Question 1

For an inductor of fixed inductance L, what happens to the inductive reactance when the operating frequency is doubled (f → 2f)?

Accepted Answer

Introduction / Context: Inductive reactance governs how strongly an inductor impedes AC. Designers frequently assess how changes in frequency alter circuit impedances for filters and resonant networks. Given Data / Assumptions: Ideal inductor with inductance L. Steady-state sinusoidal operation. Frequency doubled from f to 2f. Concept / Approach: Inductive reactance is X_L = 2 * pi * f * L. If frequency doubles, X_L(2f) = 2 * pi * (2f) * L = 2 * (2 * pi * f * L) = 2 * X_L(f). Thus, reactance doubles when frequency doubles. Step-by-Step Solution: 1) Start with X_L = 2 * pi * f * L.2) Replace f with 2f.3) Simplify to obtain 2 * X_L. Verification / Alternative check: Numerical example: If X_L = 100 Ω at f, then at 2f it becomes 200 Ω, confirming the doubling behavior. Why Other Options Are Wrong: No effect / half: Contradict linear proportionality to f.Multiply by 6.28: 2 * pi is the proportionality constant, not the change factor for doubling f.None of the above: Not applicable because doubling is correct. Common Pitfalls: Mixing inductive with capacitive reactance (which halves when frequency doubles). Final Answer: doubles the amount of inductive reactance.

Question 2

Two ideal voltage sources are connected in series but in opposing polarity. If the sources are rated 6 V and 9 V, what is the resulting total source voltage across the series pair?

Accepted Answer

Introduction / Context: When voltage sources are placed in series, their net effect depends on whether they aid or oppose each other. Understanding polarity and series addition is a foundational DC circuit skill. Given Data / Assumptions: Two ideal sources: 6 V and 9 V. Series-opposing connection (polarities oppose). No internal resistance is considered for the sum. Concept / Approach: For series aiding, voltages add. For series opposing, the net is the difference, with the sign of the larger source. Thus, V_total = |9 V − 6 V| = 3 V, with polarity of the 9 V source prevailing. Step-by-Step Solution: 1) Identify opposing polarities.2) Compute magnitude: 9 − 6 = 3.3) Assign polarity of the larger source if needed; magnitude is 3 V. Verification / Alternative check: Kirchhoff’s Voltage Law around the loop confirms that opposing sources subtract, yielding 3 V across the pair. Why Other Options Are Wrong: 16 V: That is the series-aiding sum, not opposing.7.5 V or 8 V: Arbitrary averages; not based on polarity addition rules.None of the above: Incorrect because 3 V is correct. Common Pitfalls: Ignoring polarity marks on schematics or assuming all series sources always add; they subtract when placed in opposition. Final Answer: 3 V.

Question 3

Rule of thumb for a stiff (low-impedance) voltage source: given a load resistance of 1 kΩ, what approximate range should the source’s internal resistance fall into to behave “stiff” under load?

Accepted Answer

Introduction / Context: A voltage source is called “stiff” when its terminal voltage changes very little as the load varies. Practically, this requires the internal (source) resistance to be much smaller than the load. Designers use ratios to judge whether a source will hold its voltage within acceptable regulation limits. Given Data / Assumptions: Load resistance RL = 1 kΩ. We seek a rule-of-thumb range for source resistance Rs to act stiff. Small-signal linear model for source behavior. Concept / Approach: Voltage division dictates Vout = Vs * RL / (Rs + RL). To keep Vout near Vs, Rs must be much less than RL. A common heuristic is Rs ≤ 0.01 * RL (1%) to 0.1 * RL (10%), depending on required regulation. For RL = 1 kΩ, 0.01 * RL = 10 Ω and 0.1 * RL = 100 Ω. A stricter criterion (≤ 10 Ω) ensures very stiff behavior. Step-by-Step Solution: 1) Set RL = 1000 Ω.2) Choose a stiff criterion: Rs ≤ 1% of RL.3) Compute 1% of 1000 Ω → 10 Ω.4) Therefore, Rs less than 10 Ω qualifies as “stiff.” Verification / Alternative check: If Rs = 10 Ω and RL = 1000 Ω, Vout = Vs * 1000 / 1010 ≈ 0.990 * Vs (about 1% drop), which is excellent regulation for many applications. Why Other Options Are Wrong: At least 10 Ohm: The word “at least” weakens stiffness; we need less than about 10 Ω.More than 100 k Ohm / Less than 100 k Ohm: Not tied to RL; 100 kΩ is 100× RL, which is far from stiff.None of the above: Incorrect because “less than 10 Ohm” is a valid stiff criterion here. Common Pitfalls: Using absolute resistance numbers instead of ratios to load; ignoring the required regulation percentage for the application. Final Answer: less than 10 Ohm.

