Question 1

Resistor taxonomy in electronics: What are the two major categories into which resistors are broadly classified for circuit design and selection?

Accepted Answer

Introduction / Context: Resistors are ubiquitous passive components that set currents, divide voltages, and shape time constants. For selection, engineers first distinguish between fixed-value parts and adjustable parts. This high-level categorization influences footprint, tolerance, adjustability, and use cases such as calibration or user control. Given Data / Assumptions: We are discussing everyday components used on printed circuit boards and instruments. Focus on functional categories rather than specific technologies (carbon film, metal film, wirewound, thick film). Variable devices include both manually adjustable and electronically variable forms. Concept / Approach: Fixed resistors have a single nominal value specified by tolerance (for example, 10 kΩ ± 1%). Variable resistors can be adjusted: potentiometers provide a variable divider; rheostats provide a variable series resistance; trimmers allow board-level calibration. This functional split determines whether the circuit can be tuned after assembly or must rely on component tolerance alone. Step-by-Step Solution: Identify need: Is resistance intended to be constant? → choose fixed resistor.Need adjustability (user control or calibration)? → choose variable resistor (potentiometer, trimmer, rheostat).Confirm that other labels (ohmic range, power rating) are specifications within these broad categories, not categories themselves. Verification / Alternative check: Look at distributor catalogs: filters typically offer ”fixed resistors” and ”potentiometers/trimmers” as primary families, reinforcing this classification across manufacturers. Why Other Options Are Wrong: Low/high ohmic value or power value: These are parametric ranges, not fundamental categories. Commercial/industrial: Refers to quality or environmental rating, not function. Common Pitfalls: Confusing potentiometer wiring: a potentiometer can be used as a voltage divider (three terminals) or as a rheostat (two terminals), but both are still variable resistors. Final Answer: fixed and variable

Question 2

Precise definition: In circuit theory, how is electrical resistance best defined?

Accepted Answer

Introduction / Context: Resistance is a fundamental concept relating voltage, current, and energy dissipation. It underpins Ohm’s law, thermal design, and noise analysis. A crisp definition helps prevent confusion with related but distinct ideas such as conductance, impedance, and analogies used in pedagogy. Given Data / Assumptions: Linear resistor behavior is assumed for small signals and constant temperature. Units: ohm (Ω) for resistance. Real resistors dissipate power as heat when current flows. Concept / Approach: Resistance R characterizes how a component opposes current for a given applied voltage: V = I * R. When current passes through a resistive element, electrical energy converts to heat at a rate P = I^2 * R = V^2 / R = V * I. This thermal effect is inseparable from resistance in passive materials (aside from superconductivity and idealizations). Step-by-Step Solution: State relationship: V = I * R defines resistance.Link to energy: Power dissipation P = V * I in a resistor becomes heat (Joule heating).Conclude: resistance is opposition to current that produces heat for nonzero current. Verification / Alternative check: Measure a resistor’s temperature rise under load; infrared imaging or simple touch (carefully) confirms heat generation proportional to I^2 * R and validates the definition in practice. Why Other Options Are Wrong: Directly proportional to conductance: Conductance G = 1 / R, so they are inversely proportional. Directly proportional to current and voltage: R is the ratio V / I, not proportional to both independently. Fluid flow analogy: Useful for intuition, but it is not a formal definition. Common Pitfalls: Assuming resistance is constant regardless of temperature or frequency; many resistors change value with temperature (tempco) and show parasitic inductance/capacitance at high frequency. Final Answer: the opposition to current flow accompanied by the dissipation of heat

Question 3

Core concept checkpoint: In basic circuit theory, resistance is best described as which of the following?

