Question 1

Ohm's law implication in a series circuit: If the series current in a circuit doubles, which statement best describes the corresponding change (assume the total resistance remains constant)?

Accepted Answer

Introduction: Ohm's law connects voltage, current, and resistance. When one quantity changes, the others respond according to V = I * R. Interpreting these relationships correctly depends on stating which parameter is held constant, a common source of confusion in quick conceptual questions. Given Data / Assumptions: The circuit is series and resistive. Total resistance R_total remains constant (no component value change). The observed change is that current I doubles. Concept / Approach: With R fixed, voltage and current are directly proportional. If current increases by a factor, voltage across the same resistance must increase by the same factor to satisfy Ohm's law. Therefore, doubling current requires doubling voltage when resistance is unchanged. Step-by-Step Solution: Start with V = I * R.Let R be constant; compare states 1 and 2: V2 / V1 = (I2 * R) / (I1 * R) = I2 / I1.Given I2 = 2 * I1 → V2 / V1 = 2.Therefore, V2 = 2 * V1, i.e., the voltage doubles. Verification / Alternative check: Numeric example: R = 100 Ω. If I1 = 0.5 A → V1 = 50 V. Doubling current to I2 = 1.0 A requires V2 = 100 V, exactly double, confirming the rule when R is fixed. Why Other Options Are Wrong: resistance is halved / resistance is doubled: Resistance is a physical property unless changed; assumption states R is constant. voltage is reduced: Contradicts direct proportionality when R is constant. power is halved: Power P = V * I; if both V and I double (R fixed), power quadruples, not halves. Common Pitfalls: Answering 'resistance is halved' by implicitly assuming a constant-voltage source without reading the assumption about constant R; the question here specifies R constant and asks what must change. Ignoring that multiple scenarios can produce the same current change; always check which parameter is constrained. Final Answer: voltage is doubled

Question 2

Basic circuit interpretation (DC): How do you recognize a series circuit in a schematic drawing? Choose the description that correctly captures how the components are connected end-to-end so that only one path exists for current.

Accepted Answer

Introduction / Context: Being able to visually recognize a series circuit from a schematic is a core skill in basic electronics. In a true series connection, all components share the same current because there is exactly one path for charge flow. This recognition helps with applying Ohm’s law, calculating total resistance, and predicting voltage drops. Given Data / Assumptions: We refer to ideal DC schematics with standard symbols. A “series circuit” means one continuous path for current through all elements. Drawing orientation (horizontal/vertical/diagonal) has no electrical meaning by itself. Concept / Approach: In series circuits, components are connected end to end, forming a single loop. The same current flows through each element, while voltages across the elements can differ and add to the source voltage. The spatial direction on the page is irrelevant; what matters is connectivity—one and only one current path. Step-by-Step Solution: Identify the path between the source terminals.Check that every component lies along this single path without branching nodes.Conclude that an end-to-end “string” of components defines a series circuit regardless of drawing orientation. Verification / Alternative check: Trace with a pencil from the positive source terminal to the negative terminal. If you encounter each component exactly once and never face a branch, the circuit is series. Any junction offering two different current routes would make it partly or wholly parallel. Why Other Options Are Wrong: Diagonally / horizontally / vertically: Orientation on paper is cosmetic; it doesn’t determine series behavior. Common Pitfalls: Mistaking neat alignment for series connection. Always evaluate node connectivity, not drawing style. Final Answer: end to end in a "string"

Question 3

Series resistors: What determines the total (equivalent) resistance of a series circuit containing multiple resistors?