Question 4

In atomic and electrical terminology, what defines a positive ion? Choose the option that accurately describes the change in the atom’s charged particles.

Accepted Answer

Introduction / Context: Ionization refers to the process by which a neutral atom becomes charged by gaining or losing electrons. Positive and negative ions are foundational ideas in chemistry, physics, and electronics, affecting conduction in gases, electrolytes, and semiconductors. Given Data / Assumptions: Neutral atoms contain equal numbers of protons (positive) and electrons (negative). Ionization here involves electron transfer, not nuclear changes. Proton count remains fixed for a given element in typical electrical contexts. Concept / Approach: A positive ion (cation) results when an atom has fewer electrons than protons. Since electrons carry negative charge, removing one or more electrons leaves a net positive charge. Conversely, adding electrons produces a negative ion (anion). Nuclear changes to protons would alter elemental identity and are not considered in everyday electrical ionization. Step-by-Step Solution: 1) Start with a neutral atom: total positive charge from protons equals total negative charge from electrons.2) Remove one electron: negative charge decreases by 1 elementary charge.3) Net positive charge remains: the atom becomes a positive ion. Verification / Alternative check: Charge accounting: q = (+Z) + (−(Z − 1)) = +1 (in units of electron charge) after losing one electron, confirming a cation is formed. Why Other Options Are Wrong: Gained a proton / Lost a proton: Nuclear changes, not typical ionization for electrical contexts.Gained an electron: Produces a negative ion, not positive.None of the above: Incorrect because losing an electron is correct. Common Pitfalls: Confusing electron loss with proton loss; forgetting that it is the electron population that changes in ordinary ionization while the nucleus stays the same. Final Answer: Lost an electron.

Question 5

Inductive reactance calculation in AC circuits: What is the inductive reactance X_L of a 0.1 H coil operating at a frequency of 1000 Hz?

Accepted Answer

Introduction / Context: This problem tests your ability to compute inductive reactance in alternating-current (AC) circuit analysis. Inductive reactance expresses how strongly an inductor resists a change in current at a given frequency, and it grows with both inductance and frequency. Mastery of this concept is essential for filter design, impedance matching, and understanding current limits in AC systems. Given Data / Assumptions: Inductance L = 0.1 H. Frequency f = 1000 Hz. Assume an ideal inductor (no winding resistance, no core losses). Use standard formula for inductive reactance in ohms. Concept / Approach: The inductive reactance is calculated using X_L = 2 * pi * f * L. Because X_L is proportional to frequency, doubling f doubles X_L. This linear relationship is a cornerstone of frequency-domain circuit behavior for inductors. Step-by-Step Solution: Write the formula: X_L = 2 * pi * f * L.Insert values: X_L = 2 * pi * 1000 * 0.1.Simplify: 1000 * 0.1 = 100 → X_L = 2 * pi * 100 = 200 * pi.Numerical value: 200 * pi ≈ 200 * 3.1416 ≈ 628.32 ohms.Rounded to the nearest whole number: 628 Ohm. Verification / Alternative check: Quick estimation: 2 * 3.14 * 1000 * 0.1 = 628. Confirmed by calculator and back-of-the-envelope methods; both yield approximately 628 Ω. Why Other Options Are Wrong: (a) 100 Ω ignores the factor 2 * pi. (b) “Less than 1 Ω” contradicts the strong frequency dependence. (d) 444 Ω is an arbitrary miscalculation. (e) Incorrect since 628 Ω is attainable from the standard formula. Common Pitfalls: Dropping the factor of pi, mixing units (mH vs H), or using frequency in kHz without converting to Hz correctly can all lead to wrong answers. Final Answer: 628 Ohm.

Question 6

Household switching hardware identification: In typical residential wiring, which switch type is commonly used for a standard room light control?

