Q: Current source inverter (CSI) commutation A current source inverter is said to have a simple commutation circuit. Is this statement accurate?

Introduction / Context: Commutation refers to the process of transferring current from one device to another and turning devices off. Inverters can be broadly categorized as voltage source inverters (VSIs) and current source inverters (CSIs). Their commutation requirements differ significantly. Given Data / Assumptions: CSI maintains (approximately) constant DC current using a large series inductor. Turning off SCRs in a CSI generally requires complex forced-commutation networks or load-dependent commutation. Concept / Approach: In a VSI using self-commutated devices (e.g., IGBTs), commutation is relatively straightforward. A classic SCR-based CSI typically needs elaborate capacitor-based commutation (often dependent on load characteristics) to force device turn-off because current is nearly constant and cannot naturally drop to zero. Step-by-Step Solution: Identify commutation need: SCRs require current to fall below holding current to turn off.In a CSI, the large DC inductor impedes rapid current changes, making natural commutation difficult.Hence, specialized forced-commutation circuits are required → not “simple.” Verification / Alternative check: CSI topologies in textbooks show multiple capacitors and auxiliary thyristors/diodes to achieve reliable commutation under varying load conditions. Why Other Options Are Wrong: True: Misrepresents typical CSI practice; simplicity is more associated with modern VSIs using self-commutated switches. Common Pitfalls: Assuming the term “current source” implies easy turn-off. In fact, constant current is precisely what complicates SCR commutation. Final Answer: False

Q: Load current waveform in a full-bridge inverter In a single-phase full-bridge inverter, the shape of the load current primarily depends on which factor?

Introduction / Context: Inverters synthesize AC from DC by switching. The voltage output is decided by the switching pattern, but the current waveform is shaped by the load impedance seen by that voltage. Understanding this is fundamental for harmonic performance and filter design. Given Data / Assumptions: Full-bridge inverter producing a square or PWM voltage. Load may contain resistance (R), inductance (L), and capacitance (C). Concept / Approach: By Ohm’s and impedance laws, the current spectrum equals the applied voltage spectrum multiplied by the load transfer function 1/Z(jω). Therefore, the time-domain current waveform depends on the combined RLC impedance over the switching and fundamental frequencies. Step-by-Step Solution: Square/PWM voltage contains harmonics at multiples of the switching and fundamental frequencies.Compute Z(jω) for each harmonic given R, L, C.Current harmonics In = Vn / Z(jnω) → waveform follows RLC characteristics. Verification / Alternative check: SPICE simulations with different R, L, C values show notable changes in current shape even with identical gating patterns. Why Other Options Are Wrong: R–L or L–C only: Incomplete; R also affects damping and amplitude. Gating frequency only: Affects voltage spectrum but current depends on load impedance too. Common Pitfalls: Assuming current mirrors the voltage; in reactive loads, current leads or lags and can be smoothed significantly. Final Answer: relative values of load parameters R, L and C

Q: Power flow in the basic series inverter In the basic series inverter circuit (series RLC with commutating capacitor and two SCRs), the DC source supplies the load during which part(s) of the current cycle?

Introduction / Context: The basic series inverter converts DC to an AC-like current by alternately firing two SCRs, forcing a series RLC circuit to resonate. Understanding when the source actually delivers energy helps in component rating and efficiency analysis. Given Data / Assumptions: Series inverter with DC source, two SCRs (in opposite legs), commutating capacitor, and series RLC load. Idealized operation with proper commutation and sustained oscillatory current per half-cycle. Concept / Approach: When SCR1 conducts, the source applies one polarity to the RLC, producing a quasi-sinusoidal current (positive half-cycle). When SCR2 conducts, the bridge reverses the applied polarity, and the source again feeds the load (negative half-cycle). Although reactive elements exchange energy, the topology draws energy from the source during both conduction intervals. Step-by-Step Solution: Trigger SCR1 → source supplies RLC in one polarity → current rises and decays through resonance.Commutation via the capacitor turns SCR1 off and enables SCR2.Trigger SCR2 → source now supplies in opposite polarity → negative half-cycle load current is produced. Verification / Alternative check: Instantaneous input power waveforms show positive power pulses to the load in both half-cycles, despite reactive power cycling within R and C/L. Why Other Options Are Wrong: Only positive or only part cycles: Do not reflect the bidirectional application of the DC source via alternate SCRs in a full cycle. Common Pitfalls: Confusing energy return intervals (via commutation capacitors) with the absence of source delivery; in practice, each half-cycle involves source contribution when the respective SCR conducts. Final Answer: both in positive and negative half cycles

Q: Average DC output of a 3-phase fully controlled bridge A 3-phase fully controlled bridge converter is fed from a 3-phase source whose phase voltage is v = Vm sin(ωt). If the firing angle is α (radians), what is the average DC output voltage Vdc (ign…