Accepted Answer

Introduction / Context: Three foundational quantities in circuits are voltage (electric potential difference), current (charge flow), and resistance (opposition to current). Confusing these leads to wrong expectations about how circuits behave under different loads and sources. This item reinforces the precise role played by resistance. Given Data / Assumptions: Ohm’s law applies for the element being discussed. Linear, time-invariant behavior around the operating point. No reactive elements are considered in the definition. Concept / Approach: Ohm’s law V = I * R shows resistance as the proportionality between voltage and current. For a given applied voltage, a larger resistance yields a smaller current, hence resistance opposes current flow. It does not oppose voltage; rather, voltage is the cause that pushes current through resistance, producing heat at P = I^2 * R. Step-by-Step Solution: Identify definitions: voltage pushes, current flows, resistance resists.Use V = I * R to see that increasing R decreases I for constant V.Conclude: resistance is opposition to current, not voltage. Verification / Alternative check: Compare two lamps on the same battery: the one with higher resistance draws less current and glows dimmer, illustrating the opposing effect on current. Why Other Options Are Wrong: Opposition to voltage: Misstates causality; voltage is the driving potential. Same as current or same as voltage: They are distinct physical quantities with different units (A, V, Ω). Common Pitfalls: Equating a voltage drop with ”loss” of voltage as if resistance consumes voltage; voltage is not consumed—energy is dissipated as heat while voltage remains the measure of potential difference. Final Answer: opposition to current

Question 4

Power units refresher: Power is defined as the rate at which work or energy is transferred. Which unit expression matches this definition?

Accepted Answer

Introduction / Context: Power quantifies how fast energy is converted, delivered, or consumed. In electrical and mechanical systems, correct unit handling ensures accurate sizing of supplies, thermal solutions, and protective devices. In SI, the watt is the coherent unit that ties energy and time together for power calculations. Given Data / Assumptions: Energy (or work) uses the joule (J) as the SI unit. Time uses the second (s). Power is defined as energy per unit time. Concept / Approach: Power P is defined by P = dW / dt. For constant power over an interval, this reduces to P = W / t. Therefore, the unit must be joule per second, written as J/s, which is named the watt (W). In electrical form, P = V * I, which remains consistent because 1 W = 1 V * 1 A = 1 J/s. Step-by-Step Solution: Start from definition: P = W / t.Map units: J divided by s → J/s.Recognize J/s is called the watt (W); equivalently, P = V * I is also in watts. Verification / Alternative check: Check dimensional consistency: 1 V = 1 J/C and 1 A = 1 C/s, so V * A = (J/C) * (C/s) = J/s = W, confirming equivalence across formulations. Why Other Options Are Wrong: Joules x charge or joules x voltage: Multiply energy by another quantity, producing non-power units. Joules/work: Dimensionless ratio when work equals energy; not a rate. Common Pitfalls: Confusing energy (capacity to do work) with power (rate of doing work). Battery energy is in watt-hours (Wh), but instantaneous load demand is in watts (W). Final Answer: joules/time

Question 5

Ohm’s law application: A 24 V source supplies a 100 Ω load. Calculate the load current and express the answer with appropriate SI units.

Accepted Answer

Introduction / Context: Ohm’s law is the backbone of basic circuit analysis. Converting between volts, ohms, and amperes is routine when checking supply sizing, fuse ratings, and expected temperature rise. This problem reinforces current calculation and correct use of SI prefixes for clear communication. Given Data / Assumptions: Supply voltage V = 24 V (dc or rms equivalently for a purely resistive load). Load resistance R = 100 Ω. Assume ideal source and purely resistive load with steady-state conditions. Concept / Approach: Ohm’s law states I = V / R. For resistive loads, this directly yields the current. After calculation, express the result using a convenient prefix; milliampere is common for sub-ampere currents (1 A = 1000 mA). Step-by-Step Solution: Write formula: I = V / R.Substitute values: I = 24 / 100.Compute numerically: I = 0.24 A.Convert to milliamperes: 0.24 A * 1000 mA/A = 240 mA. Verification / Alternative check: Cross-check power: P = V * I = 24 * 0.24 = 5.76 W. Alternatively, P = V^2 / R = 576 / 100 = 5.76 W. Agreement confirms the current is correct. Why Other Options Are Wrong: 2.4 A: Ten times too large; would require R = 10 Ω at 24 V. 24 mA or 2.4 mA: Underestimates current by factors of 10 and 100 respectively. Common Pitfalls: Dropping a zero when dividing by 100 or misapplying prefixes (confusing mA with A). Always include units at every step. Final Answer: 240 mA

Question 6

Instrument selection: Which piece of test equipment is specifically designed to measure resistance values accurately in ohms (Ω)?

