothly with cos(α). Verification / Alternative check: Plotting Vdc_avg versus α shows a cosine curve with maximum at 0° and minimum at 180°. The sign reversal beyond 90° is consistent with inversion (power flow reversal) capability of a full converter. Why Other Options Are Wrong: 180° and 0° reverses the true order. Pairs involving 90° or 45° do not correspond to extrema of the cosine function; 90° gives zero average, not an extremum. Common Pitfalls: Confusing the full converter with a half-controlled converter (which cannot produce negative average V). Also mixing up RMS and average values leads to wrong conclusions. Final Answer: 0° and 180° respectively

Question 9

Shockley diode application in power electronics A Shockley diode (four-layer diode) is best used for which of the following purposes?

Accepted Answer

Introduction / Context: Shockley diodes are two-terminal four-layer devices exhibiting a negative-resistance region and snap-action switching. They are historically used in triggering circuits rather than as main controllable power switches. Understanding the correct use case prevents design errors in gate-drive and protection circuits. Given Data / Assumptions: Two-terminal, no gate control (unlike SCRs). Breakover behavior similar to a DIAC-like action (though different structures exist). Focus on practical triggering of SCRs or similar devices. Concept / Approach: An SCR requires a controlled gate current pulse to turn on at the intended instant. A Shockley diode can build up voltage across a timing capacitor and then snap to conduction at a predictable breakover voltage, providing a sharp current pulse to the gate of an SCR (or TRIAC with suitable interface). Step-by-Step Solution: Identify Shockley diode property: fixed breakover threshold and rapid conduction above it.Use this threshold to deliver a clean, sharp gate pulse to an SCR at a selected phase angle.Therefore, Shockley diode is a suitable trigger device, not a power switch replacement. Verification / Alternative check: Textbook gate-drive circuits for SCRs frequently show DIAC/Shockley-like elements as triggers in phase-controlled rectifiers and lamp dimmers (with proper ratings). Why Other Options Are Wrong: Not a replacement for SCRs (no gate terminal and poor controllability). Not a linear amplifier. Not universally a substitute for a UJT oscillator (different characteristics and adjustability). Common Pitfalls: Assuming any four-layer device is interchangeable with an SCR; ignoring the lack of a separate gate terminal leads to control issues. Final Answer: As a trigger switch to fire an SCR

Question 10

Single-phase dual converter: mode comparison Regarding the transient response when switching quadrants, which statement is true for a single-phase dual converter?

Accepted Answer

Introduction / Context: Dual converters provide reversible DC voltage (four-quadrant operation) by using two full converters connected back-to-back. Two common schemes are circulating-current and non-circulating-current modes, each with different dynamic behavior, losses, and filtering needs. Given Data / Assumptions: Two converters: one set for positive average voltage, the other for negative. Circulating-current mode: both converters operate simultaneously with a small current circulating through an interphase reactor. Non-circulating-current mode: converters operate alternately with dead-bands to avoid overlap. Concept / Approach: Fast quadrant reversal requires that the output current can switch sign quickly without waiting for stored energy to dissipate or device intervals to end. With circulating current, both converters are already active, and the control simply shifts firing angles to move from positive to negative output, giving faster response at the cost of additional circulating-current losses and larger reactor requirements. Step-by-Step Solution: In circulating mode, both bridges conduct; small adjustments in control lead to rapid voltage polarity reversal.In non-circulating mode, one bridge must be turned off completely before the other takes over → delay.Therefore, quadrant change is faster in circulating-current mode. Verification / Alternative check: Manufacturer application notes and textbooks consistently list dynamic response as a chief advantage of circulating-current dual converters. Why Other Options Are Wrong: Non-circulating mode has slower transitions due to dead-time. Equal response is not observed. Interphase reactor is needed in circulating mode but does not change the truth of the faster response claim. Common Pitfalls: Overlooking losses in circulating mode; confusing steady-state efficiency with transient speed. Final Answer: Quadrant change is faster in circulating current mode

Question 11

Parallel inverter topology (transformer-coupled) In a classic transformer-coupled parallel inverter, how are the commutating capacitor and the load connected?