Accepted Answer

Introduction / Context: Total resistance in series is a foundational topic used whenever we analyze current flow, power dissipation, or voltage division across components in one path. Getting this right enables quick back-of-the-envelope calculations and safe component selection. Given Data / Assumptions: Ideal resistors connected end to end (series). Single-path current (same current through each element). Ohm’s law applies: V = I * R. Concept / Approach: In series, each resistor drops some voltage equal to I * R_i. The source must supply the sum of all drops. Therefore the equivalent series resistance R_total is the arithmetic sum of the individual resistances: R_total = R1 + R2 + ... + Rn. This directly follows from KVL (sum of voltage rises equals sum of drops around a loop). Step-by-Step Solution: Write KVL: V_source = I * R1 + I * R2 + ... + I * Rn.Factor current: V_source = I * (R1 + R2 + ... + Rn).Define R_total = R1 + R2 + ... + Rn → V_source = I * R_total. Verification / Alternative check: Measure with an ohmmeter across the string: reading equals the sum of individual ohmmeter readings taken separately, confirming the additive property of series resistors. Why Other Options Are Wrong: Largest/minus/smallest: These rules of thumb do not apply in series; all values contribute linearly. Common Pitfalls: Confusing series (add R) with parallel (add conductances). In parallel the smallest resistor dominates; in series every resistor adds to the total. Final Answer: the sum of the resistors

Question 4

Source stacking: Two DC supplies of 5 V and 16 V are connected in series-opposing. What is the resulting total voltage seen by the load?

Accepted Answer

Introduction / Context: Combining voltage sources in series is common in test setups and battery packs. Whether sources are series-aiding or series-opposing determines the net voltage delivered to the circuit. Understanding the sign convention prevents accidental under- or over-voltage conditions. Given Data / Assumptions: Ideal DC sources: 5 V and 16 V. Series-opposing orientation (polarities oppose). No internal resistance considered (idealization). Concept / Approach: For series-aiding, voltages add. For series-opposing, the net is the difference between magnitudes, with the sign of the larger source. Thus total magnitude = |16 − 5| = 11 V, polarity following the 16 V source orientation. Step-by-Step Solution: Identify opposing: one source is reversed relative to the other.Compute magnitude: 16 − 5 = 11 V.Assign polarity: direction of the larger (16 V) dominates the net. Verification / Alternative check: Apply KVL around the loop, summing rises and drops with proper signs; the algebra yields a net of +11 V in the larger source polarity. Why Other Options Are Wrong: 16 V or 21 V: 16 V would ignore the 5 V opposing source; 21 V is for series-aiding. 80 V: Not related; likely a distractor. Common Pitfalls: Confusing aiding vs opposing and forgetting to consider polarity when stacking sources. Final Answer: 11 V

Question 5

Series voltage division: In a series circuit, two resistors show equal voltage drops. What does this indicate about the resistor values?

Accepted Answer

Introduction / Context: Voltage division in a series string distributes the source voltage in proportion to the resistances. Observing equal drops can be used as a diagnostic to infer component equality or to spot faults in measurement setups. Given Data / Assumptions: Two resistors in series with the same current flowing through each. Measured voltage drops across each resistor are equal. Resistors are ideal (no tolerance or temperature effects considered). Concept / Approach: In series, V_i = I * R_i. With the same current I through both, equality of voltages implies equality of resistances: V1 = V2 ⇒ IR1 = IR2 ⇒ R1 = R2. Therefore identical voltage drops indicate equal resistor values (within measurement accuracy). Step-by-Step Solution: State voltage division: V1 = I * R1, V2 = I * R2.Given V1 = V2 with same I → R1 = R2.Conclude resistors are equal in value. Verification / Alternative check: Swap the positions of the resistors; equal drops will persist if their values are equal, confirming the inference. Why Other Options Are Wrong: Parallel: Not applicable; the circuit is series. Unequal value / voltage doubled: Both contradict the given equal drops and series current rule. Common Pitfalls: Overlooking meter loading or tolerance; in real labs, small differences may exist due to 1–5% tolerance parts. Final Answer: they are of equal value

Question 6

Power fundamentals: Choose the best definition of electrical power in physics and electronics.