Accepted Answer

Introduction / Context: Knowing common electromechanical components used in everyday installations helps connect theory to practice. Light switches in homes are designed for safety, reliability, and intuitive operation. Recognizing the typical switch mechanism is part of basic electrical literacy. Given Data / Assumptions: Standard wall-mounted switch for room lights in a typical residence. Conventional on/off control (not dimming, not smart/automated). Assume modern, code-compliant installations. Concept / Approach: The common wall switch used for on/off control is a toggle switch. The actuator lever toggles between two stable positions, maintaining state without continuous force. While specialized switches exist (rotary for fans, momentary for doorbells), the ubiquitous room light control is the toggle style. Step-by-Step Solution: Identify the use-case: simple on/off room lighting.Map to switch types: toggle (two-position, maintained), rotary (twist), momentary push button (spring return), knife (exposed, not residential).Select the most common residential device: toggle switch. Verification / Alternative check: Visual inspection of standard wall plates confirms a lever-style actuator with maintained positions. Electric codes and retail catalogs consistently list “toggle” as the default. Why Other Options Are Wrong: (a) Knife switches are large, exposed, and unsafe for residential interiors. (c) Rotary switches are used for multi-speed fans or special controls. (d) Momentary push buttons are used where action should occur only while pressed (e.g., doorbells). Common Pitfalls: Confusing decorator-style rockers with a different function. Even flat “rocker” wall switches are a subtype of maintained two-position switches serving the same purpose as toggles; functionally they are equivalent for this basic question. Final Answer: toggle switch.

Question 7

Energy conversion principle — thermal to electrical: Identify the device that directly converts a temperature difference into an electrical signal or voltage.

Accepted Answer

Introduction / Context: Transducers convert one form of energy to another. Recognizing which device maps a temperature gradient to an electrical output is crucial in instrumentation and control, where accurate measurements feed feedback loops and safety systems. Given Data / Assumptions: The question asks for direct thermal-to-electrical conversion. No external excitation beyond temperature difference is implied. Focus on the primary operating principle, not incidental effects. Concept / Approach: A thermocouple uses the Seebeck effect: when two dissimilar metals are joined and their junctions are at different temperatures, a voltage proportional to the temperature difference is produced. This is a direct thermal-to-electrical conversion and forms the basis for many industrial temperature sensors. Step-by-Step Solution: List candidates and their energy domains.Thermocouple → thermal gradient to voltage (Seebeck effect).Solar cell → light (photons) to electrical (photovoltaic effect).Chemical cell → chemical potential to electrical (electrochemistry).Piezoelectric → mechanical strain to electrical charge.Select the device that maps thermal to electrical directly: thermocouple. Verification / Alternative check: Thermocouples are standard in process industries and household appliances (e.g., gas furnaces) where measuring temperature via millivolt outputs is common. Why Other Options Are Wrong: (b) Photovoltaic devices are light-powered, not heat-powered. (c) Batteries convert chemical energy. (d) Piezo devices respond to pressure or vibration, not directly to temperature difference. Common Pitfalls: Confusing thermopiles (series thermocouples) with thermistors. Thermistors change resistance with temperature and require a measurement circuit; they do not directly generate a voltage from thermal gradients. Final Answer: thermocouple.

Question 8

Ideal transformer relationships — current calculation: A power transformer steps 100 V down to 10 V. If the primary current is 2 A, determine the secondary current (assume an ideal transformer).

Accepted Answer

Introduction / Context: Transformers trade voltage for current while conserving power (minus losses). Understanding the inverse relationship between voltage ratio and current ratio is essential for sizing conductors, fuses, and loads in power electronics and distribution. Given Data / Assumptions: Primary voltage V_p = 100 V. Secondary voltage V_s = 10 V. Primary current I_p = 2 A. Assume ideal transformer: P_in = P_out → V_p * I_p = V_s * I_s. Concept / Approach: For an ideal transformer, the current ratio is inverse of the voltage ratio: I_s / I_p = V_p / V_s. Use this to find I_s directly without needing turns counts explicitly. This reflects power conservation and magnetic coupling in the core. Step-by-Step Solution: Compute voltage ratio: V_p / V_s = 100 / 10 = 10.Relate currents: I_s = I_p * (V_p / V_s).Insert values: I_s = 2 A * 10 = 20 A.Therefore, the secondary current is 20 A (ideal case). Verification / Alternative check: Power check: P_in = 100 V * 2 A = 200 W. P_out = 10 V * 20 A = 200 W. Powers match, validating the calculation. Why Other Options Are Wrong: (a) 50 A overstates the inverse ratio. (b) 12 A misapplies ratios. (c) 5 A incorrectly uses a direct rather than inverse relationship. (e) Not applicable because 20 A is correct. Common Pitfalls: Forgetting the inverse relationship, or applying real-world efficiency (less than 100%) to an idealized question. Even with small losses, the result would remain close to 20 A. Final Answer: 20 A.

