Question 1

Using the definition of the volt from electromagnetic induction, the time required for one weber (1 Wb) of magnetic flux to cut a conductor and induce one volt (1 V) is equal to what duration?

Accepted Answer

Introduction / Context: The SI definition of the volt ties electrical potential to the rate of change of magnetic flux linkage. One volt equals one weber per second when induced by electromagnetic induction. This question checks recognition of that fundamental unit relationship. Given Data / Assumptions: Flux linkage is changing uniformly. Induced emf due to cutting or linking flux (Faraday’s law). Single-turn equivalence for simplicity. Concept / Approach: Faraday’s law (magnitude): emf = dΦ/dt for a single turn. If emf = 1 V and the total change in flux is 1 Wb, then the time required is t such that 1 V = 1 Wb / t, giving t = 1 s. Rotational “revolutions” do not directly define voltage unless related to flux change per unit time. Step-by-Step Solution: Set emf = 1 V.Let ΔΦ = 1 Wb over interval t.Then 1 = 1 / t → t = 1 s.Therefore, the required time is one second. Verification / Alternative check: In rotating machines, increasing speed reduces the time for a given flux change, increasing induced voltage proportionally—consistent with 1 V = 1 Wb/s as the base relationship. Why Other Options Are Wrong: Revolutions are mechanical counts, not time units; voltage depends on flux change rate, not merely turns. One millisecond or one minute contradicts the 1 Wb per 1 V requirement unless emf differs from 1 V. Common Pitfalls: Confusing webers (flux) with tesla (flux density) and seconds (time). Forgetting the turn count N scales emf; here we reference 1 turn equivalence for clarity. Final Answer: one second

Question 2

An ideal transformer has a 4:1 turns ratio (primary:secondary). If the measured input (primary) power is 5 W under load, what is the output (secondary) power delivered to the load (neglecting losses)?

Accepted Answer

Introduction / Context: For an ideal transformer, power in equals power out (P_in ≈ P_out), aside from small losses. While the turns ratio changes voltage and current levels, it does not create or destroy power. This question checks your understanding of power conservation across a transformer. Given Data / Assumptions: Turns ratio Np:Ns = 4:1. Measured primary (input) power = 5 W. Neglect core and copper losses (ideal device). Concept / Approach: Ideal transformer relations: V2/V1 = Ns/Np and I2/I1 = Np/Ns. Apparent power is conserved: P2 = V2 * I2 = V1 * I1 = P1. Therefore, the secondary power equals the primary power when losses are negligible. Step-by-Step Solution: Given P_primary = 5 W.Assuming ideal behavior: P_secondary = P_primary.Thus, P_secondary = 5 W. Verification / Alternative check: If the secondary voltage is V2 = V1 * (Ns/Np) = V1/4, then I2 = I1 * (Np/Ns) = 4 * I1. Multiplying gives V2 * I2 = (V1/4) * (4 * I1) = V1 * I1 = P1, confirming power equality independent of ratio. Why Other Options Are Wrong: 1.25 W or 20 mW: Incorrect scaling; power is not reduced by the turns ratio in an ideal transformer. 9.5 W: Would imply power gain without an external source—violates energy conservation. 1.25 pW: Physically nonsensical given the stated input power. Common Pitfalls: Mistaking voltage/current scaling for power scaling; turns ratio redistributes voltage and current while conserving power. Ignoring real-world losses; though small, they slightly reduce output below input in practice. Final Answer: 5.0 W

Question 3

Inductance unit check in circuit theory: If an inductor experiences a current change of 1 ampere per second and the induced voltage across it is 1 volt, this corresponds to which standard unit value?

Accepted Answer

Introduction / Context: When studying inductors in basic circuit theory, a key relationship is the voltage induced across an inductor due to a changing current. Identifying the correct unit from the voltage–current rate-of-change relationship helps cement the definition of the henry, the SI unit of inductance. Given Data / Assumptions: Induced voltage across the inductor: v = 1 V. Rate of change of current: di/dt = 1 A/s. Standard inductor behavior with linear inductance and no core saturation. Concept / Approach: The governing formula for an ideal inductor is v = L * di/dt. Rearranging gives L = v / (di/dt). Substituting the provided values immediately yields the inductance in henrys. The henry is defined so that 1 H produces 1 V when current changes at 1 A/s. Step-by-Step Solution: Start with v = L * di/dt.Solve for L: L = v / (di/dt).Insert values: L = 1 V / (1 A/s) = 1 H.Therefore, the condition describes exactly one henry of inductance. Verification / Alternative check: Dimensional analysis confirms consistency: volt = henry * ampere/second → henry = volt / (ampere/second) = voltsecond/ampere, which is the SI definition of 1 H. Why Other Options Are Wrong: a lenz: Not a unit; Lenz’s law states polarity of induced emf. an ohm: Unit of resistance; relates voltage and current directly (V = IR), not di/dt. a farad: Unit of capacitance defined by i = C * dv/dt, not v = L * di/dt. a weber: Unit of magnetic flux; not the unit for inductance. Common Pitfalls: Confusing the inductor formula with the capacitor formula and swapping roles of current and voltage derivatives. Mixing up henry with weber or tesla; those quantify flux and flux density, not inductance itself. Final Answer: a henry

Question 4

Definition in electromagnetics: What is electromagnetism in the context of a current-carrying conductor?