Accepted Answer

Introduction / Context: Proper instrument choice prevents damage to equipment and improves measurement accuracy. Resistance measurement is common for verifying components, checking sensor elements, and troubleshooting open or short circuits. Knowing which meter function to use saves time and avoids misreadings. Given Data / Assumptions: Standard benchtop or handheld digital multimeters (DMMs) are available. Device under test is unpowered during resistance measurements unless a specialized method is used. Leads are zeroed or compensated if very low resistances are being measured. Concept / Approach: An ohmmeter applies a small test current and measures the resulting voltage drop (or vice versa) to compute resistance via R = V / I internally. The ammeter measures current, and the voltmeter measures potential difference; these are not direct resistance measurement instruments, though resistance can be inferred indirectly with additional steps. A watt meter measures power and is not used for passive component value checks. Step-by-Step Solution: Select the meter's Ω function (ohmmeter mode).Isolate the resistor from active circuits to avoid parallel paths and source voltages.Place probes across the resistor and read the displayed Ω value. Verification / Alternative check: Validate with Ohm’s law using a known current source and a voltmeter: apply a known I and measure V, then compute R = V / I. The indirect result should match the ohmmeter within tolerance. Why Other Options Are Wrong: Ammeter: Measures current in amperes. Voltmeter: Measures voltage in volts. Watt meter: Measures power in watts. Common Pitfalls: Measuring resistance in-circuit while powered can damage the meter or produce incorrect readings. For low-ohm measurements, compensate for lead resistance using the REL/zero function or a 4-wire method. Final Answer: ohmmeter

Question 7

Resistor color code practice: Determine the correct 4-band color code for a 3.9 kΩ resistor with a ±5% tolerance.

Accepted Answer

Introduction / Context: The 4-band resistor color code encodes two significant digits, a power-of-ten multiplier, and a tolerance band. Fluency with the code allows quick identification of components during prototyping and troubleshooting without consulting a datasheet. Given Data / Assumptions: Target value: 3.9 kΩ = 3900 Ω. Format: 4 bands → digit1, digit2, multiplier, tolerance. Assume common ±5% tolerance for general-purpose resistors (gold). Concept / Approach: Color mapping (digits): black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9. Multiplier: red = ×10^2, orange = ×10^3, etc. 3.9 kΩ has significant digits 3 and 9, then a multiplier of ×10^2 to yield 39 × 10^2 = 3900 Ω. Tolerance gold = ±5%. Step-by-Step Solution: Digits: 3 → orange, 9 → white.Compute multiplier: 3900 Ω = 39 × 10^2 → multiplier color red.Tolerance: ±5% → gold.Final code: orange, white, red, gold. Verification / Alternative check: Cross-check by reconstructing value: 3 9 with multiplier ×10^2 = 3900 Ω = 3.9 kΩ; tolerance ±5% gives range 3.705 kΩ to 4.095 kΩ, which matches common E24 series availability. Why Other Options Are Wrong: Red, white, red, gold: 2 9 × 10^2 = 2.9 kΩ, not 3.9 kΩ. Red, green, orange, silver: 2 5 × 10^3 = 25 kΩ, tolerance ±10% (silver). Orange, green, orange, silver: 3 5 × 10^3 = 35 kΩ, tolerance ±10%. Common Pitfalls: Reading the bands from the wrong end (tolerance band is spaced farther apart), or confusing white (9) with silver (tolerance). Always locate the tolerance band first to set the reading direction. Final Answer: orange, white, red, gold

Question 8

Energy stored by charges at a given potential difference How much energy (in joules) is stored when 6.24 × 10^18 electrons are placed at a potential of 4 V (use E = Q * V and 6.24 × 10^18 electrons ≈ 1 coulomb)?