Accepted Answer

Introduction / Context: Parallel inverters (often employing class-B type commutation) use a resonant commutating capacitor so current can naturally reverse and turn off the conducting thyristor. Transformer coupling is common to match the load and provide isolation. Given Data / Assumptions: Classic parallel inverter arrangement. Commutating capacitor used to produce resonant reversal of current. Transformer provides isolation and load matching; load is typically placed on the secondary. Concept / Approach: In the parallel inverter, the commutation is achieved via an LC path placed on the primary side so the thyristor current can be forced through zero. The load is commonly connected on the transformer secondary, allowing the resonant action to occur primarily on the primary side where the commutating elements reside. Step-by-Step Solution: Identify commutation requirement: create a resonant path to reverse current through the active device.Place the capacitor across the primary to participate directly in the device current loop.Connect the load on the secondary for isolation and appropriate voltage/current scaling. Verification / Alternative check: Standard power-electronics texts depict the commutating capacitor across the primary with secondary feeding the load in typical parallel inverter schematics. Why Other Options Are Wrong: Placing the capacitor solely on the secondary (or in series with the load) complicates or prevents proper commutation of the primary devices. The arrangement in (a) matches the classic design intent. Common Pitfalls: Confusing series and parallel inverter topologies; assuming commutating elements always sit with the load rather than with the switching devices. Final Answer: Capacitor across the transformer primary; load connected to the secondary

Question 12

Fully controlled bridge feeding a purely resistive load How do the output voltage and output current waveshapes compare in a fully controlled bridge converter with a purely resistive load?

Accepted Answer

Introduction / Context: For resistive (R) loads, voltage and current are in phase and proportional. In controlled rectifiers, this means the instantaneous current waveform directly tracks the instantaneous output voltage during conduction, which drives the answer to this question. Given Data / Assumptions: Fully controlled single-phase bridge. Purely resistive load (no L or C). Ideal switches; ignore commutation overlap. Concept / Approach: With R load, Ohm’s law applies instantaneously: i(t) = v(t) / R. Therefore, whenever the converter outputs a particular v(t), the current has exactly the same shape scaled by 1/R. Changes in firing angle α clip or shift voltage segments, and the current follows identically during conduction intervals. Step-by-Step Solution: Write i(t) = v(t)/R for all conducting intervals.No phase shift or energy storage exists to distort the current relative to the voltage.Hence, the two waveforms are geometrically similar (scaled by 1/R). Verification / Alternative check: Examining waveforms for various α values shows identical shapes where conduction occurs. At α ≥ 90°, the average becomes negative, yet i(t) continues to mirror v(t) during the fired periods. Why Other Options Are Wrong: Claims of dissimilarity arise when inductance is present; with pure R, similarity always holds. The special case α = 0° is not required for similarity; it applies for any α. Common Pitfalls: Confusing R loads with RL loads; in RL, current lags and waveforms are not similar, especially with freewheeling intervals. Final Answer: They are always similar in shape

Question 13

RC snubber across an SCR: statement and reason Assertion (A): A snubber circuit consists of an R–C series network connected in parallel with an SCR. Reason (R): The voltage across a capacitor cannot change instantaneously.