Accepted Answer

Introduction / Context: Electromagnetism connects electricity and magnetism. A foundational observation is that electric current flowing through a conductor produces a magnetic field encircling the wire. Recognizing this definition is essential for understanding motors, relays, inductors, and transmission lines. Given Data / Assumptions: Steady or time-varying current through a straight conductor. Classical field behavior (no quantum effects required for the concept). Right-hand rule applies to field direction around the conductor. Concept / Approach: By Ampere’s law and experimental evidence, a current I establishes a circumferential magnetic field H around the conductor. The field intensity is proportional to current and inversely related to distance from the wire. This effect underlies inductance and is different from induction caused by changing magnetic fields (Faraday’s law). Step-by-Step Solution: Identify the phenomenon: current → encircling magnetic field.Direction by right-hand rule: thumb points with current, curled fingers show field direction.Note the magnitude dependence: stronger current → stronger field.Recognize applications: electromagnets, solenoids, and magnetic actuators rely on this effect. Verification / Alternative check: Using a compass near a current-carrying wire demonstrates deflection that reverses with current direction, confirming the magnetic field produced by the current. Why Other Options Are Wrong: external voltage causing a magnetic field: Voltage alone does not create a magnetic field; current does. voltage caused by a magnetic field: That describes electromagnetic induction (emf) from changing flux, not the definition of electromagnetism here. current generated by an external magnetic field: That is induction again, requiring changing flux or motion. conversion of flux to heat: Not a definition; losses can cause heat but are not electromagnetism itself. Common Pitfalls: Confusing electromagnetism (field due to current) with electromagnetic induction (emf due to changing magnetic field). Ignoring field orientation; use the right-hand rule to avoid sign mistakes. Final Answer: the magnetic field generated around a conductor when a current passes through it

Question 5

Parallel inductors calculation: Two coils of 5 H and 100 mH are connected in parallel. What is the total equivalent inductance of the combination?

Accepted Answer

Introduction / Context: Combining inductors is common in filter design and energy storage networks. For inductors in parallel, the equivalent value decreases, analogously to parallel resistors. This question reinforces correct use of the parallel inductance formula and careful unit handling between henry and millihenry. Given Data / Assumptions: L1 = 5 H. L2 = 100 mH = 0.1 H. Coils are ideal and not magnetically coupled (no mutual inductance considered). Concept / Approach: For two uncoupled inductors in parallel, the equivalent inductance is L_eq = (L1 * L2) / (L1 + L2). This mirrors the product-over-sum form used for two resistors in parallel, but applies to inductors when mutual coupling is negligible. Step-by-Step Solution: Convert units: 100 mH = 0.1 H.Apply formula: L_eq = (5 * 0.1) / (5 + 0.1) H.Compute numerator: 0.5; denominator: 5.1 → L_eq = 0.5 / 5.1 ≈ 0.098039 H.Convert to mH: 0.098039 H ≈ 98.0 mH. Verification / Alternative check: Because one inductor (0.1 H) is much smaller than the other (5 H), the parallel combination should be slightly less than 0.1 H. The result 98 mH is consistent with this expectation. Why Other Options Are Wrong: 4.76 mH / 33.3 mH / 150.0 mH: Do not satisfy the parallel formula for the given values. 5.10 H: This is the series sum, not a parallel result. Common Pitfalls: Forgetting to convert millihenry to henry before calculation. Confusing series and parallel formulas or accidentally adding instead of using product-over-sum. Final Answer: 98.0 mH

Question 6

Faraday’s law — core idea: Faraday’s law primarily concerns which situation leading to an induced electromotive force (emf)?

Accepted Answer

Introduction / Context: Faraday’s law of electromagnetic induction explains how changing magnetic conditions produce an emf. This law underpins transformers, generators, and inductive sensors. Understanding the precise trigger for induction clarifies many practical designs. Given Data / Assumptions: Conductors or coils exposed to time-varying magnetic flux. Relative motion or changing field is present (dΦ/dt ≠ 0). Lenz’s law determines emf polarity opposing the change. Concept / Approach: Faraday’s law states that induced emf is proportional to the time rate of change of magnetic flux linkage. Practically, this occurs when a conductor cuts through magnetic field lines or when flux through a coil changes. The essential condition is changing flux linkage, commonly summarized as a magnetic field cutting a conductor (or equivalently, changing flux through a loop). Step-by-Step Solution: Identify mechanism: changing magnetic flux linkage → induced emf.Interpret “cutting a conductor”: relative motion of conductor and field or time-varying field causes changing linkage.Result: an emf and current (if closed path) are produced with polarity opposing the change (Lenz).Applications: generators, transformers, induction cookers, and pickup coils. Verification / Alternative check: Move a wire loop rapidly into or out of a magnetic field region; a measurable voltage appears only when the flux linkage changes, verifying Faraday’s law in practice. Why Other Options Are Wrong: a magnetic field in a coil / in a conductor: A static magnetic field with no change does not induce emf. hystersis: Misspelling of hysteresis; it concerns lagging magnetization and losses, not the induction condition. a static electric field: Not the Faraday induction mechanism. Common Pitfalls: Assuming a constant magnetic field is sufficient; the key is change in flux linkage. Confusing induction (emf due to changing flux) with electromagnetism (field due to current). Final Answer: a magnetic field cutting a conductor