Accepted Answer

Introduction / Context: This problem checks your understanding of the relationship between electric charge, potential (voltage), and energy in basic circuit theory. When charges are moved through a potential difference, electrical potential energy is stored according to E = Q * V. Knowing the common equivalence 6.24 × 10^18 electrons ≈ 1 coulomb is a standard electronics shortcut. Given Data / Assumptions: Number of electrons n = 6.24 × 10^18. Elementary charge e ≈ 1.602 × 10^-19 C per electron. Voltage V = 4 V. Neglect any losses; treat all charge at the stated potential. Concept / Approach: First convert the count of electrons into total charge using Q = n * e. Then compute energy with E = Q * V. In many introductory problems, 6.24 × 10^18 electrons is used because it is essentially one coulomb of charge (to three significant figures), which makes the arithmetic straightforward and reinforces unit intuition. Step-by-Step Solution: Compute total charge: Q = n * e ≈ (6.24 × 10^18) * (1.602 × 10^-19) ≈ 1.00 C.Apply energy formula: E = Q * V.Substitute values: E ≈ 1.00 C * 4 V = 4 J.Therefore, the stored energy is 4 joules. Verification / Alternative check: Dimensional analysis: coulomb times volt equals joule, which confirms unit consistency. The electron-count-to-coulomb equivalence is also consistent with 1 C ≈ 6.24 × 10^18 electrons. Why Other Options Are Wrong: 1.56 × 10^18 electrons: this is a charge count, not energy.1.56 coulombs: incorrect charge; the given electron count equals about 1 C, not 1.56 C.2.496 × 10^19 electrons: incorrect and still not an energy unit. Common Pitfalls: Confusing charge, voltage, and energy units; forgetting to convert electron count to coulombs; or attempting to use capacitor energy formulas without a capacitance value. Here, E = Q * V is sufficient. Final Answer: 4 joules

Question 9

SI unit for electrical resistance In basic electrical measurements, what is the standard unit (designator) used to express the value of resistance?

Accepted Answer

Introduction / Context: Every electrical quantity has an SI unit. Recognizing the correct unit for resistance is essential for interpreting datasheets, calculating with Ohm’s law, and selecting components. The unit symbol and name are universally standardized to avoid confusion in engineering practice. Given Data / Assumptions: Quantity: electrical resistance. We are working with SI units and standard circuit theory. Symbols: A for ampere, V for volt, W for watt, Ω (ohm) for resistance. Concept / Approach: By definition, resistance R relates voltage and current via Ohm’s law: V = I * R. The SI unit for R is the ohm (Ω), which is equivalent to volt per ampere (V/A). Knowing this allows dimensional checks in formulas and helps avoid unit mistakes. Step-by-Step Solution: Recall Ohm’s law: V = I * R.Rearrange to R = V / I.Units: V/A is defined as one ohm (Ω).Therefore, the correct unit designator is the ohm. Verification / Alternative check: Cross-verify with component labels: resistors are specified in Ω, kΩ, and MΩ. Meters display resistance in Ω as well. Why Other Options Are Wrong: Ampere: unit of current.Volt: unit of electric potential.Watt: unit of power. Common Pitfalls: Confusing resistance (Ω) with reactance (also expressed in ohms but frequency dependent) or with conductance (siemens, S, the reciprocal of ohms). Final Answer: ohm

Question 10

Safe measurement practice for resistors in-circuit Which single step is the most important to perform before measuring a resistor with a meter in a circuit?

Accepted Answer

Introduction / Context: Measuring resistance is a routine task, but doing it incorrectly can damage the meter, disturb the circuit, or yield nonsense readings. The most crucial safety and accuracy rule is to ensure that no external voltage is present across the resistor under test. Given Data / Assumptions: Digital or analog multimeter used for resistance measurement (ohmmeter function). The resistor may be in-circuit. We aim to prevent meter damage and false readings. Concept / Approach: Ohmmeters inject a small, known current and measure the resulting voltage to compute resistance. If the circuit is powered, external sources inject additional voltage/current that will corrupt the measurement and can harm the meter. Therefore, power must be removed, and ideally the resistor isolated from parallel paths if high accuracy is needed. Step-by-Step Solution: Turn off and disconnect the power source to the unit under test.Discharge capacitors to avoid stored energy affecting the meter.If precision is required, lift one resistor lead to eliminate parallel paths.Measure resistance using the ohmmeter; interpret values in Ω, kΩ, or MΩ as needed. Verification / Alternative check: Compare measured value to color code or schematic. If in-circuit reading differs significantly, isolate the component and remeasure. Why Other Options Are Wrong: Use highest scale: may reduce resolution and does not address safety.Keep leads short: helpful against noise, but secondary compared to de-energizing.Zero the meter: relevant for analog meters, but still less critical than removing power. Common Pitfalls: Forgetting to power down, measuring across energized nodes, or trusting in-circuit readings without considering parallel components. Final Answer: remove power from the circuit