Question 9

Atomic bonding in conductors — copper valence electron: What is the relative strength of attraction between a copper atom’s single valence electron and its nucleus?

Accepted Answer

Introduction / Context: Electrical conductivity depends on how tightly outer electrons are bound to atoms. Copper is a premier conductor used in wiring and electronics. Understanding why hinges on the binding of its valence electron, which affects electron mobility and resistivity. Given Data / Assumptions: Element: copper (Cu), atomic number 29. Electronic configuration (simplified): [Ar] 3d^10 4s^1. We consider the effective nuclear attraction on the outermost (valence) electron. Concept / Approach: In metals like copper, the single 4s valence electron is relatively loosely bound due to shielding by inner electron shells and the metallic bonding environment. This weak attraction allows electrons to move freely under an electric field, producing high conductivity and low resistivity compared to semiconductors or insulators. Step-by-Step Solution: Recognize copper’s valence electron occupies a higher-energy shell (4s) shielded by filled inner shells.Effective nuclear charge on this electron is reduced by shielding, weakening attraction.In a metallic lattice, valence electrons form an electron “sea,” enabling easy drift motion.Therefore, the attraction is best described as weak compared to inner-shell electrons. Verification / Alternative check: Empirical data: copper’s low resistivity and high conductivity are consistent with a loosely bound valence electron, corroborating the conceptual explanation. Why Other Options Are Wrong: (a) Strong attraction contradicts copper’s excellent conductivity. (b) “Neutral” is not a meaningful descriptor of electrostatic attraction. (d) It is possible to infer; materials science and band theory support the weak-binding model. Common Pitfalls: Confusing atomic binding with lattice energy; assuming all outer electrons are tightly bound as in covalent solids (e.g., diamond). Final Answer: Weak.

Question 10

Series RC circuit fundamentals: Which statement correctly describes the current behavior throughout a series RC circuit driven by a single source?

Accepted Answer

Introduction / Context: Series and parallel circuit behaviors differ fundamentally. In series networks, the same current flows through each element because there is a single path. This question checks recognition of that principle in the context of a resistor-capacitor (RC) series circuit. Given Data / Assumptions: One source drives a series connection of R and C. Steady-state sinusoidal operation is implied. Ideal components (no parasitic branching). Concept / Approach: In a series circuit, Kirchhoff’s Current Law (KCL) implies the same current at every point along the single path. Voltages across R and C differ in amplitude and phase (V_R in phase with current, V_C lags current by 90 degrees), but the current itself is identical through each element. Step-by-Step Solution: Identify topology: series → single current path.Apply KCL: the current entering a series element equals the current leaving it.Conclude: I_R = I_C = I_total in amplitude and phase at any instant.Note: Only voltages split and phase-shift across elements. Verification / Alternative check: Phasor analysis: I is common, while V_R = I * R (in phase with I), and V_C = I * X_C (lags I by 90 degrees). Their vector sum equals the source voltage, confirming series behavior. Why Other Options Are Wrong: (b), (c), (d) all imply separate branch currents being summed, which describes parallel circuits, not series. Common Pitfalls: Mixing series and parallel concepts; assuming different instantaneous currents in reactive elements due to phase, which is incorrect in a single-path series network. Final Answer: The current always has the same amplitude and phase for every part of the circuit.

Question 11

Magnetism basics — identifying a magnet’s south pole: Which statement correctly describes the south-seeking pole of a bar magnet with respect to the Earth and other magnets?