Introduction / Context: The 3-phase fully controlled bridge (six-pulse) is a workhorse rectifier in drives and HVDC front-ends. Its average DC output depends on the firing angle α and the amplitude of the phase voltages. Given Data / Assumptions: Phase voltage given as v = Vm sin(ωt), so Vm is the peak value of the phase-to-neutral sinusoid. Ideal commutation (no overlap), balanced source. Concept / Approach: For a six-pulse converter expressed in terms of phase peak Vm, the average output with firing angle α is Vdc = (3 Vm / π) cos α. This follows from integrating the line-to-line segments that appear at the DC terminals during each 60° conduction interval and summing over one electrical cycle. Step-by-Step Solution: At α = 0 (natural commutation), the ideal average is Vdo = 3 Vm / π.Introducing delay α reduces the projection by cos α: Vdc = Vdo * cos α.Therefore, Vdc = (3 Vm / π) cos α. Verification / Alternative check: When phase voltage is specified by RMS value Vph(rms), an equivalent common form is Vdc = 2.34 Vph(rms) cos α. Rewriting with Vm = √2 Vph(rms) recovers (3 Vm / π) cos α. Why Other Options Are Wrong: (3√2 Vm / π) cos α: Double-counts √2; Vm here is already peak. Forms with (1 ± cos α): Not applicable to this rectifier’s average expression. Common Pitfalls: Mixing up whether Vm is phase peak, line peak, or RMS; always track the definition used in the problem statement. Final Answer: Vdc = (3 Vm / π) cos α

Q: Power delivered by a single-phase cycloconverter to a resistive heater In a cycloconverter feeding a pure resistance heating load, which spectral components of the output voltage contribute to real heating power?

Introduction / Context: Cycloconverters synthesize low-frequency AC by segmenting the line waveform. The output is non-sinusoidal and contains a fundamental plus harmonics. For a resistive heater, heating depends on RMS voltage across the element, not solely the fundamental component. Given Data / Assumptions: Resistive (pure R) heating element. Non-sinusoidal cycloconverter output with harmonics. No reactive energy exchange with the load. Concept / Approach: Real power in a resistor is P = V_rms^2 / R. If the voltage contains harmonics, the squared RMS includes contributions from each harmonic because V_rms^2 = Σ(Vn_rms^2) for orthogonal sinusoidal components. Therefore, both fundamental and harmonics raise the RMS and contribute to heating. Step-by-Step Solution: Express v(t) as sum of components: v(t) = Σ Vn sin(nωt + φn).Compute RMS: V_rms^2 = Σ Vn_rms^2 (cross-terms average to zero over cycles).Power: P = V_rms^2 / R → contributions from fundamental and all harmonics add.Hence, real heating is due to both fundamental and harmonic content. Verification / Alternative check: Measure temperature rise or power using a wattmeter on a distorted supply to a resistor; readings correlate with total RMS, not just the fundamental. Why Other Options Are Wrong: Only fundamental: ignores additional RMS from harmonics. Only harmonics: ignores the dominant fundamental contribution. Either-only choices are incomplete. Zero power: false for any nonzero RMS. Common Pitfalls: Confusing power factor issues (relevant with reactive loads) with pure resistance where all components dissipate power. Final Answer: both fundamental and higher harmonics in the output wave

Question 1

Freewheeling action in a 3-phase semiconverter For a 3-phase semiconverter feeding an R–L load with a freewheeling diode across the DC output, the freewheeling diode conducts when the firing angle α is:

Accepted Answer

Introduction / Context: Three-phase semiconverters (half-controlled bridges) often include a freewheeling diode (FWD) to provide a path for inductive load current when the converter’s instantaneous output voltage goes negative. The timing of freewheeling depends on the firing angle α and the phase voltages. Given Data / Assumptions: 3-phase semiconverter supplying an R–L load. Freewheeling diode connected across the DC side. Ideal, continuous current operation. Concept / Approach: In a semiconverter, the instantaneous converter output can become negative during certain intervals. If α is small (close to the natural commutation instant), the load current still needs a positive path; the FWD provides this by clamping the load voltage near zero and circulating current internally. As α increases, the negative portions shrink and beyond a threshold (≈60°) freewheeling ceases to be needed under ideal assumptions. Step-by-Step Solution: For α < 60°, intervals exist where the converter’s line-to-line selection would impose reverse voltage at the output.The FWD conducts during those intervals, maintaining current continuity and preventing negative output voltage across the inductive load.At α ≥ 60°, the converter’s selection keeps the output from going negative in the same way; freewheeling becomes unnecessary in the idealized analysis. Verification / Alternative check: Standard waveforms in power electronics texts show freewheeling conduction lobes for small α in semiconverters and vanishing FWD conduction beyond ≈60°. Why Other Options Are Wrong: Equal to / more than 60° / more than 90°: Opposite to the established condition. Zero only: Too restrictive; freewheeling exists for a range below 60°. Common Pitfalls: Assuming freewheeling is always present; it depends on α and the intersection of phase voltages. Final Answer: less than 60°

Question 2

Current source inverter (CSI) commutation A current source inverter is said to have a simple commutation circuit. Is this statement accurate?