Question 11

Temperature coefficient and metallic conductors If a metallic conductor exhibits a positive temperature coefficient of resistance, how does its resistance change as temperature increases?

Accepted Answer

Introduction / Context: Most metals have a positive temperature coefficient of resistance (TCR). Understanding TCR is important for sensor design, power electronics, and precision measurement because temperature changes alter circuit behavior and can require compensation. Given Data / Assumptions: Material is a typical metallic conductor (e.g., copper, aluminum). Temperature changes within normal operating ranges. No phase changes or extreme cryogenic effects. Concept / Approach: In metals, increased temperature causes more lattice vibrations (phonons). These increase electron scattering, which raises resistivity. The resistance approximately follows R(T) ≈ R0 * [1 + α * (T − T0)], where α > 0 for metals. Therefore, as temperature rises, resistance increases. Step-by-Step Solution: Start with R(T) = R0 * [1 + α * (T − T0)] for α > 0.If T increases, (T − T0) increases.Since α is positive, the product α * (T − T0) is positive, so R(T) > R0.Thus, resistance increases with temperature. Verification / Alternative check: Observe practical devices: incandescent filaments (tungsten) have much higher resistance hot than cold, explaining inrush current behavior. Why Other Options Are Wrong: Resistance decreases with temperature: true for many semiconductors or carbon, not metals.As current increases, resistance decreases: mixes variables; TCR is about temperature, not current directly.As voltage increases, current increases: that is Ohm’s law, not TCR behavior. Common Pitfalls: Confusing metallic behavior with NTC thermistors or semiconductor resistivity trends, which often show negative TCR. Final Answer: as temperature increases, resistance increases

Question 12

Standard resistivity of copper at room temperature Select the closest typical resistivity of copper at 20 °C, expressed with standardized SI units.

Accepted Answer

Introduction / Context: Resistivity is a material property that determines how strongly a given material opposes electric current. For conductors like copper, knowing the typical resistivity at 20 °C is critical for wire sizing, power loss estimation, and signal integrity. Given Data / Assumptions: Room temperature reference: 20 °C. Need an approximate, widely accepted value for copper. Use SI units (Ω·m) and convenient prefixes (nΩ·m). Concept / Approach: Copper's resistivity at 20 °C is commonly taken as about 1.68 × 10^-8 Ω·m. Expressed in nano-ohm-meters, this is approximately 16.8 nΩ·m. Engineering tables often round to about 17 nΩ·m for practical calculations, which is within typical tolerance and alloy variations. Step-by-Step Solution: Reference value: ρ ≈ 1.68 × 10^-8 Ω·m.Convert to nΩ·m: 1.68 × 10^-8 Ω·m = 16.8 nΩ·m.Round to standard tabulated value: ≈ 17.0 nΩ·m.Therefore, 17.0 nΩ·m is the best choice. Verification / Alternative check: Compare with common handbooks and cable datasheets; most list values near 1.68 × 10^-8 Ω·m at 20 °C with small variations depending on purity. Why Other Options Are Wrong: 9.9 nΩ·m and 10.7 nΩ·m: too low for copper at 20 °C.16.7 nΩ·m: close but slightly low; 17.0 nΩ·m is the typical rounded reference. Common Pitfalls: Mixing units such as μΩ·cm and Ω·m; always convert to a consistent SI unit before comparison. Final Answer: 17.0 nΩ·m

Question 13

Convert a ratio to percentage What is the ratio 13:47 expressed as a percentage (rounded to one decimal place as in typical engineering practice)?