Accepted Answer

Introduction / Context: SCRs are sensitive to dv/dt. A snubber network (a series R–C connected across the thyristor) is widely used to control voltage transients and limit dv/dt, preventing inadvertent triggering and overstress during switching. Given Data / Assumptions: RC snubber connected across SCR terminals. Capacitor has the physical property that its voltage cannot change instantaneously. Resistor is included to damp oscillations and dissipate energy. Concept / Approach: The capacitor initially behaves as a short circuit to a sudden voltage step, thereby reducing dv/dt across the SCR. The resistor moderates peak currents and prevents sustained ringing. This directly follows from the fundamental property of capacitors and explains the topology of the snubber network. Step-by-Step Solution: Identify threat: high dv/dt across SCR can cause turn-on via displacement current.Place C across SCR → voltage cannot jump; dv/dt limited.Add R in series with C → control charging current and damp transients. Verification / Alternative check: Oscilloscope waveforms with and without snubbers show reduced overshoot and dv/dt. Application notes universally advocate RC snubbers for dv/dt control. Why Other Options Are Wrong: Given R states a core capacitor property that directly justifies the design in A; they are not independent facts. Common Pitfalls: Confusing snubbers with gate networks; overlooking that snubbers mainly protect against dv/dt and voltage spikes, not conduction failures. Final Answer: Both A and R are correct and R is the correct explanation of A

Question 14

Line-commutated AC–DC converters: commutation class Which commutation method (class) is associated with conventional AC–DC line-commutated converters (thyristor rectifiers)?

Accepted Answer

Introduction / Context: Thyristor rectifiers that are tied directly to the AC mains rely on the line voltage reversal to turn devices off. This form of natural commutation is categorized under a specific commutation class used in standard power-electronics nomenclature. Given Data / Assumptions: AC–DC converter without auxiliary resonant circuits. Thyristors are turned off by the AC supply going through current zero. Concept / Approach: In line commutation, the AC source itself provides the necessary current zero and reverse voltage to recover each thyristor. This is contrasted with load or auxiliary commutation that requires LC or forced circuits to achieve turn-off. Step-by-Step Solution: Identify commutation source: the line voltage and current zero crossings.Match to classification: Class F (line commutation). Verification / Alternative check: Standard converter classifications list line-commutated rectifiers under Class F, widely used in HVDC and industrial drives prior to widespread self-commutated devices. Why Other Options Are Wrong: Classes A, C, D, E all require specific LC or auxiliary switching, not natural line reversal. Thus they do not describe standard AC–DC mains commutation. Common Pitfalls: Confusing forced commutation (for DC–AC inverters or DC choppers) with natural, line-provided commutation. Final Answer: Class F (line commutation)

Question 15

Silicon Controlled Switch (SCS) terminations How many external leads (terminals) does a Silicon Controlled Switch (SCS) typically have?

Accepted Answer

Introduction / Context: A Silicon Controlled Switch (SCS) is a four-layer, four-junction device related to the SCR but with additional control terminals. Recognizing its terminals is important in legacy trigger and control circuits. Given Data / Assumptions: SCS has both anode and cathode gate controls. It is not as common today, but knowledge remains relevant for understanding thyristor families. Concept / Approach: Unlike an SCR, which has three terminals (anode, cathode, gate), an SCS typically adds a second gate terminal so that turn-on and turn-off can be controlled through gate actions at either polarity, yielding four external leads. Step-by-Step Solution: List terminals: Anode (A), Cathode (K), Anode Gate (AG), Cathode Gate (KG).Total count = 4 leads. Verification / Alternative check: Reference device datasheets and power electronics texts confirm the four-terminal structure and dual-gate control of SCS devices. Why Other Options Are Wrong: 2-lead implies a diode; 3-lead corresponds to SCR/triac; 5 or 6 leads are not used for SCS in standard practice. Common Pitfalls: Assuming all four-layer switches have only one gate; mixing up SCS with SCR or TRIAC terminal counts. Final Answer: 4 leads

Question 16

SCR terminal count (gate connections) How many gate terminals does a standard SCR (silicon controlled rectifier) have?