Accepted Answer

Introduction / Context: Power connects energy and time. In circuits it determines heating, sizing of supplies, and efficiency. Knowing the correct definition helps relate formulas like P = V * I and P = I^2 * R back to physical meaning. Given Data / Assumptions: Standard physics definitions. Energy measured in joules (J), time in seconds (s), power in watts (W). Electrical work equals charge moved times potential difference. Concept / Approach: Power is the time rate of doing work or transferring energy. Mathematically: P = dW/dt or P = dE/dt. In steady DC circuits, it reduces to algebraic forms like P = V * I because work per unit charge is V and charge per unit time is I. Step-by-Step Solution: Start from definition: P = dE/dt.For electrical systems: E transferred each second by current at voltage V equals V * I.Relate to other forms: P = I^2 * R or P = V^2 / R derived from Ohm’s law. Verification / Alternative check: Unit analysis: V * A = (J/C) * (C/s) = J/s = W, confirming consistency. Why Other Options Are Wrong: Work: That is energy, not its time rate. Conversion of energy: Too vague; power quantifies the rate of conversion. Joules: A unit of energy, not power. Common Pitfalls: Confusing energy with power; using watt-hours (energy) when watts (power) are intended. Final Answer: the rate at which work is done

Question 7

Series drop with a lamp: An 8 Ω resistor is in series with a lamp. The circuit current is 1 A and the applied supply is 20 V DC. What voltage is available across the lamp?

Accepted Answer

Introduction / Context: Series circuits share the same current, but sources divide their voltage among components according to their resistances. This practical problem shows how a series “dropping resistor” reduces the voltage applied to a lamp—useful for quick design checks and troubleshooting. Given Data / Assumptions: Resistor R = 8 Ω in series with a lamp. Current I = 1 A through the series path. Supply voltage V_s = 20 V DC. Lamp modeled as a load that takes the remaining voltage. Concept / Approach: Use Ohm’s law to find the resistor’s voltage drop, then subtract from the source to find the lamp voltage. In any series loop, V_s = V_R + V_lamp. With known I and R, V_R = I * R. Step-by-Step Solution: Compute resistor drop: V_R = I * R = 1 A * 8 Ω = 8 V.Apply KVL: V_lamp = V_s − V_R = 20 V − 8 V.Result: V_lamp = 12 V. Verification / Alternative check: Power check: P_R = I^2 * R = 1^2 * 8 = 8 W; P_lamp = V_lamp * I = 12 * 1 = 12 W; total 8 W + 12 W = 20 W = V_s * I, confirming consistency. Why Other Options Are Wrong: 4 V or 8 V: 8 V is the resistor drop, not the lamp. 4 V is unsupported by the data. 20 V: Would be true only with no series resistor drop (not our case). Common Pitfalls: Forgetting that the same current flows through both elements; mixing up which voltage belongs to which component. Final Answer: 12 V

Question 8

Ideal source behavior: When a battery is connected to a purely series circuit, the current it delivers depends primarily on which single factor?

Accepted Answer

Introduction / Context: Ohm’s law gives a direct relationship among voltage, current, and resistance in simple DC circuits. Recognizing what sets the current helps with power budgeting, fuse sizing, and verifying whether a design will overload a source. Given Data / Assumptions: Ideal battery providing a fixed DC voltage. All elements are in series (single path for current). No internal resistance or nonlinearities considered for the basic principle. Concept / Approach: For an ideal source of voltage V connected to a series resistance R_total, the current is I = V / R_total. Polarity sets direction, not magnitude. Terms such as “primary/secondary” relate to transformers, not DC sources. “Average resistance” is not an electrical parameter; only the algebraic sum matters in series. Step-by-Step Solution: Compute total resistance: R_total = R1 + R2 + ... + Rn.Apply Ohm’s law: I = V / R_total.Conclude that current depends solely on total resistance for a fixed V. Verification / Alternative check: Measure current while adding another series resistor; current decreases according to I_new = V / (R_total + ΔR), confirming dependence on total resistance. Why Other Options Are Wrong: Primary/secondary difference: Not applicable to simple battery circuits. Polarity connections: Affect direction of current, not magnitude for given R_total. Average resistance: Not an electrical standard; magnitude is set by the true total. Common Pitfalls: Ignoring internal battery resistance in real life; while small, it can limit current. The ideal model still teaches the governing dependency. Final Answer: total resistance

Question 9

Ohm’s law in a series circuit: If the total resistance in a series circuit doubles while the applied source voltage remains constant, how will the circuit current change?