Accepted Answer

Introduction / Context: Converting ratios to percentages is a frequent task in test data analysis, yield reporting, and specification compliance. A clear method avoids calculator mistakes and ensures consistent rounding. Given Data / Assumptions: Given ratio: 13 to 47. Percentage form required. Round to about one decimal place as commonly presented. Concept / Approach: A percentage is simply a fraction times 100. For a ratio a:b, compute a/b to get the fraction of the whole represented by a, then multiply by 100 to express it as a percent. Step-by-Step Solution: Compute fraction: 13 / 47 ≈ 0.276595744.Convert to percent: 0.276595744 * 100 ≈ 27.6595744%.Round to one decimal place: ≈ 27.7%.Thus, 13:47 expressed as a percentage is 27.7%. Verification / Alternative check: Back-check: 47 * 0.277 ≈ 13.019, close to 13, consistent with rounding. Why Other Options Are Wrong: 2.76% and 3.60%: order of magnitude too small.36.1%: too large; would correspond to about 17/47. Common Pitfalls: Forgetting to multiply by 100 or misplacing the decimal; not rounding consistently across datasets. Final Answer: 27.7%

Question 14

Mechanism of power dissipation in a resistor In practical circuits, by what physical process is electrical power dissipated inside a resistor?

Accepted Answer

Introduction / Context: Resistors convert electrical energy into another form as current flows through them. Understanding what that form is explains why resistors warm up, require power ratings, and sometimes need heat sinks or derating with temperature. Given Data / Assumptions: Ohmic conductor under steady DC or AC conditions. No special thermoelectric or radiative devices involved. Macroscopic view of energy conversion. Concept / Approach: Electrical power in a resistor is P = V * I = I^2 * R = V^2 / R. On the microscopic level, moving electrons collide with the lattice, transferring energy and increasing lattice vibrations. This manifests as temperature rise—thermal energy (heat). The resistor then dissipates this heat to its surroundings by conduction, convection, and radiation. Step-by-Step Solution: Compute electrical power using P = I^2 * R or P = V^2 / R.Recognize conversion: electrical energy → thermal energy inside the resistive material.Observe: body temperature of the resistor increases as it dissipates heat.Thermal equilibrium: heat output balances ambient heat removal, defining allowable continuous power (the power rating). Verification / Alternative check: Touch-safe observation and IR thermography show resistors warming under load. Datasheets specify temperature rise versus power and ambient conditions. Why Other Options Are Wrong: By resistance/voltage/current: these are parameters in the electrical equations, not mechanisms of energy conversion. The physical manifestation is heat. Common Pitfalls: Ignoring power ratings and placing low-wattage resistors in high-dissipation positions, leading to overheating or failure. Final Answer: by heat

Question 15

Common conductor choice in electronics wiring and PCB interconnects Which material is most widely used as the primary electrical conductor in electronic equipment and interconnects?

Accepted Answer

Introduction / Context: Material selection for conductors balances conductivity, cost, manufacturability, solderability, mechanical properties, and corrosion behavior. In practical electronics—from PCB traces to hookup wire—one material dominates due to its favorable overall profile. Given Data / Assumptions: General-purpose electronics (wiring, PCB traces, cables). Cost sensitivity and ease of processing matter. No exotic, niche applications (e.g., RF silver plating) implied. Concept / Approach: Copper offers high conductivity (second only to silver among common metals), good ductility, excellent solderability, and reasonable cost. It can be drawn into fine wires, electroplated, and etched for PCBs. While silver is slightly more conductive, its cost and tarnishing issues limit general use; aluminum is common in power distribution but is less favored inside compact electronics; gold is used selectively for corrosion-resistant contacts, not bulk conductors. Step-by-Step Solution: Compare conductivity and cost: copper balances both well.Manufacturing: copper laminates are standard for PCBs; magnet wire is copper.Reliability: copper solders readily and forms stable interconnects.Therefore, copper is the most common conductor in electronics. Verification / Alternative check: Check PCB material specs: FR-4 boards use copper cladding (e.g., 1 oz/ft²). Hookup wires and cables list copper strands (tinned copper, OFHC copper, etc.). Why Other Options Are Wrong: Aluminum: lighter and cheaper but harder to solder; used more in power and utility distribution.Gold: excellent for contacts; too costly for bulk conductors.Silver: best conductivity but expensive; used in specialty RF or plating. Common Pitfalls: Assuming the “best” conductor (silver) is always chosen; in practice, cost and manufacturability dominate. Final Answer: copper

Question 16

Effect of increasing load resistance on load current (Ohm’s law context) If the load resistance in a simple source–load circuit increases while the source voltage remains the same, how will the load current change?