Accepted Answer

Introduction / Context: Commutation refers to the process of transferring current from one device to another and turning devices off. Inverters can be broadly categorized as voltage source inverters (VSIs) and current source inverters (CSIs). Their commutation requirements differ significantly. Given Data / Assumptions: CSI maintains (approximately) constant DC current using a large series inductor. Turning off SCRs in a CSI generally requires complex forced-commutation networks or load-dependent commutation. Concept / Approach: In a VSI using self-commutated devices (e.g., IGBTs), commutation is relatively straightforward. A classic SCR-based CSI typically needs elaborate capacitor-based commutation (often dependent on load characteristics) to force device turn-off because current is nearly constant and cannot naturally drop to zero. Step-by-Step Solution: Identify commutation need: SCRs require current to fall below holding current to turn off.In a CSI, the large DC inductor impedes rapid current changes, making natural commutation difficult.Hence, specialized forced-commutation circuits are required → not “simple.” Verification / Alternative check: CSI topologies in textbooks show multiple capacitors and auxiliary thyristors/diodes to achieve reliable commutation under varying load conditions. Why Other Options Are Wrong: True: Misrepresents typical CSI practice; simplicity is more associated with modern VSIs using self-commutated switches. Common Pitfalls: Assuming the term “current source” implies easy turn-off. In fact, constant current is precisely what complicates SCR commutation. Final Answer: False

Question 3

Load current waveform in a full-bridge inverter In a single-phase full-bridge inverter, the shape of the load current primarily depends on which factor?

Accepted Answer

Introduction / Context: Inverters synthesize AC from DC by switching. The voltage output is decided by the switching pattern, but the current waveform is shaped by the load impedance seen by that voltage. Understanding this is fundamental for harmonic performance and filter design. Given Data / Assumptions: Full-bridge inverter producing a square or PWM voltage. Load may contain resistance (R), inductance (L), and capacitance (C). Concept / Approach: By Ohm’s and impedance laws, the current spectrum equals the applied voltage spectrum multiplied by the load transfer function 1/Z(jω). Therefore, the time-domain current waveform depends on the combined RLC impedance over the switching and fundamental frequencies. Step-by-Step Solution: Square/PWM voltage contains harmonics at multiples of the switching and fundamental frequencies.Compute Z(jω) for each harmonic given R, L, C.Current harmonics In = Vn / Z(jnω) → waveform follows RLC characteristics. Verification / Alternative check: SPICE simulations with different R, L, C values show notable changes in current shape even with identical gating patterns. Why Other Options Are Wrong: R–L or L–C only: Incomplete; R also affects damping and amplitude. Gating frequency only: Affects voltage spectrum but current depends on load impedance too. Common Pitfalls: Assuming current mirrors the voltage; in reactive loads, current leads or lags and can be smoothed significantly. Final Answer: relative values of load parameters R, L and C

Question 4

Power flow in the basic series inverter In the basic series inverter circuit (series RLC with commutating capacitor and two SCRs), the DC source supplies the load during which part(s) of the current cycle?

Accepted Answer

Introduction / Context: The basic series inverter converts DC to an AC-like current by alternately firing two SCRs, forcing a series RLC circuit to resonate. Understanding when the source actually delivers energy helps in component rating and efficiency analysis. Given Data / Assumptions: Series inverter with DC source, two SCRs (in opposite legs), commutating capacitor, and series RLC load. Idealized operation with proper commutation and sustained oscillatory current per half-cycle. Concept / Approach: When SCR1 conducts, the source applies one polarity to the RLC, producing a quasi-sinusoidal current (positive half-cycle). When SCR2 conducts, the bridge reverses the applied polarity, and the source again feeds the load (negative half-cycle). Although reactive elements exchange energy, the topology draws energy from the source during both conduction intervals. Step-by-Step Solution: Trigger SCR1 → source supplies RLC in one polarity → current rises and decays through resonance.Commutation via the capacitor turns SCR1 off and enables SCR2.Trigger SCR2 → source now supplies in opposite polarity → negative half-cycle load current is produced. Verification / Alternative check: Instantaneous input power waveforms show positive power pulses to the load in both half-cycles, despite reactive power cycling within R and C/L. Why Other Options Are Wrong: Only positive or only part cycles: Do not reflect the bidirectional application of the DC source via alternate SCRs in a full cycle. Common Pitfalls: Confusing energy return intervals (via commutation capacitors) with the absence of source delivery; in practice, each half-cycle involves source contribution when the respective SCR conducts. Final Answer: both in positive and negative half cycles

Question 5

Average DC output of a 3-phase fully controlled bridge A 3-phase fully controlled bridge converter is fed from a 3-phase source whose phase voltage is v = Vm sin(ωt). If the firing angle is α (radians), what is the average DC output voltage Vdc (ign…

Accepted Answer

Introduction / Context: The 3-phase fully controlled bridge (six-pulse) is a workhorse rectifier in drives and HVDC front-ends. Its average DC output depends on the firing angle α and the amplitude of the phase voltages. Given Data / Assumptions: Phase voltage given as v = Vm sin(ωt), so Vm is the peak value of the phase-to-neutral sinusoid. Ideal commutation (no overlap), balanced source. Concept / Approach: For a six-pulse converter expressed in terms of phase peak Vm, the average output with firing angle α is Vdc = (3 Vm / π) cos α. This follows from integrating the line-to-line segments that appear at the DC terminals during each 60° conduction interval and summing over one electrical cycle. Step-by-Step Solution: At α = 0 (natural commutation), the ideal average is Vdo = 3 Vm / π.Introducing delay α reduces the projection by cos α: Vdc = Vdo * cos α.Therefore, Vdc = (3 Vm / π) cos α. Verification / Alternative check: When phase voltage is specified by RMS value Vph(rms), an equivalent common form is Vdc = 2.34 Vph(rms) cos α. Rewriting with Vm = √2 Vph(rms) recovers (3 Vm / π) cos α. Why Other Options Are Wrong: (3√2 Vm / π) cos α: Double-counts √2; Vm here is already peak. Forms with (1 ± cos α): Not applicable to this rectifier’s average expression. Common Pitfalls: Mixing up whether Vm is phase peak, line peak, or RMS; always track the definition used in the problem statement. Final Answer: Vdc = (3 Vm / π) cos α