Accepted Answer

Introduction / Context: This question tests core understanding of Ohm’s law and how current behaves in a simple series circuit when total resistance changes. In many troubleshooting and design scenarios, recognizing proportional relationships between current, resistance, and voltage is essential for quick, reliable reasoning. Given Data / Assumptions: Total resistance in a series circuit doubles. The source (supply) voltage is constant. Ideal components with no temperature-induced resistance change during comparison. Single-loop series circuit so one current flows through all elements. Concept / Approach: Ohm’s law states I = V / R. If V is constant and R increases, I must decrease proportionally. Specifically, if R becomes 2R, then I becomes V / (2R) = (1/2) * (V / R). Thus current is halved. This inverse proportionality between current and resistance at fixed voltage is a cornerstone of basic circuit analysis. Step-by-Step Solution: Initial current: I1 = V / R_total.After doubling resistance: R_new = 2 * R_total.New current: I2 = V / R_new = V / (2 * R_total) = (1/2) * (V / R_total).Therefore, I2 = I1 / 2, i.e., the current is halved. Verification / Alternative check: Use numerical example. Let V = 10 V and R_total = 100 Ω → I1 = 10 / 100 = 0.1 A. If resistance doubles to 200 Ω → I2 = 10 / 200 = 0.05 A, exactly half. The numerical check confirms the proportional reasoning. Why Other Options Are Wrong: Be the same: would require resistance unchanged or voltage doubled to compensate; not our case.Be doubled: happens if resistance halves at constant voltage, not when it doubles.Reduce source voltage: the source voltage is given as constant; the current change does not “reduce” the source. Common Pitfalls: Confusing proportional and inverse proportional relationships. Remember: at constant V, current varies inversely with resistance (I ∝ 1/R). At constant R, current varies directly with voltage (I ∝ V). Final Answer: be halved

Question 10

Series circuit open-circuit measurement: A 20 V DC source supplies an 8 Ω resistor in series with a lamp. If the lamp is removed (leaving an open circuit at the lamp socket), what voltage will a voltmeter read across the lamp socket terminals?

Accepted Answer

Introduction / Context: Measuring voltages in series circuits requires understanding where drops occur. When a component is removed, the circuit may become open, changing how voltage is distributed. This question reinforces the concept that with zero current, resistive drops vanish and the source appears across the open terminals. Given Data / Assumptions: DC source voltage: 20 V. Series elements: 8 Ω resistor and a lamp originally in series. The lamp is removed, creating an open circuit at the lamp socket. Voltmeter has ideally infinite input resistance and is connected across the lamp socket. Concept / Approach: Ohm’s law dictates the voltage drop across a resistor is V_R = I * R. In an open circuit, the loop current I is zero. Therefore, the drop across the 8 Ω resistor becomes 0 V, and the entire source voltage appears across the open terminals (the lamp socket). Step-by-Step Solution: Lamp removed → circuit open → I = 0 A.Resistor drop: V_R = I * R = 0 * 8 = 0 V.KVL around loop: source 20 V must appear across the only remaining break → lamp socket sees 20 V.Voltmeter reading across lamp socket = 20 V. Verification / Alternative check: Model the lamp socket as two open terminals. With no closed path, current is zero. Any series resistive element has zero drop, leaving the full source across the open—consistent with standard open-circuit behavior. Why Other Options Are Wrong: 0 V: would require a short across the socket, not an open.8 V or 12 V: arbitrary partial drops contradict zero-current condition (no drop across finite resistance with I = 0). Common Pitfalls: Forgetting that voltmeters do not provide a current path. A high-impedance meter does not “close” the circuit; thus no current flows and no series drop occurs. Final Answer: 20 V

Question 11

Flashlight battery polarity: A flashlight uses three 1.5 V cells in series. If one cell is inserted backward (reverse polarity), what happens to the flashlight output?