Accepted Answer

Introduction / Context: Terminal identification is basic but critical. An SCR is a three-terminal device: anode, cathode, and a single gate used to initiate conduction at the chosen firing angle. Given Data / Assumptions: Standard SCR structure (not SCS or TRIAC). Single gate that requires a trigger current pulse. Concept / Approach: To turn on an SCR in the forward-blocking state, a suitable gate current pulse is injected between gate and cathode. Only one gate terminal exists, and there is no additional control terminal like in SCS devices. Step-by-Step Solution: SCR terminals: A (anode), K (cathode), G (gate).Number of gates = 1. Verification / Alternative check: All SCR datasheets and symbols show a single gate lead. Multi-gate thyristor variants are different devices. Why Other Options Are Wrong: Options with 3, 4, or 6 gates are not applicable. A gate-less device would be a diode or Shockley diode, not an SCR. Common Pitfalls: Confusing SCR with TRIAC (still one gate) or SCS (two gates), or mixing total leads with number of gates. Final Answer: 1

Question 17

dv/dt triggering of a thyristor: assertion–reason Assertion (A): A high dv/dt across a thyristor can cause unintended triggering. Reason (R): A high dv/dt drives a displacement (charging) current through the device junctions and capacitances.

Accepted Answer

Introduction / Context: Thyristors contain junction capacitances. Rapid changes of voltage (high dv/dt) can force displacement currents that mimic gate-trigger current, inadvertently turning the device on. Protection against dv/dt is a fundamental aspect of gate and snubber design. Given Data / Assumptions: SCR in forward-blocking state. Non-zero junction capacitances are present. No intentional gate drive applied. Concept / Approach: Displacement current through a capacitance is i = C * dv/dt. If this current flows through the gate-cathode or internal junction path, it can exceed the latching threshold and cause turn-on even without a gate pulse. Step-by-Step Solution: High dv/dt → high iC = C * dv/dt through internal capacitances.This current can be equivalent to gate current → unintended triggering.Therefore, both the assertion and the reason are correct and causally linked. Verification / Alternative check: Datasheets specify maximum dv/dt ratings and recommend RC snubbers to limit dv/dt and avoid false turn-on. Why Other Options Are Wrong: It is not unrelated; the reason precisely explains the mechanism. Claims that the assertion is false contradict well-known thyristor behavior. Common Pitfalls: Neglecting layout-induced stray capacitances; assuming that only gate drive controls turn-on without recognizing dv/dt effects. Final Answer: Both A and R are correct and R is the correct explanation of A

Question 18

Power electronics – thermal design of SCR/thyristor A thyristor has a maximum allowable junction temperature of 110°C. The ambient (cooling air) temperature is 40°C. If the device's maximum internal power dissipation is 50 W, compute the required ov…

Accepted Answer

Introduction / Context: In power electronics thermal design, the allowable thermal resistance from junction to ambient determines whether a thyristor (SCR) can safely dissipate a specified power without exceeding its junction temperature limit. This governs the choice of heatsink and any interface materials. Given Data / Assumptions: Maximum junction temperature Tj,max = 110°C. Ambient temperature Ta = 40°C. Maximum internal power dissipation Pmax = 50 W. We assume steady state and that the single overall thermal resistance Rth,ja lumps junction–case, case–sink, and sink–ambient as required. Concept / Approach: The thermal analogy mirrors Ohm’s law: temperature rise equals power multiplied by thermal resistance. Hence, Rth,ja = (Tj,max − Ta) / Pmax. Keeping this value at or below the computed number ensures the junction does not exceed 110°C under 50 W dissipation. Step-by-Step Solution: Temperature rise ΔT = Tj,max − Ta = 110 − 40 = 70°CRth,ja = ΔT / Pmax = 70 / 50 °C/WRth,ja = 1.4 °C/W Verification / Alternative check: If you used a heatsink such that the measured temperature rise at 50 W is near 70°C, the device junction will be near its limit. Selecting a heatsink to achieve Rth,ja less than 1.4 °C/W adds safety margin. Why Other Options Are Wrong: 2.0 or 2.2 °C/W would allow a rise of about 100–110°C at 50 W, pushing Tj toward 140–150°C, which exceeds the limit. 0.7 °C/W is safe but not the minimum required; it implies extra margin beyond the calculation. Common Pitfalls: Ignoring interface resistances (thermal pad/grease) or using sink ratings without accounting for airflow can underpredict Rth,ja. Always include junction–case and case–sink contributions. Final Answer: 1.4° C/W