Question 6

Thyristor switching behavior in practice In an ordinary silicon controlled rectifier (SCR), how do the typical turn-on time and turn-off (recovery) time compare?

Accepted Answer

Introduction / Context: This question tests understanding of dynamic switching characteristics of a silicon controlled rectifier (SCR). In power electronics, the relative magnitudes of turn-on time (the time to establish conduction after a gate trigger) and turn-off time (the time required to regain forward blocking capability after current goes to zero) determine allowable firing schemes, commutation methods, and maximum operating frequency. Given Data / Assumptions: Ordinary line-commutated SCR (not a fast-switching GTO or IGCT). Conduction in the forward direction after proper gate triggering. Operation at line or low kHz frequencies typical of rectifiers and AC regulators. Concept / Approach: Turn-on involves carrier injection and spreading across the SCR structure. With adequate gate current, this process is rapid. Turn-off, however, requires removing stored charge from the device’s junctions and allowing minority carriers to recombine or be swept out. This recovery takes longer than turn-on, which is why ordinary SCRs are used mostly in line-commutated (natural commutation) systems where current naturally crosses zero each half-cycle. Step-by-Step Solution: Define t_on: time from gate pulse to full conduction.Define t_q (turn-off time): interval after current zero before the SCR can block forward voltage again.Physical reasoning: carrier removal and re-establishment of depletion regions take longer than carrier injection → t_q > t_on.Conclusion: turn-off time exceeds turn-on time. Verification / Alternative check: Typical data sheets show t_on in microseconds, whereas t_q is generally several tens of microseconds (or more) for standard devices, confirming the relationship. Why Other Options Are Wrong: Equal times: not supported by device physics or data sheets. Turn-on longer than turn-off: contradicts typical values. “May be equal/less/more”: too vague and not representative of standard SCRs. Turn-off time equals zero: impossible; recovery is always needed. Common Pitfalls: Confusing fast special devices (e.g., GTOs) with ordinary SCRs. Ignoring the impact of junction temperature and current on recovery time. Final Answer: turn off time is more than turn on time

Question 7

UJT peak-point condition with interbase bias A unijunction transistor (UJT) has an interbase voltage VBB applied. What is the emitter voltage at the peak point?

Accepted Answer

Introduction / Context: The UJT is widely used for triggering, relaxation oscillators, and timing circuits. Its operation hinges on the intrinsic standoff ratio, usually denoted by η (here shown as h), which sets the peak-point voltage at which the device switches into its negative-resistance region. Given Data / Assumptions: Interbase bias VBB is applied between B2 and B1. η (written as h in the options) is the intrinsic standoff ratio (0.5–0.8 typically). VD is the forward diode drop of the emitter junction (about 0.2–0.7 V depending on device). Concept / Approach: The well-known UJT peak-point relation is VP = η * VBB + VD. Physically, as the emitter voltage rises and equals the potential at the emitter junction plus the diode drop, the device conducts strongly and its dynamic resistance becomes negative, enabling sawtooth generation in relaxation circuits. Step-by-Step Solution: Write the peak-point formula: V_P = η * VBB + V_D.Identify symbols in options: η ≡ h; therefore V_P = hVBB + VD.Select matching option accordingly. Verification / Alternative check: Check a typical UJT datasheet or textbook: the same formula is quoted and used for design of timing networks. Why Other Options Are Wrong: hVBB omits the diode drop term. (h + 1) VBB is dimensionally incorrect and not standard. VD alone ignores the standoff partitioning. VBB − VD is unrelated to the internal resistive divider physics. Common Pitfalls: Assuming VD is negligible; it matters at low VBB values. Confusing η with a fixed 0.5; it varies by device. Final Answer: hVBB + VD

Question 8

Free-wheeling diode conduction in a rectifier A single-phase half-wave rectifier includes a free-wheeling diode. Under which load condition(s) will the free-wheeling diode conduct?