Accepted Answer

Introduction / Context: This question complements the common discussion of a magnet’s north pole. Here we consider the south-seeking end. The Earth’s magnetic labeling can be confusing: near the geographic South, the planet behaves magnetically like a north pole, attracting a magnet’s south pole. Given Data / Assumptions: Standard bar magnet with defined north and south poles. “South pole” means the end that seeks geographic South. Earth’s geographic South corresponds to a magnetic north polarity region. Concept / Approach: Magnet interactions: unlike poles attract; like poles repel. The Earth’s geographic South is associated with a magnetic north region. Therefore, a magnet’s south pole will be attracted toward that area. Between magnets, a south pole attracts a north pole and repels another south pole. Step-by-Step Solution: Identify Earth’s effective polarities: geographic South ≈ magnetic north region.A magnet’s south pole is attracted to magnetic north.Hence, it is drawn toward the Earth’s north magnetic pole (near geographic South).Therefore, statement (a) is correct. Verification / Alternative check: Compass logic reversed: the south-seeking end points toward geographic South because it is attracted to magnetic north, confirming the polarity relationship. Why Other Options Are Wrong: (b) Random domain orientation describes a demagnetized material. (c) Attraction to Earth’s magnetic south would attract a magnet’s north, not its south. (d) A south pole is attracted to a north pole, not repelled. Common Pitfalls: Confusing geographic with magnetic labels; forgetting that attraction occurs between unlike poles. Final Answer: that would be attracted to the earths north magnetic pole.

Question 12

Thermodynamics reference point — absolute zero on Celsius scale: Choose the correct Celsius temperature that corresponds to absolute zero.

Accepted Answer

Introduction / Context: Absolute zero is the theoretical temperature at which particles have minimum thermal motion. It anchors the Kelvin scale and has a fixed conversion to Celsius. Understanding this value is fundamental in physics, cryogenics, and semiconductor behavior at low temperatures. Given Data / Assumptions: Absolute zero corresponds to 0 K on the Kelvin scale. Kelvin and Celsius scales have identical increments; they differ by an offset. Standard rounded conversion is requested. Concept / Approach: Use the conversion T_C = T_K − 273.15. Exact value is −273.15 °C; many basic multiple-choice contexts round to −273 °C. Recognize that 0 °C (freezing point of water) and 25 °C (room temperature) are far above absolute zero. Step-by-Step Solution: Start with absolute zero: T_K = 0.Convert to Celsius: T_C = 0 − 273.15 = −273.15 °C.Rounded choice closest to the exact value: −273 °C. Verification / Alternative check: Reverse conversion: −273.15 °C + 273.15 = 0 K. This confirms consistency between scales. Why Other Options Are Wrong: (a) 0 °C is the freezing point of water. (c) −276 °C is not the standard conversion. (d) 25 °C is ambient room temperature, not absolute zero. Common Pitfalls: Mixing −273 with −273.15; for scientific precision, keep two decimal places; for general MCQs, −273 °C is accepted. Final Answer: -273o C.

Question 13

Resistor color code interpretation: A resistor shows bands: red (1st), red (2nd), orange (multiplier), gold (tolerance). Determine its resistance value and tolerance.

Accepted Answer

Introduction / Context: Reading resistor color codes is a foundational lab skill. The first two bands encode significant figures, the third band is a power-of-ten multiplier, and the fourth band gives tolerance. Rapid decoding enables quick part identification and verification. Given Data / Assumptions: Band 1: red (digit 2). Band 2: red (digit 2). Band 3: orange (multiplier 10^3). Band 4: gold (tolerance ±5%). Concept / Approach: Use the standard 4-band code: value = (first digit * 10 + second digit) * 10^(multiplier). Tolerance is looked up from the fourth band. Ensure commas for readability when expressing thousands. Step-by-Step Solution: Form the base number: red-red → 22.Apply multiplier: orange → 10^3 → 1000.Compute resistance: 22 * 1000 = 22,000 ohms.Tolerance: gold → ±5%. Verification / Alternative check: Cross-check with standard tables or mnemonic (e.g., Black 0, Brown 1, Red 2, Orange 3, …; Gold ±5%). The interpretation is consistent. Why Other Options Are Wrong: (a) and (b) use 220 Ω, which would require a red-red-brown pattern. (d) Gives ±10% tolerance (silver), not gold. (e) Incorrect because a correct choice exists. Common Pitfalls: Confusing orange (3) with red (2), misreading gold vs silver tolerance, or misplacing the multiplier band order. Final Answer: 22,000 Ohm, 5%.