Question 7

Electromagnetic induction – Core meaning of Faraday’s law Statement: “Faraday’s law states that relative motion between a magnetic field and a coil induces a voltage across the coil.”

Accepted Answer

Introduction / Context: Faraday’s law is fundamental to transformers, generators, and inductors. It relates induced electromotive force (emf) to the rate of change of magnetic flux linkage through a coil. This item checks your qualitative grasp of what causes induction. Given Data / Assumptions: We consider a coil with N turns linking magnetic flux. Either the magnetic field varies in time, or the coil moves relative to the field (or both). Idealized conditions suffice to judge the statement. Concept / Approach: Faraday’s law: induced emf e = − dλ/dt where λ = N*Φ is flux linkage. A nonzero emf arises when flux linkage changes with time. Relative motion between coil and magnetic field is one common cause of changing flux (generator action). Another cause is a time-varying field with a stationary coil (transformer action). The statement cites one valid cause—relative motion—which is consistent with the law, so it is true as worded. Step-by-Step Solution: Identify mechanism 1: Move the coil in a static magnetic field → flux through the coil area changes with time → e ≠ 0.Identify mechanism 2: Keep coil fixed but vary magnetic field with time (e.g., AC magnetization) → dΦ/dt ≠ 0 → e ≠ 0.General statement: any change in flux linkage (motion and/or time-varying field) induces emf per Faraday’s law. Verification / Alternative check: Practical examples include bicycle dynamos (motion-induced emf) and transformers (time-varying field-induced emf without motion). Why Other Options Are Wrong: “False unless flux is constant” contradicts the law—the emf requires changing, not constant, flux. Coil resistance does not determine whether emf is induced, only the resulting current if a closed path exists. Common Pitfalls: Thinking motion is required—transformers show that motion is not necessary; any dλ/dt suffices. Final Answer: True.

Question 8

Induction vs. steady sources – Does a dc source produce induced voltage? Statement: “An induced voltage is produced as a result of a dc voltage.”

Accepted Answer

Introduction / Context: Induced voltage (emf) arises from changing magnetic flux linkage. This question draws a line between steady dc conditions and the dynamic changes required for induction, which is crucial when reasoning about transformers and inductors. Given Data / Assumptions: “Induced voltage” refers to Faraday-law emf: e = − dλ/dt. “dc voltage” means a constant (time-invariant) source after transients have decayed. We consider ideal elements unless otherwise noted. Concept / Approach: A constant dc source produces constant currents and constant magnetic flux in steady state (ignoring saturation and temperature drift). Since dλ/dt = 0 in steady state, the induced emf is zero. Only when the current or flux changes—such as at the moment of switching on/off or during a ramp—does induction occur. Therefore, the statement as written (implying steady dc) is false. Step-by-Step Solution: 1) For t → ∞ with a dc source applied to an inductor, iL becomes constant.2) Magnetic flux Φ ∝ iL is constant → dΦ/dt = 0.3) Induced emf e = −N * dΦ/dt = 0.4) Only during changes (switching transients) does e briefly appear. Verification / Alternative check: Transformers do not pass dc: a constant primary current produces no time-varying flux in steady state, so no sustained secondary emf is induced. Why Other Options Are Wrong: “True” is incorrect in steady state. “True only if the dc source is very large” is irrelevant—magnitude does not substitute for d/dt. “True only during switching transients” is contextually right, but the statement under test lacks that qualifier; hence the correct evaluation is False. Common Pitfalls: Assuming “voltage causes induction” by itself; it is the time variation of flux linkage that matters. Final Answer: False.

Question 9

Definition check – What does inductance do? Statement: “Inductance is the property of an inductor that produces an opposition to any change in current.”