Accepted Answer

Introduction / Context: Free-wheeling (flyback) diodes are added to rectifiers feeding inductive loads to provide a path for the load current when the main rectifying device is reverse-biased. This protects components and smooths current, improving performance in drives and controlled rectifiers. Given Data / Assumptions: Single-phase half-wave rectifier topology. One additional diode connected across the load (polarity to conduct when source reverses). Load could be R, L, or R–L. Concept / Approach: Inductance resists sudden changes in current. When the input source voltage becomes negative (or the rectifier device turns off), the inductive energy forces current to continue in the same direction through an alternative path. The free-wheeling diode provides that low-loss path, clamping the load voltage and allowing current to decay safely. Step-by-Step Solution: Pure R load: current is in phase with voltage; when input reverses, current instantly goes to zero → free-wheeling diode has no role.L or R–L load: current lags input and cannot instantly stop at the moment the rectifier is reverse-biased → the free-wheeling diode conducts, circulating current through the load.Therefore, conduction occurs for purely inductive or R–L loads. Verification / Alternative check: Waveforms of an R–L rectifier show continuous or quasi-continuous current with a clamp at approximately one diode drop during the free-wheel interval. Why Other Options Are Wrong: Pure R: no energy storage → no need for a free-wheel path. Pure C: current leads voltage and free-wheeling diode is not the correct protection mechanism. R only or L only answers are incomplete. Common Pitfalls: Assuming free-wheeling reduces average output voltage in all cases; its main role is current continuity and device protection with inductive loads. Final Answer: load is purely inductive or combination of R and L

Question 9

Three-phase bridge inverter in 180° conduction mode At any instant in steady-state 180° conduction, how many thyristors conduct simultaneously?

Accepted Answer

Introduction / Context: In a six-step, three-phase bridge inverter, switching patterns define how many devices conduct at a time. The 180° conduction mode is a standard gating scheme where each device conducts for half a cycle, with overlaps forming line-to-line square-wave segments to the load. Given Data / Assumptions: Three-phase full bridge with six thyristors or transistors. 180° conduction per device; commutation every 60° electrical. Balanced three-phase load (usually star or delta connected). Concept / Approach: In 180° conduction, at any instant one device from the upper group and two devices from the lower group (or vice versa) conduct, producing three nonzero phase connections to the DC bus. The switching sequence ensures that exactly three devices conduct together, maintaining a nearly rectangular line-to-line voltage across the load phases. Step-by-Step Solution: Each device conducts for 180°, with turn-on events every 60°.Conduction sets: at each 60° interval, three devices share conduction (one from one leg and two from the other legs), keeping the current paths complete.Hence, the number of simultaneously conducting devices is 3. Verification / Alternative check: Standard six-step inverter timing tables (gating sequence A+, B−, C+, etc.) show three switches on at all times in 180° mode, confirming the count. Why Other Options Are Wrong: 1 or 2 devices cannot form all three phase connections. 4 or 6 devices would short parts of the DC bus or overconstrain paths in this mode. Common Pitfalls: Confusing 180° conduction with 120° conduction (where two devices conduct at a time). Final Answer: 3

Question 10

Empirical conduction law for a thyristor For a thyristor in forward conduction, the empirical relation i = k * v^a is sometimes used around the operating point. The approximate value of the exponent a is:

Accepted Answer

Introduction / Context: While a piecewise linear model (on-state drop plus dynamic resistance) is common for SCRs, some analyses use an empirical power law i = k * v^a in the conduction region to capture the nonlinearity of the PNPN structure near a given operating point. Given Data / Assumptions: Forward-conducting SCR after latching. Voltage v is the incremental on-state voltage above the knee. k is an empirical constant depending on device and temperature. Concept / Approach: In practice, the exponent a is near 2 in many thyristor conduction approximations, reflecting a moderately nonlinear current increase with voltage around the knee region. This offers a convenient analytical fit when precise device equations are not required. Step-by-Step Solution: Recognize that a < 1 would imply very weak nonlinearity (not typical).Very large a (e.g., 20) would indicate an extremely sharp rise, beyond practical ranges for averaged analysis.Empirical studies and texts frequently use a ≈ 2. Verification / Alternative check: Comparisons of i–v curves fitted around nominal operating currents show quadratic-like behavior in certain regions, supporting a ≈ 2 as a rough guide. Why Other Options Are Wrong: 0.5 or 1/3: too shallow a slope for an SCR in conduction. 5 or 20: unrealistically steep for typical power ranges (would be closer to a switching step than a conduction curve). Common Pitfalls: Treating the power law as universal; it is only a local fit around operating points and not a fundamental device law. Final Answer: about 2

Question 11

Power delivered by a single-phase cycloconverter to a resistive heater In a cycloconverter feeding a pure resistance heating load, which spectral components of the output voltage contribute to real heating power?

Accepted Answer

Introduction / Context: Cycloconverters synthesize low-frequency AC by segmenting the line waveform. The output is non-sinusoidal and contains a fundamental plus harmonics. For a resistive heater, heating depends on RMS voltage across the element, not solely the fundamental component. Given Data / Assumptions: Resistive (pure R) heating element. Non-sinusoidal cycloconverter output with harmonics. No reactive energy exchange with the load. Concept / Approach: Real power in a resistor is P = V_rms^2 / R. If the voltage contains harmonics, the squared RMS includes contributions from each harmonic because V_rms^2 = Σ(Vn_rms^2) for orthogonal sinusoidal components. Therefore, both fundamental and harmonics raise the RMS and contribute to heating. Step-by-Step Solution: Express v(t) as sum of components: v(t) = Σ Vn sin(nωt + φn).Compute RMS: V_rms^2 = Σ Vn_rms^2 (cross-terms average to zero over cycles).Power: P = V_rms^2 / R → contributions from fundamental and all harmonics add.Hence, real heating is due to both fundamental and harmonic content. Verification / Alternative check: Measure temperature rise or power using a wattmeter on a distorted supply to a resistor; readings correlate with total RMS, not just the fundamental. Why Other Options Are Wrong: Only fundamental: ignores additional RMS from harmonics. Only harmonics: ignores the dominant fundamental contribution. Either-only choices are incomplete. Zero power: false for any nonzero RMS. Common Pitfalls: Confusing power factor issues (relevant with reactive loads) with pure resistance where all components dissipate power. Final Answer: both fundamental and higher harmonics in the output wave

Question 12

Full-bridge inverter fed from 30 V DC battery If the inverter produces a 50% duty rectangular AC output of amplitude ±Vdc across a load, what is the output voltage RMS value?