Accepted Answer

Introduction / Context: Ohm’s law governs the relationship between voltage, current, and resistance in linear circuits. Understanding how current responds when resistance changes at a fixed source voltage is foundational for troubleshooting and design. Given Data / Assumptions: Ideal DC source with constant voltage. Single effective load resistance (or equivalent resistance) connected. Linear, ohmic behavior with no active regulation. Concept / Approach: Ohm’s law states I = V / R. With V held constant, current is inversely proportional to resistance. Therefore, if R increases, I must decrease. This principle holds for both single resistors and equivalent resistances after simplifying more complex networks. Step-by-Step Solution: Start with I = V / R.Hold V constant; consider R → R + ΔR with ΔR > 0.Compute new current: I_new = V / (R + ΔR) < V / R = I_old.Thus, the load current decreases as load resistance increases. Verification / Alternative check: Numerical example: V = 10 V, R from 1 kΩ to 2 kΩ. Current changes from 10 mA to 5 mA, confirming the inverse relationship. Why Other Options Are Wrong: Vary: too vague; direction is deterministically downward.Remain constant: would require a constant-current source, not a fixed-voltage source.Increase: opposite of Ohm’s law with fixed voltage. Common Pitfalls: Forgetting that some supplies regulate current; here the assumption is a fixed-voltage source. Misinterpreting “load increase” as power instead of resistance value. Final Answer: decrease

Question 17

Core relationship in Ohm’s law Which statement correctly describes the proportionality between current and resistance when the applied voltage is held constant?

Accepted Answer

Introduction / Context: Ohm’s law is the cornerstone of basic circuit analysis. It defines a simple linear relationship among voltage, current, and resistance, allowing quick predictions of how one variable changes when another is adjusted. Given Data / Assumptions: Ohmic components and linear operating region. Applied voltage is constant. Temperature and material properties assumed stable. Concept / Approach: Ohm’s law: V = I * R. Solving for current yields I = V / R. With V fixed, it is clear that current varies inversely with resistance: doubling R halves I; halving R doubles I. This inverse proportionality is fundamental to resistor networks and load-line analysis. Step-by-Step Solution: Start from V = I * R.Hold V constant and isolate I: I = V / R.Observe: I is proportional to 1/R.Therefore, current is inversely proportional to resistance at constant voltage. Verification / Alternative check: Plot I versus R for fixed V: a rectangular hyperbola passing through (R, I) pairs such as (1 kΩ, 10 mA) and (2 kΩ, 5 mA). Why Other Options Are Wrong: Resistance directly proportional to voltage: not a general law; R is material/geometry dependent.Voltage indirectly proportional to power: mixing relationships; power depends on both V and I.Current directly proportional to resistance: contradicts I = V / R. Common Pitfalls: Ignoring temperature dependence in real resistors; at high power, R may change, but the law’s proportionality at a given instant still applies. Final Answer: current is inversely proportional to resistance

Question 18

In basic electrical safety and protection practice, which component is specifically designed to protect equipment and wiring from excessive current by melting and opening the circuit when the current exceeds a rated value?