Question 14

Conventional current direction in basic circuit theory: By definition, conventional current flows in which direction relative to the polarity of a source?

Accepted Answer

Introduction / Context: Conventional current is a historical definition that treats current as the flow of positive charge from the positive terminal toward the negative terminal of a source. Although electrons physically move in the opposite direction in metallic conductors, the conventional definition is used universally in circuit analysis. Given Data / Assumptions: We use standard circuit-theory conventions. Metallic conduction is assumed (electron flow is opposite conventional current). No special semiconductor or ionic contexts override the convention. Concept / Approach: Conventional current direction was established before electron discovery. It simplifies sign conventions and remains embedded in textbooks, schematics, and engineering formulas. Therefore, current is considered to flow from a higher electric potential to a lower electric potential through an external circuit. Step-by-Step Solution: Identify the positive terminal as the point of higher potential.By convention, positive charge would leave the positive terminal, traverse the circuit, and return to the negative terminal.Thus, conventional current flows from positive to negative. Verification / Alternative check: Examine passive sign convention: power absorbed by a resistor is P = V * I when I enters the positive-labeled terminal. This aligns with current considered from positive to negative through passive elements. Why Other Options Are Wrong: (a) Describes electron flow, not conventional current. (c) “Left to right” is arbitrary and depends on drawing orientation. (d) “Neutral to positive” applies to AC distribution terminology, not the abstract direction of conventional current. Common Pitfalls: Interchanging electron flow and conventional current; forgetting that many device equations assume conventional current for sign consistency. Final Answer: from positive to negative.

Question 15

Automotive batteries: identify the correct cell type and classification used in common cars Choose the statement that best describes standard “auto” batteries found in passenger vehicles.

Accepted Answer

Introduction / Context: Understanding the type of battery used in cars is a fundamental concept in basic electrical engineering and automotive technology. “Primary” batteries are single-use cells, whereas “secondary” batteries are rechargeable. Most automotive starting, lighting, and ignition systems rely on rechargeable batteries, and the construction details (wet cell vs. dry cell) determine maintenance and safety considerations. Given Data / Assumptions: Typical passenger vehicles use lead–acid batteries. Lead–acid batteries are rechargeable, hence they are secondary cells. Traditional lead–acid automotive batteries contain liquid electrolyte (sulfuric acid solution), which classifies them as wet cells (even maintenance-free designs still contain liquid or absorbed electrolyte). Concept / Approach: Classify by two axes: rechargeability (primary vs. secondary) and electrolyte physical state (wet vs. dry). Combine both to determine the correct statement. Automotive batteries provide high cranking current, a hallmark of lead–acid chemistry with liquid electrolyte plates submerged in acid, designed for repeated charge–discharge cycles from the alternator. Step-by-Step Solution: 1) Identify chemistry: automotive batteries are lead–acid.2) Determine rechargeability: lead–acid auto batteries are rechargeable → secondary.3) Determine electrolyte form: conventional designs use liquid sulfuric acid → wet cell.4) Combine: secondary + wet cell → “secondary wet-cell batteries.” Verification / Alternative check: Automotive alternators continuously recharge the battery while the engine is running. This operational behavior confirms that the battery must be secondary (rechargeable). Service manuals and safety labels reference electrolyte handling and venting, consistent with wet-cell architecture (including AGM/VRLA variants, which are still lead–acid wet systems, though often absorbed). Why Other Options Are Wrong: Primary wet-cell or dry-cell types are not rechargeable and therefore unsuitable for automotive use. “Secondary dry-cell” usually refers to chemistries like NiMH or Li-ion in sealed formats, not standard car starter batteries. Common Pitfalls: Confusing “maintenance-free” with “dry-cell.” Maintenance-free lead–acid batteries still contain electrolyte; they are not dry primary cells. Final Answer: Auto batteries are secondary wet-cell batteries.

Question 16

Diode power calculation: for a 1N4001 with 0.93 V at 1 A forward current, compute power dissipation (P = V * I) Assume steady-state conduction and use basic electrical power relations.