Accepted Answer

Introduction / Context: Inductance is a basic electromagnetic property central to filters, energy storage, and transient behavior. This item checks the textbook definition that relates inductance to opposition against current change (not against current itself—that is resistance). Given Data / Assumptions: Inductance L relates voltage and current by v = L * di/dt for ideal inductors. We consider both air-core and magnetic-core inductors. Circuits may be dc or ac; the statement concerns change in current. Concept / Approach: Because vL = L * di/dt, a nonzero voltage appears across an inductor only when current changes with time. This induced voltage resists the change (Lenz’s law). In dc steady state (di/dt = 0), an ideal inductor behaves as a short, indicating no opposition to constant current—only to its change. Hence the statement matches the formal definition and is true. Step-by-Step Solution: 1) Write the inductor constitutive relation: vL = L * di/dt.2) If current attempts to increase, vL polarizes to oppose the increase; if current attempts to decrease, vL flips polarity to oppose the decrease.3) In steady dc (di/dt = 0), vL = 0 → no opposition to constant current. Verification / Alternative check: Transient tests show exponential current rise i(t) = Ifinal*(1 − e^(−t/τ)) in RL circuits, evidence of inductive opposition to change characterized by time constant τ = L/R. Why Other Options Are Wrong: “False” contradicts the constitutive law. “True only for ac circuits” ignores dc transients. “True only with magnetic cores” is incorrect since air-core inductors also have inductance. Common Pitfalls: Confusing inductance with resistance or reactance; forgetting that opposition is to change (di/dt), not to the steady value of current. Final Answer: True.

Question 10

Inductive Reactance: Relationship of XL with Frequency and Inductance  In AC circuit analysis, the inductive reactance XL of an inductor is said to vary with the signal frequency and with the inductance value. Evaluate the statement: “XL is directly…

Accepted Answer

Introduction / Context: Inductive reactance is a cornerstone concept in AC circuit theory. It quantifies how strongly an inductor resists changes in alternating current. The statement under review claims that inductive reactance depends linearly on both the excitation frequency and the inductance value. Understanding this helps with filter design, impedance matching, and predicting current draw in power electronics and signal-processing applications. Given Data / Assumptions: An ideal inductor with inductance L (henry). A sinusoidal source with frequency f (hertz). Steady-state AC conditions (phasor analysis). No core nonlinearity, parasitics, or saturation effects considered. Concept / Approach: For an ideal inductor, the voltage-current relation in the time domain is v(t) = L * di/dt. In sinusoidal steady state, the phasor form relates voltage and current by an imaginary impedance jXL, where XL is the inductive reactance. By definition, XL rises with frequency because faster current changes induce larger opposing voltages. It also scales directly with L because a larger inductance produces a larger induced voltage for the same rate of current change. Step-by-Step Solution: Start from v(t) = L * di/dt for a sinusoidal current i(t) = I_max * sin(2π f t).Differentiate: di/dt = I_max * 2π f * cos(2π f t).Thus v(t) = L * 2π f * I_max * cos(2π f t).In phasor form, V = j 2π f L * I, so the impedance Z_L = j XL with XL = 2π f L.Therefore XL is directly proportional to f and to L (linear dependence). Verification / Alternative check: Units confirm consistency: L has units of henry, and f is in hertz. Multiplying 2π f L yields ohms (Ω), the correct unit of reactance. Experimental Bode plots show a +20 dB/decade rise of |Z_L| with frequency for an ideal inductor, aligning with XL ∝ f. Why Other Options Are Wrong: “False” contradicts the standard formula XL = 2π f L. “True only at resonance” is irrelevant; resonance concerns LC combinations, not a lone inductor. “Depends only on core material” ignores frequency dependence. “True only for DC” is incorrect because XL at DC (f = 0) is 0 Ω, not meaningful for proportionality claims. Common Pitfalls: Confusing reactance XL with resistance R, or misapplying the formula to non-sinusoidal signals without proper harmonic analysis. Real inductors also have winding resistance and parasitic capacitance that modify behavior at high frequency, but the first-order relationship XL = 2π f L remains fundamental. Final Answer: True

Question 11

Inductance Dependence on Geometry and Material  Assess the statement: “Inductance is indirectly (inversely) proportional to the square of the number of turns, the permeability, and the core cross-sectional area.”

Accepted Answer

Introduction / Context: Coil inductance depends on physical geometry and magnetic properties. Designers adjust turns, core area, path length, and permeability to set target inductance in chokes, filters, resonators, and transformers. This item challenges a common misconception about the direction of proportionality. Given Data / Assumptions: Solenoidal coil approximation with uniform core. Magnetic path length l, cross-sectional area A, relative permeability μ_r, vacuum permeability μ_0, number of turns N. Linear, unsaturated magnetic material (no hysteresis nonlinearity considered). Concept / Approach: For a typical coil, an approximate formula is L ∝ μ * N^2 * A / l, where μ = μ_0 * μ_r. That is, inductance increases with the square of turns, increases with permeability, increases with cross-sectional area, and decreases with magnetic path length. The prompt claims the opposite sign (indirectly proportional) with respect to N^2, μ, and A, which is incorrect. Step-by-Step Solution: Use the standard proportionality: L ∝ μ * N^2 * A / l.Holding l fixed, increasing N raises L quadratically (double N → four times L).Increasing μ_r (better magnetic coupling) increases L proportionally.Increasing core area A increases L proportionally by reducing reluctance.Therefore, L is directly (not inversely) proportional to N^2, μ, and A. Verification / Alternative check: Magnetic circuit analogy: Reluctance ℜ = l / (μ A). Inductance L = N^2 / ℜ = μ N^2 A / l. Physical intuition agrees: more turns or higher permeability gives stronger flux linkage for the same current, producing higher inductance. Why Other Options Are Wrong: “True”, “True only for air-core”, and “True only at very high frequency” contradict the governing proportionality. “Indeterminate without wire gauge” is irrelevant to the fundamental geometric/material dependence (wire gauge mainly affects resistance and current handling, not the primary L proportionality in first order). Common Pitfalls: Confusing inductance L with stored energy or with copper loss. Also, mixing up the inverse proportionality to path length l with the direct proportionalities to N^2, μ, and A leads to errors in preliminary designs. Final Answer: False