Accepted Answer

Introduction / Context: Series battery stacks add voltages algebraically, taking polarity into account. Many small flashlights are designed for three 1.5 V cells (nominal 4.5 V) to drive a bulb or LED plus driver. Reversing one cell changes the net series sum and can prevent operation entirely. Given Data / Assumptions: Three cells rated 1.5 V each, intended to be in series and oriented correctly. One cell is reversed, contributing negative polarity relative to the others. Flashlight electronics (bulb/LED driver) expect approximately 4.5 V. Idealized cells assumed for the polarity-sum explanation. Concept / Approach: Series voltages add with sign. With correct orientation, V_total = 1.5 + 1.5 + 1.5 = 4.5 V. With one reversed, V_total = 1.5 + 1.5 − 1.5 = 1.5 V. Most lamps or driver circuits designed for ~4.5 V will not operate properly at ~1.5 V; an incandescent filament may not glow perceptibly, and many LED drivers have undervoltage lockout or cannot maintain current regulation. Step-by-Step Solution: Compute nominal: three cells correct → 4.5 V.Reverse one cell: algebraic sum → 1.5 V total.Compare to required operating voltage: 1.5 V is far below design point.Conclusion: no visible output; flashlight is effectively off. Verification / Alternative check: Practical test: a 4.5 V incandescent bulb at 1.5 V draws much less current and produces negligible light; an LED driver typically shuts down under low input voltage. Both cases appear “off” to a user. Why Other Options Are Wrong: Brighter than normal / the same: contradict the reduced supply voltage.Dimmer than normal: while technically some small glow could occur with simple bulbs, in typical products the result is functionally off; the robust answer is off. Common Pitfalls: Ignoring polarity in series stacks. One reversed cell subtracts from the total, and in some electronics can also stress protection circuitry due to reverse biasing. Final Answer: off

Question 12

Voltage division in series: A 45 V DC source is applied to a series network with total resistance 3300 Ω. If one of the resistors, R3, is 1200 Ω, what is the voltage drop across R3?

Accepted Answer

Introduction / Context: Voltage division in series circuits is a fundamental technique for predicting how a source voltage distributes across individual elements. This problem directly applies the voltage divider rule to determine the drop across one known resistor when total resistance and source voltage are given. Given Data / Assumptions: Total series resistance, R_total = 3300 Ω. Source voltage, V_s = 45 V DC. Target resistor, R3 = 1200 Ω (in series). Ideal resistors; no additional elements. Concept / Approach: For series circuits, current I is the same through all resistors: I = V_s / R_total. The voltage across any resistor R_x is V_x = I * R_x. Combining, V_x = V_s * (R_x / R_total). This is the standard voltage divider formula. Step-by-Step Solution: Compute the ratio: R3 / R_total = 1200 / 3300 = 0.363636…Apply divider: V_R3 = 45 * 0.363636…Multiply: 45 * 0.363636… = 16.3636… V.Round sensibly to two decimals: V_R3 ≈ 16.36 V. Verification / Alternative check: Current method: I = 45 / 3300 = 0.013636… A. Then V_R3 = I * 1200 = 0.013636… * 1200 = 16.3636… V. Both methods agree. Why Other Options Are Wrong: 32.72 V: would correspond to a much larger fraction (about 0.727) not matching 1200/3300.10.90 V: too small; implies R3 is roughly 800 Ω of the total, which it is not.15.00 V: a rounded guess, not the precise divider result. Common Pitfalls: Forgetting that only series elements share the same current; mixing up series and parallel results leads to incorrect voltage predictions. Ensure total resistance includes all series elements when using the divider rule. Final Answer: 16.36 V

Question 13

Series resistors — evaluating the claim: “Total series resistance equals the difference between largest and smallest resistor.” Is this statement true or false?