Accepted Answer

Introduction / Context: Estimating power dissipation in semiconductor devices is essential for thermal management and reliability. A common rectifier diode such as the 1N4001 will drop a forward voltage when conducting. Multiplying the forward voltage by the forward current gives instantaneous power dissipated as heat in the junction, which must be within device and heatsinking limits. Given Data / Assumptions: Forward voltage Vf = 0.93 V. Forward current If = 1 A. Use P = V * I for electrical power. Assume DC or average values; ignore dynamic switching losses. Concept / Approach: The basic power relation is P = V * I. For a diode in forward conduction, power converts to heat in the junction. This calculation is the first step to check safe operating area against the diode’s datasheet (maximum average forward current, thermal resistance, and junction temperature limits). Step-by-Step Solution: 1) Identify formula: P = V * I.2) Substitute known values: P = 0.93 * 1.3) Compute numeric result: P = 0.93 W.4) Interpret: 0.93 W of heat must be dissipated; ensure ambient and package can handle it. Verification / Alternative check: Units check: volts * amperes = watts. If the current were pulsed with duty cycle D, average power would be D * (V * I_peak). Here the steady 1 A condition makes the simple product valid. Why Other Options Are Wrong: 0.93 V and 1 A are given parameters, not power. 9.3 W would require 10 A or 9.3 V at 1 A, which is not the case. “None of the above” is invalid since 0.93 W is correct. Common Pitfalls: Confusing peak with average values in rectified waveforms, or neglecting thermal derating, which can be critical even for seemingly small power levels. Final Answer: 0.93 W

Question 17

Transistor structure: how many distinct doped regions does a standard bipolar junction transistor (BJT) contain? Choose the most accurate count and relate it to the named terminals.

Accepted Answer

Introduction / Context: The bipolar junction transistor (BJT) is foundational in analog and digital electronics. Its physical construction directly influences operation, gain, and biasing. Knowing the number of doped regions helps connect device physics to practical terminal names and circuit models used in amplifiers and switches. Given Data / Assumptions: BJTs come in two polarities: NPN and PNP. Each BJT has three external terminals: emitter (E), base (B), collector (C). Each terminal corresponds to a distinct, intentionally doped semiconductor region. Concept / Approach: A BJT is formed by joining three doped regions in sequence: N–P–N or P–N–P. The central base region is thin and lightly doped; the emitter is heavily doped to inject carriers; the collector is moderately doped and physically designed to collect carriers and dissipate heat. Thus, the device consists of three distinct doped regions mapping to its three terminals. Step-by-Step Solution: 1) List terminals: emitter, base, collector.2) Map to structure: each terminal is a separate doped region.3) Count regions: 3 doped regions.4) Conclude: the correct answer is three. Verification / Alternative check: Device cross-sections in textbooks show layered doping profiles: for NPN, N+ emitter, thin P base, N collector. This visualization confirms the three-region structure. Why Other Options Are Wrong: One or two regions cannot form necessary PN junctions (a BJT needs two junctions). Four regions would describe devices like thyristors, not BJTs. Common Pitfalls: Confusing the BJT with a diode (two regions) or MOSFET structure (channel formation is different and controlled by a gate oxide, not a junction trio). Final Answer: 3

Question 18

Series RLC qualitative behavior below resonance: which simpler series circuit does it resemble when operating at frequencies lower than resonance? Assume ideal components and sinusoidal steady-state.

Accepted Answer

Introduction / Context: Series RLC circuits display different qualitative behaviors depending on frequency relative to resonance. Recognizing whether the circuit behaves more like RL or RC helps predict current phase, impedance magnitude, and filter characteristics without exhaustive mathematics. Given Data / Assumptions: Series connection of R, L, and C. Operating at ω below resonant frequency ω0. Idealized components to focus on reactance trends. Concept / Approach: Reactances: X_L = ωL (increases with frequency) and X_C = 1/(ωC) (decreases with frequency). Below resonance, ω is small, so X_L is relatively small, and X_C is relatively large. In a series sum X_total = R + j(X_L − X_C), the capacitive magnitude tends to dominate (X_C > X_L), yielding a net capacitive reactance. Thus, the circuit looks like a series RC (capacitive) network from a phase perspective (current leads voltage). Step-by-Step Solution: 1) Write reactances: X_L = ωL; X_C = 1/(ωC).2) Evaluate at ω < ω0: X_C is large; X_L is smaller.3) Net reactance: X = X_L − X_C is negative → capacitive behavior.4) A series network with dominant capacitive behavior resembles a series RC circuit. Verification / Alternative check: Bode plots of phase for a series RLC show phase leading below resonance, consistent with capacitive dominance. Above resonance, phase lags due to inductive dominance, confirming the mirror behavior. Why Other Options Are Wrong: Series RL corresponds to inductive dominance (true above resonance). “Purely resistive” occurs only at exact resonance in an ideal series RLC. Option C does not answer the “below resonance” case. Common Pitfalls: Mixing series and parallel intuitions; remember, series below resonance → capacitive, parallel below resonance → inductive. Final Answer: series RC circuit

Question 19

Capacitance unit equivalence: select the correct statement for 1 microfarad (1 µF) Express the value relative to picofarads, millifarads, or farads.