Question 12

Meaning of Permeability (μ) in Magnetic Materials  Evaluate the statement: “The permeability of a core material indicates the ability of the material to establish (support) a magnetic field.”

Accepted Answer

Introduction / Context: Permeability (μ) is fundamental in electromagnetics and magnetic circuit design. It influences inductance, transformer behavior, and the confinement of magnetic flux. This question checks conceptual understanding of how μ characterizes a material’s magnetic response. Given Data / Assumptions: Magnetostatics or low-frequency magnetic behavior in linear regions. Relationship between magnetic flux density B and magnetic field intensity H. Homogeneous material approximation for clarity. Concept / Approach: The constitutive relation is B = μ H, where μ = μ_0 μ_r. A higher μ means the material supports a larger magnetic flux density B for the same applied field H. Thus, permeability is a measure of how readily the material “conducts” magnetic flux, akin to electrical conductivity for current but in the magnetic domain (with important differences). Step-by-Step Solution: Start with B = μ H: for a fixed H, B increases linearly with μ in a linear material.In a magnetic circuit, reluctance ℜ = l / (μ A); larger μ reduces ℜ, allowing more flux Φ = NI / ℜ for a given magnetomotive force NI.Thus, higher μ indicates greater ability to establish and guide magnetic flux through a core.This increased flux linkage directly raises inductance L ∝ μ N^2 A / l. Verification / Alternative check: Transformer and inductor cores use materials with μ_r » 1 (e.g., ferrites) to concentrate flux and achieve higher inductance in compact volumes. Air, with μ_r ≈ 1, provides much lower flux density for the same H, confirming the meaning of μ. Why Other Options Are Wrong: “False” denies the B–H relation. “True only for ferromagnets” is too restrictive; the definition applies to all media (though μ_r may be close to 1 for paramagnetic/diamagnetic materials). “True only at DC” is unnecessary; μ applies at AC as well, although it can be frequency dependent. “Permeability relates to electric field” is incorrect—that is permittivity (ε). Common Pitfalls: Confusing permeability with permittivity, or assuming μ is constant across all fields and frequencies (real cores are nonlinear and dispersive). Final Answer: True

Question 13

Inductors in Networks: Series vs. Parallel Combination Rule  Consider the statement: “Inductors add in parallel.” Decide whether this statement is correct in the context of ideal components and steady-state AC analysis.

Accepted Answer

Introduction / Context: Combining inductors is common in filter and power designs. Knowing when inductances add directly helps avoid design mistakes and interpret equivalent circuits correctly. The rule differs for series and parallel connections, similar to resistors but with an important inversion in parallel. Given Data / Assumptions: Ideal inductors with inductances L1, L2, … No mutual coupling (unless explicitly stated otherwise). Linear operation in steady-state AC or DC conditions. Concept / Approach: For series: inductances add directly. For parallel: the reciprocal inductances add, i.e., the total is smaller than the smallest branch (analogous to resistors but with roles reversed compared to capacitors). With mutual coupling, equivalent inductance can differ, but the basic no-coupling rule stands. Step-by-Step Solution: Series combination: L_eq(series) = L1 + L2 + …Parallel combination (no coupling): 1/L_eq = 1/L1 + 1/L2 + …Hence “inductors add in parallel” is incorrect; they add directly in series, not in parallel.With tight coupling, L_eq may involve mutual terms ±2M, but this does not reverse the core rule. Verification / Alternative check: Impedance perspective: Z_Lk = j ω L_k. For parallel branches, admittances add: Y_total = Σ (1/Z_Lk) = Σ (1/(j ω L_k)) = (1/j ω) Σ (1/L_k) ⇒ L_eq = 1 / Σ (1/L_k). This matches the reciprocal rule. Why Other Options Are Wrong: “True” contradicts the formula. “True only when mutual coupling is present” is misleading; coupling modifies values but does not make parallel addition into simple arithmetic sums. “True for DC, false for AC” is irrelevant; the formula is topological, independent of frequency (aside from reactance magnitude). “Indeterminate without Q” confuses loss with inductance combination rules. Common Pitfalls: Assuming capacitors’ rules apply to inductors; in fact, capacitors add in parallel, not inductors. Also, forgetting mutual inductance when coils are magnetically close. Final Answer: False

Question 14

Where an Inductor Stores Energy: Magnetic vs. Electric Fields  Evaluate the statement: “Energy is stored by an inductor in an electrostatic field.”