Accepted Answer

Introduction / Context: A single-phase full-bridge inverter connected to a DC source ideally produces a square-wave AC output that toggles between +Vdc and −Vdc. For many introductory problems, the interest is in the RMS magnitude of this square wave. Given Data / Assumptions: DC input Vdc = 30 V. Ideal switches, 50% duty symmetric square wave. Load is such that the inverter maintains ±Vdc across it (e.g., stiff DC link, appropriate gating). Concept / Approach: The RMS of a bipolar square wave that alternates between +A and −A with equal durations is simply A. Unlike sine waves, there is no √2 relation here; that relation applies to sinusoidal waveforms (V_rms = V_peak/√2). For square waves of amplitude Vdc, V_rms = Vdc. Step-by-Step Solution: Define waveform: v(t) = +Vdc for half cycle, −Vdc for half cycle.Compute RMS: V_rms = √[(1/T) ∫_0^T v^2(t) dt] = √[(1/T)(Vdc^2 * T)] = Vdc.Insert Vdc = 30 V → V_rms = 30 V. Verification / Alternative check: Fourier series shows a fundamental of 4Vdc/π, but RMS of the full square wave remains Vdc because higher harmonics restore total mean-square value. Why Other Options Are Wrong: 15 V and 21.2 V apply to different duty or sinusoidal assumptions. 152 V and 302 V are nonsensical for a 30 V DC link. Common Pitfalls: Using sinusoidal conversion V_rms = V_peak/√2 incorrectly for a square wave. Final Answer: 30 V

Question 13

Devices with negative-resistance characteristics Which of the following devices exhibit a negative-resistance region in their I–V characteristics?

Accepted Answer

Introduction / Context: Negative-resistance devices are essential in relaxation oscillators and trigger circuits. A region of negative differential resistance means that as the voltage increases, current decreases (or vice versa), enabling oscillation and switching behaviors without complex active devices. Given Data / Assumptions: UJT: Unijunction transistor. PUT: Programmable unijunction transistor. SBS: Silicon bilateral switch. Concept / Approach: The UJT and PUT are classic devices used to create sawtooth waveforms and provide triggers due to their negative-resistance region after reaching the peak (for UJT) or firing point (for PUT). The SBS is a symmetrical, two-terminal device that similarly shows a breakover and negative-resistance characteristic used in triggering TRIACs and timing circuits. Step-by-Step Solution: UJT: exhibits peak and valley points with a negative slope between them → negative resistance present.PUT: programmable analog of UJT, also shows negative resistance after triggering.SBS: bilateral triggering device with a characteristic similar to a DIAC; negative-resistance region present.Hence all three listed devices exhibit negative resistance. Verification / Alternative check: Characteristic curves in component datasheets depict the peak/valley behavior leading to negative differential resistance regions. Why Other Options Are Wrong: Listing fewer devices ignores known behavior of the omitted component(s). “None” contradicts standard device physics. Common Pitfalls: Confusing negative differential resistance with simple threshold switching; the former is a slope property of the I–V curve. Final Answer: UJT, PUT and SBS

Question 14

Natural (line) commutation applicability Natural commutation of thyristors can be used effectively in:

Accepted Answer

Introduction / Context: Commutation refers to turning a thyristor off after it has latched on. Natural (line) commutation exploits the inherent current zero crossings in AC systems, allowing the device to recover its blocking ability without auxiliary circuits. Given Data / Assumptions: Thyristors are line-commutated devices in rectifiers and AC controllers. DC circuits do not have natural current zeros unless artificially created. Concept / Approach: In AC circuits, the sinusoidal source forces current through zero every half-cycle. If the thyristor current falls to zero and a reverse voltage is applied for the recovery interval, the SCR regains blocking capability automatically. In DC circuits, current does not reverse or go to zero by itself; forced commutation (capacitors, auxiliary switches) or natural load current interruption is required. Step-by-Step Solution: Identify requirement: current must go to zero and a reverse voltage must be applied for the turn-off time.AC satisfies this naturally each half-cycle → natural commutation works.DC lacks natural zeros → cannot rely on line commutation. Verification / Alternative check: Rectifier bridges and AC regulators using SCRs are line-commutated; DC choppers/inverters using SCRs require forced commutation schemes. Why Other Options Are Wrong: DC only: incorrect because no inherent zero-crossing exists. Both AC and DC: only true if DC has additional forced commutation, which is not “natural”. None: incorrect since AC clearly allows it. Common Pitfalls: Assuming current ripple in DC equals true zero-crossing; it does not guarantee recovery. Final Answer: AC circuits only

Question 15

Location of the gate connection in an SCR structure In a conventional thyristor, the external gate lead is bonded to which internal layer?