Accepted Answer

Introduction / Context: Working across unit prefixes is routine in electronics. From tiny picofarad capacitors in RF circuits to microfarad electrolytics in power supplies, it is vital to translate quickly among pF, nF, µF, mF, and F. This question checks your fluency with SI prefixes for capacitance. Given Data / Assumptions: 1 picofarad (pF) = 10^-12 farad. 1 microfarad (µF) = 10^-6 farad. 1 millifarad (mF) = 10^-3 farad. Concept / Approach: Convert 1 µF into pF by dividing 10^-6 by 10^-12 to get 10^6 pF. Also compare with mF and F to reject incorrect equivalences. Always track exponents carefully and remember that “micro” is six orders of magnitude larger than “pico.” Step-by-Step Solution: 1) Start with 1 µF = 10^-6 F.2) Convert to pF: 10^-6 F / 10^-12 F per pF = 10^(−6 − (−12)) = 10^6 pF.3) Therefore, 1 µF equals 1,000,000 pF.4) Cross-check against mF: 1 mF = 10^-3 F, so 1000 mF = 1 F, not 1 µF. Verification / Alternative check: Intermediate conversion: 1 µF = 1000 nF and 1 nF = 1000 pF. Multiplying 1000 * 1000 = 1,000,000 pF confirms the result. Why Other Options Are Wrong: “1 millionth of a picofarad” equals 10^-6 pF = 10^-18 F, far smaller than 1 µF. “1000 millifarads” is 1 F, much larger. “1 million farads” is astronomically larger and unrealistic for standard components. Common Pitfalls: Confusing milli (10^-3), micro (10^-6), nano (10^-9), and pico (10^-12). A quick mnemonic: m (−3) → µ (−6) → n (−9) → p (−12). Final Answer: 1 million picofarads

Question 20

Purely inductive AC circuit: what happens to current when the operating frequency is doubled? Assume constant applied voltage amplitude and ideal inductor behavior.

Accepted Answer

Introduction / Context: For sinusoidal steady-state analysis, an ideal inductor’s opposition to AC is captured by inductive reactance X_L. Designers need intuition about how current changes with frequency at fixed voltage to predict heating, magnetic fields, and resonance behavior in filters and power systems. Given Data / Assumptions: Ideal inductor L driven by a fixed-amplitude sinusoidal source. Inductive reactance X_L = 2 * pi * f * L. Linearity and no core saturation or resistance. Concept / Approach: Ohm’s law for AC magnitudes gives I = V / X_L for a purely inductive branch. Because X_L is proportional to frequency f, doubling f doubles X_L. Therefore, with the same applied voltage, current is inversely proportional to frequency and will be halved when f is doubled. Step-by-Step Solution: 1) Use X_L = 2 * pi * f * L.2) Double frequency: f → 2f → X_L(new) = 2 * pi * (2f) * L = 2 * X_L.3) Current relation: I = V / X_L → I(new) = V / (2 * X_L) = I / 2.4) Conclude: current is cut in half. Verification / Alternative check: Numerical example: V = 10 V, L = 100 mH. At 50 Hz, X_L ≈ 31.4 ohm → I ≈ 0.318 A. At 100 Hz, X_L ≈ 62.8 ohm → I ≈ 0.159 A, approximately half, confirming the proportionality. Why Other Options Are Wrong: “Doubles” contradicts inverse proportionality; “no effect” ignores X_L dependence; “requires complete analysis” is unnecessary because the ideal formula fully predicts the change. Common Pitfalls: Including winding resistance or core effects unintentionally; while real inductors have losses, the idealized relation still guides first-order design. Final Answer: cuts the current through the inductors one-half

Electronic Principles Questions