Accepted Answer

Introduction / Context: Energy storage mechanisms define how reactive components behave in AC and transient circuits. Capacitors store energy in electric (electrostatic) fields, whereas inductors store energy in magnetic fields. Misunderstanding this distinction leads to incorrect intuitions about phase relations and resonance. Given Data / Assumptions: Ideal inductor L and ideal capacitor C. Linear materials without saturation or dielectric breakdown. Sinusoidal steady-state or transient analysis. Concept / Approach: The energy stored in an inductor is W_L = (1/2) * L * I^2, associated with the magnetic field generated by current flow. For a capacitor, W_C = (1/2) * C * V^2, associated with the electric field between plates. Thus, an inductor’s storage is magnetic, not electrostatic. Step-by-Step Solution: Recall the field relations: B ∝ μ H for magnetic energy, E relates to D = ε E for electric energy.Inductor: energy density u_B = (1/2) * B * H; integrated over core/space gives (1/2) * L * I^2.Capacitor: energy density u_E = (1/2) * E * D; integrated volume yields (1/2) * C * V^2.Therefore the statement claiming electrostatic storage for an inductor is incorrect. Verification / Alternative check: Phase behavior corroborates: in an inductor, voltage leads current by 90 degrees due to energy cycling in the magnetic field; in a capacitor, current leads voltage by 90 degrees as energy cycles in the electric field. LC resonance exchanges energy between magnetic and electric fields, consistent with these storage mechanisms. Why Other Options Are Wrong: Any variant asserting electrostatic storage for inductors contradicts fundamental electromagnetics. Core material or frequency does not change the basic mechanism; these only affect magnitude and losses. Common Pitfalls: Equating large inductor voltage at high di/dt with electric-field storage; the induced voltage arises from changing magnetic flux (Faraday’s law), not from electrostatic energy storage. Final Answer: False

Question 15

Terminology: Why an Inductor Used to Block High Frequencies Is Called a “Choke”  Evaluate the statement: “The term choke is more commonly used for an inductor used to block off high frequencies.”

Accepted Answer

Introduction / Context: Inductors in signal and power lines are frequently named according to their application. The word “choke” is historically used to describe inductors that impede alternating currents—especially higher-frequency components—while passing DC or lower-frequency components. Understanding this terminology clarifies datasheets and schematics in RF and power electronics. Given Data / Assumptions: Ideal inductor behavior: XL = 2π f L increases with frequency. Use in series with a line to attenuate high-frequency noise (EMI/RFI suppression). Context includes RF chokes, common-mode chokes, and power-supply chokes. Concept / Approach: Because inductive reactance grows with frequency, inductors present larger impedance to high-frequency currents. Placing such an inductor in series “chokes off” the unwanted high-frequency components, hence the term “choke.” This is common in LC filters, input EMI filters, and RF decoupling networks. Step-by-Step Solution: Use XL = 2π f L: as f increases, XL grows, opposing high-frequency current.In power rails, a choke in series limits switching ripple while capacitors to ground shunt residual high-frequency energy.In RF front ends, RF chokes provide a high impedance bias feed, isolating DC bias from RF paths.Common-mode chokes increase impedance to common-mode noise without significantly affecting differential signals. Verification / Alternative check: Device catalogs and application notes label inductors intended for EMI suppression or RF isolation as “chokes,” e.g., RF chokes or common-mode chokes. Measurements show reduced high-frequency current through the line when a choke is inserted. Why Other Options Are Wrong: “False” and variants ignoring the high-frequency role conflict with XL ∝ f. A choke does not specifically “block low frequencies”; in fact, it is chosen to have acceptably low drop at the intended passband while rejecting higher-frequency noise. Common Pitfalls: Assuming any inductor is a choke; application and frequency range matter. Also, overlooking saturation and core losses that limit choke effectiveness under large DC bias. Final Answer: True

Question 16

Core Materials for Coils: Are All Coil Cores Made of Iron?  Assess the statement: “All coil cores are made of iron.”