Accepted Answer

Introduction / Context: An SCR is a four-layer PNPN device with terminals anode, cathode, and gate. Understanding the internal structure clarifies why the gate effectively controls turn-on by injecting carriers into a specific junction region. Given Data / Assumptions: Layer sequence (from anode to cathode): P1–N1–P2–N2. Anode is connected to P1, cathode to N2. Gate terminal must effectively modulate the device near the cathode junction. Concept / Approach: The gate is bonded to the inner p-base region (P2), which is adjacent to the cathode (N2). A positive gate current (with respect to cathode) injects holes into this region, lowering the required anode-to-cathode voltage for turn-on and triggering regenerative action of the PNPN structure. Step-by-Step Solution: Identify controllable junction: J2 (between N1 and P2) is influenced by gate injection.Thus, the gate must contact P2, the p-layer nearest the cathode.Therefore, the correct internal layer for the gate bond is the p layer nearest to the cathode. Verification / Alternative check: Cross-sectional drawings of SCRs consistently show the gate metallization on the P2 region adjacent to the cathode emitter fingers. Why Other Options Are Wrong: Anode p-layer (P1) is not used for gate control. N-layer near anode or “outside n layer” does not yield the desired minority carrier injection into the correct junction. “Metal substrate only” is irrelevant to junction control. Common Pitfalls: Mistaking the external package pin locations for the internal diffused layer contacts. Final Answer: p layer nearest to the cathode terminal

Question 16

Chopper classification in power electronics Which chopper class (as per standard A–E classification) can operate in all four quadrants of the V–I plane, providing reversible voltage and reversible current (i.e., full four-quadrant operation)?

Accepted Answer

Introduction / Context: Four-quadrant DC–DC conversion is required in high-performance drives and bidirectional energy systems. The standard chopper classes (A to E) describe how voltage and current polarities can be controlled. This question asks which topology inherently supports operation in all four quadrants of the voltage–current plane. Given Data / Assumptions: Conventional chopper class definitions: A (first quadrant), B (second), C (I & II), D (I & IV), E (I, II, III, IV). Ideal switches and diodes are assumed to explain principle operation. Load can accept bidirectional current and voltage where applicable. Concept / Approach: To cover all four quadrants, the converter must be able to apply both polarities of average voltage to the load and allow current to flow in either direction, with controlled power flow in motoring and regenerating modes. The Class E chopper achieves this by combining switching legs and freewheel paths so that voltage and current direction can be independently set by gating patterns. Step-by-Step Solution: Class A: step-down, first quadrant only (V > 0, I > 0).Class B: step-up regenerating, second quadrant (V > 0, I < 0 through load).Class C: combination of A and B (first and second quadrants).Class D: bridge-type giving first and fourth quadrants (reversible voltage, current typically one direction).Class E: full bridge/bidirectional architecture enabling all four quadrants. Verification / Alternative check: Reviewing quadrant diagrams in standard power-electronics texts shows Class E as the only class covering I, II, III, and IV quadrants explicitly under controlled switching sequences. Why Other Options Are Wrong: Class A/B/C/D each miss at least one quadrant; they cannot independently reverse both voltage and current under control, hence not four-quadrant. Common Pitfalls: Confusing Class D (which reverses output voltage) with true four-quadrant capability; overlooking that current reversal under control is also necessary. Final Answer: Class E chopper

Question 17

HVDC transmission converters Which pulse-number converter is predominantly used in classic line-commutated high-voltage direct current (HVDC) transmission schemes?

Accepted Answer

Introduction / Context: In line-commutated HVDC, the converter topology and pulse number determine characteristic harmonics, filtering requirements, and performance. Utilities standardised on particular pulse numbers to reduce harmonics on both AC and DC sides while keeping station complexity manageable. Given Data / Assumptions: Traditional LCC (thyristor-based) HVDC systems. 12-pulse arrangements formed by two 6-pulse bridges with a 30° phase shift. Focus is on common practice, not rare specialised schemes. Concept / Approach: A 12-pulse converter cancels the lowest characteristic harmonics (notably the 5th and 7th on the AC side and the 6th on the DC side), substantially cutting filter size and losses compared with a single 6-pulse bridge. It is realised using a converter transformer with star/delta secondaries to achieve the requisite 30° phase displacement between the two 6-pulse bridges. Step-by-Step Solution: Identify desired harmonic mitigation → higher pulse number reduces characteristic harmonics.Compare 6-pulse vs 12-pulse → 12-pulse offers better harmonic performance with practical complexity.Industry practice → 12-pulse is the standard building block for LCC-HVDC terminals. Verification / Alternative check: Utility specifications and classic HVDC references cite the 12-pulse arrangement as the norm for thyristor-based terminals. Why Other Options Are Wrong: 3-pulse and 6-pulse have poor harmonic performance; 24-pulse exists but is complex and uncommon for full stations; 18-pulse is rare in HVDC LCC practice. Common Pitfalls: Assuming “more pulses is always better” without considering transformer design, cost, and practicality; in practice 12-pulse strikes the balance. Final Answer: 12-pulse converter

Question 18

Chopper commutation principle A DC–DC chopper cannot be line-commutated (natural commutation by AC line zero crossings). State whether this statement is true or false.