Accepted Answer

Introduction / Context: This item checks fundamental circuit theory for series connections. In series, the same current flows through each element, and resistances combine in a straightforward way. Misconceptions here can cascade into errors in power dissipation and voltage-divider design. Given Data / Assumptions: N resistors R1, R2, …, RN connected in series. Ideal components (no temperature coefficients or parasitics considered). Concept / Approach: The equivalent resistance of series elements is the sum of their resistances because voltage drops add while current is common: R_eq = R1 + R2 + … + RN. A “difference between largest and smallest” (R_max − R_min) ignores the contribution of intermediate elements and is physically unjustified except in trivial corner cases that still do not generalize. Step-by-Step Solution: State series rule: R_eq = sum over all individual resistances.Counterexample: with 2 Ω, 5 Ω, 8 Ω in series, R_eq = 2 + 5 + 8 = 15 Ω; R_max − R_min = 8 − 2 = 6 Ω, not equal to 15 Ω.Explain why: each resistor adds an incremental voltage drop at the same current, so contributions are additive, not canceling. Verification / Alternative check: Measure total resistance with an ohmmeter across the series string—the reading is the arithmetic sum. Kirchhoff’s Voltage Law likewise confirms additive drops around the loop. Why Other Options Are Wrong: Choosing “True” contradicts both KVL and the definition of resistance in series. Common Pitfalls: Confusing series and parallel formulas; mistakenly subtracting because voltage drops can oppose in some AC phasor contexts (which is not applicable to purely resistive DC series networks). Final Answer: False

Question 14

Source connections — interpreting “series opposing” polarity Does the term “series opposing” mean that sources are in series with opposite polarities?

Accepted Answer

Introduction / Context: When combining independent sources, polarity/orientation dictates the net voltage. The phrase “series aiding” or “series opposing” commonly appears in power systems, batteries, and signal sources connected in series. Understanding it prevents wiring mistakes and miscomputed net voltages. Given Data / Assumptions: Two or more ideal voltage sources placed in series. Polarity marks (+/−) referenced consistently along the loop. Concept / Approach: “Series opposing” explicitly means the sources are oriented so that one’s positive terminal faces the other’s positive (or one negative faces the other negative) along the series path, causing their voltages to subtract. Conversely, “series aiding” places opposite terminals together so voltages add. The resultant source equals algebraic sum with sign set by assumed current/loop orientation. Step-by-Step Solution: Let V1 and V2 be source magnitudes; choose loop orientation.Wire “opposing”: + of V1 to + of V2 (or − to −).Net voltage V_net = ±(V1 − V2) depending on orientation; magnitude equals |V1 − V2| when exactly opposing. Verification / Alternative check: Apply KVL around the loop; voltage rises and drops corresponding to source polarities yield subtraction for opposing orientation. Why Other Options Are Wrong: Answering “False” would deny the standard definition used in texts and manufacturer battery-pack guidelines. Common Pitfalls: Reversing a cell inadvertently in a battery string—this forces the pack to work against itself and can overheat the reversed cell; always verify polarity labels. Final Answer: True

Question 15

Series circuits and current: Does a series network function as a current divider?  Consider a basic direct-current (DC) series circuit with two or more resistors connected end-to-end and powered by an ideal voltage source. Evaluate whether such a se…

Accepted Answer

Introduction / Context: Students often confuse the behaviors of series and parallel connections. This item probes whether a series circuit acts as a current divider, which is a foundational distinction in circuit analysis and troubleshooting. Given Data / Assumptions: Ideal DC source with negligible internal resistance. Two or more passive elements (e.g., resistors) connected strictly in series. Steady-state DC (no transient analysis required). Concept / Approach: A current divider is a network that splits a total current into branches according to branch impedances. By definition, current division requires multiple parallel paths. In a pure series circuit, there is only a single path for charge flow; therefore, the same current must pass through every element. Step-by-Step Solution: Identify topology: series → single continuous path.Apply charge conservation: electrons that leave the source must pass sequentially through each element.Use Ohm’s law and KCL: series path enforces identical current at every point along that path.Conclude: no branching → no current division; instead, voltages divide across elements (voltage divider). Verification / Alternative check: Compute a simple example: two series resistors R1 and R2 across V. The branch count is one. The current I = V / (R1 + R2) flows through both resistors identically. By contrast, for parallel resistors, I splits as I1 = V / R1 and I2 = V / R2, exhibiting true current division. Why Other Options Are Wrong: “True” contradicts the requirement of multiple paths for current division. “Only if the source is AC and not DC” is irrelevant; topology, not waveform, governs division. “Only when all component values are equal” still yields identical current, not divided paths. “Reactive components” do not create parallel branches by themselves. Common Pitfalls: Confusing voltage division (series) with current division (parallel). Another pitfall is assuming component value differences in series change current in individual elements; they only change individual voltage drops. Final Answer: False