Accepted Answer

Introduction / Context: Coil core selection impacts inductance, loss, linearity, and frequency response. Many core materials exist to meet distinct electrical and mechanical requirements. This item checks awareness of the diversity of core options beyond iron. Given Data / Assumptions: Common core types: air (no core), ferrite, powdered iron, laminated silicon steel, amorphous metal, nanocrystalline alloys. Applications span RF chokes, power converters, audio transformers, and EMI filters. Frequency, flux density, and loss constraints guide material choice. Concept / Approach: While “iron” (including silicon steel laminations) is widely used in power-frequency transformers and inductors, many applications require non-iron or composite materials. Ferrites (ceramic, high electrical resistivity) excel at RF and high-frequency power. Powdered iron offers distributed air gaps for stable inductance with DC bias. Air-core coils avoid core loss and saturation for high-Q RF inductors. Step-by-Step Solution: Identify application frequency and flux: low-frequency power often uses laminated steel (iron-based), high-frequency uses ferrites or powdered iron.Consider losses: eddy currents scale with frequency; ferrites mitigate via high resistivity.For very high Q or high linearity at RF, choose air cores to eliminate core nonlinearity and hysteresis.Therefore, the universal claim “all cores are iron” is false. Verification / Alternative check: Datasheets from inductor and transformer vendors list diverse materials and permeability values (μ_r ranges from ~1 for air to thousands for certain ferrites), confirming broad material usage. Why Other Options Are Wrong: “True” contradicts common RF and EMI practice. “True for power inductors only” or “True for RF inductors only” overgeneralize; many power inductors use ferrite or powdered iron, and RF inductors are often air-core or ferrite-core depending on Q needs. Common Pitfalls: Assuming “iron” covers powdered iron and ferrite; ferrites are ceramic compounds with iron oxides but very different properties from metallic iron laminations. Final Answer: False

Question 17

Inductive reactance formula — evaluate the statement: the magnitude of inductive reactance is given by XL = 2π f L for a linear inductor at frequency f (hertz) and inductance L (henry).

Accepted Answer

Introduction / Context: Inductive reactance quantifies how an inductor impedes alternating current due to the changing magnetic field. It plays a central role in AC analysis, filter design, resonance calculations, and impedance matching. The standard relationship ties reactance to frequency and inductance linearly in magnitude. Given Data / Assumptions: L is the inductance in henry (H). f is the signal frequency in hertz (Hz). The inductor is linear over the operating range (no core saturation, negligible parasitics). Steady-state sinusoidal analysis is assumed. Concept / Approach: For a sinusoidal steady state, the inductor voltage-current relation is v(t) = L * di/dt. In phasor form, this becomes V = j ω L * I, where ω = 2π f is the angular frequency. The impedance of the inductor is therefore Z_L = j ω L. The magnitude of this impedance is |Z_L| = ω L = 2π f L, which is by definition the inductive reactance, X_L. Thus, X_L grows linearly with frequency and inductance; at DC (f = 0), X_L = 0 Ω, behaving as a short in ideal form. Step-by-Step Solution: Write the time-domain relation: v = L * di/dt.Move to phasor domain: Z_L = j ω L with ω = 2π f.Take magnitude: X_L = |Z_L| = ω L = 2π f L.Interpretation: increasing f or L increases reactance proportionally. Verification / Alternative check: Example: L = 10 mH at f = 1 kHz → X_L = 2π * 1000 * 0.01 = about 62.8 Ω. A measurement with an LCR meter at 1 kHz would read a similar reactance (ignoring ESR and parasitics). Why Other Options Are Wrong: “Incorrect” contradicts the standard derivation from v = L di/dt.DC-only, iron-core-only, or kilohertz-only caveats are unnecessary; the formula applies broadly to linear inductors across frequencies where the lumped model holds. Common Pitfalls: Forgetting units (henry and hertz) leading to numeric errors; confusing reactance magnitude X_L with the complex impedance j ω L; neglecting nonidealities like winding resistance and self-resonance at very high frequencies. Final Answer: Correct

Question 18

Electromagnetism — definition check: Does self-inductance describe the property of a conductor (or coil) by which a changing current in itself induces an opposing electromotive force (emf) in the same circuit?

Accepted Answer

Introduction / Context: Self-inductance is a foundational idea in circuit theory and electromagnetics. Whenever the current through a conductor or coil changes, the associated magnetic field also changes. This changing flux links the same conductor and induces a voltage that opposes the change. Understanding this definition is crucial for analyzing RL transients, switch behavior, energy storage in magnetic fields, and practical issues such as inductive kickback in relays and motor windings. Given Data / Assumptions: Standard lumped-element model (coil modeled as an ideal inductor L in series with winding resistance). Quasi-static conditions where circuit dimensions are small relative to wavelengths of interest. No special core is required; self-inductance exists for air-core coils and even straight conductors (though the magnitude may be small). Concept / Approach: By Faraday’s law, induced emf magnitude is proportional to the time rate of change of linked magnetic flux. For a coil with N turns, v_L = L * di/dt, where L (henry) quantifies self-inductance. Lenz’s law gives the polarity: the induced emf acts to oppose the change in current. Thus, a rising current induces a counter-voltage that resists the rise; a falling current induces a voltage that tries to keep current flowing, leading to familiar spark/kickback phenomena if a path is suddenly opened. Step-by-Step Solution: State definition: self-inductance is the property of a circuit where its own changing current induces an emf in itself.Relate to formula: v_L = L * di/dt, showing proportionality to di/dt.Apply Lenz’s law for polarity: induced voltage opposes the change in current.Conclude: the stem statement correctly describes self-inductance. Verification / Alternative check: Observe an RL step response: when a DC source is suddenly applied, current does not jump to its final value; the inductor’s induced emf initially equals the source and then decays as current builds. This behavior confirms that the inductor generates an opposing emf due to its own changing current. Why Other Options Are Wrong: “Incorrect” contradicts Faraday–Lenz behavior. “Only at very high frequency,” “only in superconductors,” and “only with an iron core” are misconceptions; self-inductance exists broadly and does not require a core or extreme frequency, though L’s magnitude and parasitic effects may vary. Common Pitfalls: Confusing induced emf with power loss (ideal inductors store/return energy, they do not dissipate). Assuming a core is mandatory (air-core inductors are common in RF). Final Answer: Correct