Question 19

Induction motor V/f control (constant flux) A 3-phase induction motor is controlled with constant V/f. At 50 Hz, its shaft speed is 1440 rpm. Estimate the expected speed at 25 Hz under similar load (assume slip percentage remains approximately the s…

Accepted Answer

Introduction / Context: With constant V/f (volts per hertz) control, an induction motor roughly maintains constant air-gap flux. For the same torque condition, the slip percentage tends to remain similar, so the speed scales mainly with synchronous speed, which is proportional to frequency. Given Data / Assumptions: Shaft speed at 50 Hz: 1440 rpm (typical of a 4-pole motor with Ns = 1500 rpm and about 4% slip). New frequency: 25 Hz (half of 50 Hz). Constant V/f, similar load → similar slip percentage. Neglect deep saturation and nonlinear effects. Concept / Approach: Synchronous speed Ns = 120 * f / P. Halving frequency halves Ns. If slip percentage s stays approximately the same, mechanical speed n ≈ (1 − s) * Ns at the new frequency, so it also halves approximately. Step-by-Step Solution: At 50 Hz with 4 poles: Ns,50 = 120 * 50 / 4 = 1500 rpmMeasured speed n50 = 1440 rpm → slip s ≈ (1500 − 1440) / 1500 = 0.04 (4%)At 25 Hz: Ns,25 = 120 * 25 / 4 = 750 rpmAssuming similar slip percentage: n25 ≈ (1 − 0.04) * 750 = 0.96 * 750 = 720 rpm Verification / Alternative check: Constant V/f keeps torque per ampere characteristics comparable; thus slip for the same load torque remains close, yielding half the original speed when frequency is halved. Why Other Options Are Wrong: 1350 rpm corresponds to near 50 Hz operation, not 25 Hz. 360 rpm suggests ~50% of 720 rpm, which would require doubled slip percentage under the same torque—unlikely with proper V/f. “Either (b) or (c)” undermines the physics; (b) is the consistent result. Common Pitfalls: Confusing synchronous speed scaling with load-dependent slip; treating slip as a fixed rpm rather than a percentage under V/f control. Final Answer: about 720 rpm

Question 20

Protecting an SCR against excessive di/dt (rate of rise of current) Which protective element is correctly used to limit di/dt through an SCR during turn-on in power circuits?

Accepted Answer

Introduction / Context: SCRs (thyristors) are sensitive to excessive di/dt during turn-on because conduction begins in a small area of the junction and must spread. High di/dt can cause localized overheating and device failure. Proper circuit elements are used to control both di/dt and dv/dt. Given Data / Assumptions: Focus is on limiting current rate of rise (di/dt) at turn-on. General power converter environment with inductive/resistive loads. Standard passive components available. Concept / Approach: Inductors inherently oppose changes in current (v = L * di/dt). Placing an inductor in series with the SCR limits di/dt. Capacitors influence dv/dt rather than di/dt; snubber capacitors and RC networks are for dv/dt and transient voltage control, not di/dt limiting through the device. Step-by-Step Solution: Identify the hazard: excessive di/dt near turn-on.Apply the inductor property: di/dt = v/L → larger L reduces di/dt for a given applied voltage.Thus, add a small series inductor (or leakage inductance) with the SCR. Verification / Alternative check: Manufacturer application notes specify series inductance or choke for di/dt protection and RC snubbers for dv/dt protection, confirming the choice. Why Other Options Are Wrong: Capacitors (series or parallel) primarily shape voltage transients (dv/dt), not the SCR’s current rise at turn-on. Parallel inductance does not limit device current; it offers an alternate path instead. Common Pitfalls: Mixing up di/dt and dv/dt protections; assuming an RC snubber addresses both equally well. Final Answer: an inductance in series with SCR

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