Question 16

Faults in series circuits: Does a short circuit in a series path prevent current flow?  Analyze the effect of an unintended short (near-zero resistance connection) placed in series with other elements powered by a DC source.

Accepted Answer

Introduction / Context: Mistaking the effect of a short in a series circuit is common. This question checks whether learners understand that a short generally lowers resistance and increases current, rather than preventing it. Given Data / Assumptions: DC steady-state operation. An “ideal short” means resistance approaching zero. Components are in series unless a fault bridges across something. Concept / Approach: In series networks, total resistance RT is the sum of element resistances. Introducing a short as a replacement for a series element reduces that element’s resistance to approximately zero, thus lowering RT and increasing current. A condition that truly prevents current is an open circuit (infinite resistance), not a short (near-zero resistance). Step-by-Step Solution: Model the shorted element: Rshort ≈ 0 Ω.Compute total resistance: RT_new = R1 + 0 + R3 + ... ≤ RT_old.Current with Ohm’s law: I_new = V / RT_new ≥ V / RT_old.Thus, current is not prevented; it usually increases, potentially to unsafe levels. Verification / Alternative check: Compare with an open: replacing an element by an open makes RT → ∞ and I → 0, which truly prevents current. Therefore, “prevents current” describes an open, not a short, in a series path. Why Other Options Are Wrong: “True” confuses short with open. Polarity reversal does not convert a short to an open; current direction changes sign but still flows. “Only when the short is across the source terminals” actually creates extremely large current, still not zero (though it is a dangerous fault). AC/reactive specifics do not change the fundamental effect of a short’s very low impedance. Common Pitfalls: Assuming “fault” automatically means no current. Shorts can cause excessive current and damage rather than interruption. Final Answer: False

Question 17

Uniform current in series circuits: If you know the current at any one point, do you know the current everywhere in that same series loop?  Evaluate this statement for an ideal DC series network with no branching.

Accepted Answer

Introduction / Context: Consistency of current in series networks is a cornerstone of circuit analysis. This question tests recognition that a series loop provides exactly one path for charge, enforcing the same current through each element. Given Data / Assumptions: Ideal DC conditions with a single closed loop (no parallel branches). Lumped elements; wire resistance may be small but forms part of the single path. Steady state (no transient capacitive/inductive effects considered). Concept / Approach: Kirchhoff’s Current Law (KCL) states that current entering a node equals current leaving it. In a series path, every node connects to exactly two elements, so the same current must flow from element to element. Ohm’s law then determines individual voltage drops based on that same current and each resistance value. Step-by-Step Solution: Recognize topology: exactly one continuous path for charge.Apply KCL at any junction: I_in = I_out → currents are identical in magnitude throughout the loop.Use Ohm’s law locally: V_k = I * R_k for each element k; voltages vary, current does not.Therefore, measuring the loop current once suffices to know it everywhere along that loop. Verification / Alternative check: Numeric example: with R1 = 1 kΩ and R2 = 3 kΩ in series across 8 V, I = 8 / 4000 = 2 mA flows through both resistors. Voltage drops differ (2 V and 6 V), but current remains 2 mA in each component and wire segment. Why Other Options Are Wrong: Equal resistor values are unnecessary; current equality does not depend on value matching. AC steady-state series circuits also have the same current through all series impedances. Nonzero wire resistance does not break current continuity; it simply adds to the series impedance. Common Pitfalls: Confusing current uniformity with voltage distribution. In series, current is uniform; voltage divides according to resistance or impedance. Final Answer: True

Question 18

Voltage is relative: Is the voltage at one point in a circuit always measured with respect to another reference point?  Clarify the meaning of “voltage at a node” by considering reference selection (e.g., ground).