Question 19

Electromagnetism — Lenz’s law comprehension: Does Lenz’s law state that an induced current (or induced emf) always acts to oppose the change in magnetic flux that produced it, thereby opposing the cause of motion or flux change?

Accepted Answer

Introduction / Context: Lenz’s law determines the direction (polarity) of induced currents and voltages in electromagnetic induction. It is a qualitative statement that ensures energy conservation and aligns with Faraday’s law. Engineers rely on it when predicting back-emf in motors, inductive kickback in coils, eddy current braking, and transformer polarities. Given Data / Assumptions: Changing magnetic flux through a conducting loop or coil. Faraday’s induction principle applies: magnitude of induced emf is proportional to rate of change of linked flux. Conventional passive sign convention and standard circuit orientation. Concept / Approach: Lenz’s law: the induced emf produces currents whose magnetic field opposes the original change in flux. If flux increases, the induced current creates an opposing field to reduce the increase. If flux decreases, the induced current creates a field that tries to maintain it, resisting the decrease. This opposition manifests as mechanical forces resisting motion (e.g., in generators) or electrical voltages resisting current change (e.g., in inductors). Step-by-Step Solution: Identify the cause: changing flux linkage through a loop.Apply Faraday–Lenz: induced emf polarity chosen so that its effect opposes the change in flux.Infer current direction: right-hand/clock rules yield the loop direction that creates the opposing field.Conclude: the statement matches Lenz’s law precisely. Verification / Alternative check: Consider moving a magnet toward a loop: the induced current direction creates a magnetic field repelling the magnet (opposing the approach). Pulling the magnet away flips the current to attract it (opposing separation). This physical opposition is a direct demonstration of Lenz’s law. Why Other Options Are Wrong: “Incorrect” conflicts with the definition. Limiting it to DC, to increases only, or to ferromagnetic cores is false—Lenz’s law applies generally to any changing flux linkage in conductive loops. Common Pitfalls: Confusing “oppose the change” with “oppose the flux.” It opposes the change in flux, not necessarily the flux itself. Final Answer: Correct

Question 20

Circuit laws — applicability: Does Kirchhoff’s Voltage Law (KVL) fail to apply to a simple series R–L circuit driven by a source in lumped-element analysis?

Accepted Answer

Introduction / Context: Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltage drops around any closed loop is zero at every instant. This law is widely used in analyzing RL, RC, and RLC circuits for both transient and steady-state conditions. The claim that KVL does not apply to series RL circuits is a misconception and is corrected here. Given Data / Assumptions: Lumped-element model (component dimensions small vs. wavelength; negligible radiation). Ideal components: resistor R, inductor L, and a voltage source. Quasi-static field conditions without distributed transmission-line effects. Concept / Approach: KVL emerges from electrostatic field conservativeness in lumped circuits and is valid instant-by-instant. In a series RL loop driven by v_s(t), the loop equation is v_s(t) − v_R(t) − v_L(t) = 0, where v_R(t) = i(t) * R and v_L(t) = L * di/dt. This is the standard starting point for deriving the RL differential equation and its step response. Step-by-Step Solution: Write KVL for the loop: v_s(t) = v_R(t) + v_L(t).Substitute element laws: v_R(t) = iR, v_L(t) = Ldi/dt.Obtain RL DE: Ldi/dt + Ri = v_s(t).Conclude: KVL holds at all times under lumped conditions. Verification / Alternative check: Measure with an oscilloscope: the instantaneous source voltage equals the instantaneous sum of resistor and inductor voltages. Simulations (SPICE) also confirm v_s = v_R + v_L for arbitrary inputs (steps, sinusoids, pulses). Why Other Options Are Wrong: Limiting KVL to resistive circuits, steady state, or low frequency is incorrect within lumped-element validity. Only when circuits become distributed (high-frequency transmission lines, significant radiation) do we need full Maxwell’s equations instead of simple KVL. Common Pitfalls: Confusing instantaneous addition with RMS magnitudes; in AC, phasor magnitudes do not add arithmetically, but the time-domain KVL always holds. Final Answer: Incorrect

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