Accepted Answer

Introduction / Context: Commutation refers to how a power switch turns off. “Line commutation” uses the alternating supply voltage/current zero crossing, typical in AC line-commutated rectifiers. DC–DC choppers, however, operate from a DC source, so there is no natural line zero crossing to effect turn-off. Given Data / Assumptions: Input source for a chopper is DC. No inherent AC zero crossing is present. Switches are thyristors or self-commutated devices (IGBT/MOSFET) with forced turn-off control. Concept / Approach: Because the input is DC, a thyristor in a chopper cannot rely on line commutation. Either self-commutated devices (MOSFETs/IGBTs) are used, which turn off via gate control, or additional commutation circuits are provided to force current to zero (auxiliary/forced commutation for thyristor-based choppers). Step-by-Step Solution: Identify commutation method required for DC → forced/self commutation.Observe absence of AC line → line commutation impossible.Therefore, the statement is true. Verification / Alternative check: Power electronics texts classify choppers under forced/self-commutated converters, unlike LCC rectifiers which are line-commutated. Why Other Options Are Wrong: “False” contradicts the DC nature; qualifiers about class or frequency do not create AC zero crossings, so they are incorrect. Common Pitfalls: Confusing inverter/rectifier line commutation with DC chopper operation; assuming any oscillatory commutation equals line commutation. Final Answer: True

Question 19

SCR thermal path and heat sink material: assertion–reason Assertion (A): A typical overall thermal resistance from device source to heat sink for a power SCR can be about 0.3 °C/W (order of magnitude value with an adequate heat sink). Reason (R): He…

Accepted Answer

Introduction / Context: Thermal management of thyristors (SCRs) is critical to reliability. The thermal resistance chain includes junction-to-case, case-to-sink, and sink-to-ambient. Designers often quote order-of-magnitude values when sizing heat sinks and airflow. Aluminium is a standard heat sink material due to its excellent thermal properties per cost and weight. Given Data / Assumptions: Power SCR mounted on an appropriately sized aluminium heat sink with good interface (grease/insulator). “About 0.3 °C/W” treated as an indicative value achievable with a robust sink, not a universal constant. Aluminium heat sinks are commonplace in power converters. Concept / Approach: The assertion states an order-of-magnitude thermal resistance figure. Such a value is plausible for sizeable sinks and moderate airflow. The reason correctly states that aluminium is widely used, but the actual thermal resistance achieved depends on sink geometry, airflow, mounting, and interface materials—not merely the choice of aluminium. Therefore, while both statements are true, R does not fully explain the specific numerical value in A. Step-by-Step Solution: Recognise thermal path: R_th(j-c) + R_th(c-s) + R_th(s-a).Select large finned aluminium sink → low R_th(s-a), potentially around a few tenths °C/W.A is plausible as an indicative figure; R is true but only part of the story. Verification / Alternative check: Catalogues show aluminium sinks achieving 0.2–1.0 °C/W depending on size and airflow; junction/case/interface add to the total, reinforcing the “about” nature of A. Why Other Options Are Wrong: (a) Overstates the causal link; aluminium alone does not set 0.3 °C/W. (c) claims R is wrong, but it is correct. (d) would dismiss the plausible magnitude in A. (e) rejects both, which is not justified. Common Pitfalls: Treating thermal resistance numbers as constants; ignoring interface quality and airflow; assuming copper sinks are always necessary (aluminium is standard and economical). Final Answer: Both A and R are correct but R is not the correct explanation of A

Question 20

Integral-cycle control (on–off control) of AC regulators For integral-cycle control of an AC regulator, the control period (m + n)T should be chosen how, relative to the mechanical or thermal time constant of the load/system, to ensure smooth output?

Accepted Answer

Introduction / Context: Integral-cycle control (also called on–off or burst firing) applies whole cycles of AC to a load followed by whole cycles of no power. The average power is controlled by the duty ratio m/(m+n). To obtain a smooth process variable (speed, temperature), the modulation period must be short compared with the system’s response time. Given Data / Assumptions: (m + n)T is the burst period, with T = cycle time of mains. Load has a dominant mechanical or thermal time constant τ. Goal is to minimise ripple in the controlled variable. Concept / Approach: If the burst period is much shorter than τ, the load integrates (averages) the on/off power, yielding a nearly steady output. If the period is long compared with τ, the process variable will oscillate noticeably (hunting), which is undesirable for quality and component stress. Step-by-Step Solution: Model load as first-order system with time constant τ.Choose burst period P = (m+n)T such that P ≪ τ.Result: smooth temperature/speed with minimal ripple. Verification / Alternative check: Control engineering practice recommends carrier (modulation) frequency high enough that the plant cannot respond cycle-by-cycle; the same principle applies to burst firing on heaters and some motors. Why Other Options Are Wrong: Periods longer than τ cause visible cycling; “does not matter” is incorrect; exact equality is not a design requirement; “very high” in the sense of much larger than τ is the wrong direction. Common Pitfalls: Confusing electrical ripple with process ripple; assuming more cycles on at once is always better regardless of τ. Final Answer: Less than the mechanical or thermal time constant

Power Electronics Questions