Accepted Answer

Introduction / Context: Protecting electrical equipment and conductors from excessive current is fundamental to safety and reliability. The simplest and most widely used overcurrent protection device in low-voltage systems is the fuse, whose core protective element is a calibrated fusible wire link that melts when current exceeds a safe value. Given Data / Assumptions: The question asks for the protective element that interrupts excess current. Focus is on general-purpose, passive overcurrent protection. No reset or active control is implied. Concept / Approach: A fuse contains a fusible alloy or wire link engineered to heat according to I^2 * R and melt at a predictable temperature. When it melts, the circuit opens and current flow stops, preventing overheating, insulation breakdown, or fire. The glass tube and metal end caps commonly seen in cartridge fuses are merely the package; the actual protection is delivered by the fusible link. Step-by-Step Solution: Identify the function: interrupt current automatically under overload/fault.Map to device internals: a calibrated fusible wire link melts at overcurrent.Therefore, the protective element is the fusible wire link (the essence of a fuse). Verification / Alternative check: Fuse datasheets specify time–current curves linking overcurrent magnitude to melting time, confirming the link as the operating element. Field practice requires replacing a blown fuse with one of identical rating and characteristics (fast-blow, time-delay) to preserve protection. Why Other Options Are Wrong: Insulated glass container and metal-ended coil describe packaging, not the protective principle. “Circuit opener” is generic and not specific. Resettable thermal switch is a different protective device (PTC/thermal breaker), not a fusible link. Common Pitfalls: Confusing the fuse's housing with its protective element or substituting oversized fuses, which defeats protection. Final Answer: fusible wire link

Question 19

According to Ohm’s law in a constant-voltage circuit, what happens to the electric current when the circuit resistance decreases (all other conditions unchanged)?

Accepted Answer

Introduction / Context: Ohm’s law establishes the relationship among voltage, current, and resistance in linear circuits. Understanding how current responds to a change in resistance at constant voltage is essential for troubleshooting and safe design, including power estimation and component selection. Given Data / Assumptions: Applied voltage is constant. Resistance decreases. The conductor behaves linearly (Ohmic behavior) without temperature-induced nonlinearity. Concept / Approach: Ohm’s law states I = V / R. With voltage V fixed, current I is inversely proportional to resistance R. Therefore, reducing R increases I. This also impacts power: P = V * I = V^2 / R; as R decreases, power rises, potentially stressing components. Step-by-Step Solution: Start with I = V / R.Decrease R while holding V constant.Since I is inversely proportional to R, I must increase.Consequent effect: P = V^2 / R also increases, raising thermal stress. Verification / Alternative check: Example: V = 10 V. If R changes from 1 kΩ to 500 Ω, I changes from 10 mA to 20 mA, confirming current increases as R decreases. Why Other Options Are Wrong: “Decrease” and “remain the same” contradict I = V / R with fixed V. “Double” is only true for a specific halving of R, not a general statement. “Drop to zero” is impossible unless V is zero or an open circuit exists. Common Pitfalls: Ignoring power dissipation during resistance changes; excessive current can overheat components. Final Answer: increase

Question 20

In practical design, wirewound resistors are typically selected for applications characterized primarily by which operational condition?

Accepted Answer

Introduction / Context: Resistor technologies include carbon composition, carbon film, metal film, metal oxide, and wirewound. Selecting the correct type depends on current, power, tolerance, noise, and stability requirements. Wirewound resistors are known for their robust power handling and low resistance values. Given Data / Assumptions: We seek the main operating condition favoring wirewound construction. General-purpose electronic applications are considered. Thermal and reliability aspects matter. Concept / Approach: Wirewound resistors use a helical resistive wire on a ceramic core, enabling high wattage and the ability to handle substantial current without excessive temperature rise. They excel at low resistance values where I^2 * R losses are significant and stability under load is essential. Although they can tolerate higher voltages in some packages, their hallmark strength is current/power handling, not negative temperature coefficients (that is typical of thermistors). Step-by-Step Solution: Identify requirement: high current implies high power dissipation.Select construction: wirewound provides superior power handling and thermal mass.Confirm: manufacturers rate wirewounds at watts to tens of watts, unlike small film resistors. Verification / Alternative check: Datasheets for wirewound parts show higher wattage ratings and current capability relative to metal film of the same size, validating suitability for high-current paths and power resistors. Why Other Options Are Wrong: Negative temperature coefficient is associated with NTC thermistors, not standard wirewounds. Low power favors compact film resistors. “High voltage” can be a requirement, but long-body high-voltage resistors are typically specialized film designs; wirewound's defining trait is power/current handling. Common Pitfalls: Ignoring inductance inherent in wirewound resistors, which can affect high-frequency circuits. For RF, use noninductive types. Final Answer: high current

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