Accepted Answer

Introduction / Context: Voltage is not an absolute quantity; it is the electrical potential difference between two points. This question checks understanding of reference selection (ground) and why voltmeters have two terminals. Given Data / Assumptions: Any practical measurement uses a two-terminal instrument (voltmeter, oscilloscope probe with ground clip). The circuit may or may not be earthed; a local reference (circuit common) still exists. Applies to both DC and AC analysis. Concept / Approach: “Voltage at node A” implicitly means “voltage of node A relative to a defined reference node,” commonly called ground (0 V). Without specifying the second point, the phrase is incomplete. Instruments measure potential difference: V_AB = potential(A) − potential(B). Step-by-Step Solution: Define a reference node (ground) and set its potential to 0 V by convention.Express any other node voltage as V_node = potential(node) − potential(reference).Recognize instrument behavior: a voltmeter’s leads connect to two points, reporting their difference.Therefore, every voltage reading is inherently relative to another node. Verification / Alternative check: On an oscilloscope, moving the ground clip changes the displayed “zero” baseline because the reference changes. SPICE simulations also require selecting a reference node for nodal analysis to compute node voltages. Why Other Options Are Wrong: “False” assumes voltage is absolute; it is not. Limiting the principle to DC or only across passive components is incorrect; potential difference is universal. Earth ground is optional; a floating system still measures voltages relative to a chosen reference node. Common Pitfalls: Confusing “ground” with safety earth. In many devices, circuit common is isolated and chosen for analysis without earth bonding. Final Answer: True

Question 19

Power in series networks: Are individual element powers additive to give the total power consumed from the source?  Consider a DC series circuit with multiple resistive elements and an ideal voltage source.

Accepted Answer

Introduction / Context: Power accounting is essential for thermal design and energy budgeting. This question asks whether the total power drawn equals the sum of powers dissipated by each element in a series path. Given Data / Assumptions: Steady-state DC with resistive elements. No energy storage or conversion elsewhere (no ideal lossless transformers or active sources inside the series chain). Ideal source with negligible internal resistance (or internal resistance treated as an additional series element). Concept / Approach: Conservation of energy dictates that input electrical power from the source equals the total power dissipated as heat in resistors (and any other elements that consume power). For each element, Pk = Vk * Ik = I^2 * Rk in series (same I). The source delivers P_total = V_source * I. Since V_source = Σ Vk, it follows that P_total = Σ (Vk * I) = Σ Pk. Step-by-Step Solution: Compute the series current: I = V_source / ΣR.Find each element’s drop: Vk = I * Rk.Element power: Pk = I^2 * Rk.Total power: ΣPk = I^2 * ΣR = (V_source^2) / (ΣR) = V_source * I, matching the source power. Verification / Alternative check: Numerical check: with R1 = 100 Ω and R2 = 300 Ω across 20 V, I = 20 / 400 = 0.05 A. P1 = I^2 * 100 = 0.25 W, P2 = I^2 * 300 = 0.75 W. ΣPk = 1.0 W. Source power = V * I = 20 * 0.05 = 1.0 W, confirming additivity. Why Other Options Are Wrong: Equality of drops or resistor values is unnecessary; power still sums. AC caveat: when averaged over a cycle, the same conservation holds for passive elements; DC was assumed for simplicity. Common Pitfalls: Mixing instantaneous versus average power in AC; however, the additive property still holds for passive components when power is computed consistently. Final Answer: True

Question 20

Source combinations: Does “series aiding” correctly describe two voltage sources connected in series with the same polarity so their voltages add?  Assess the terminology used for combining DC sources.

Accepted Answer

Introduction / Context: Engineers frequently combine sources to obtain a desired voltage. The terms “series aiding” and “series opposing” describe polarity relationships. This question tests recognition of correct terminology and effect. Given Data / Assumptions: Two DC voltage sources connected in series. Polarity marks available to establish orientation. Ideal sources or sources with small internal resistance compared to the load. Concept / Approach: When sources are connected such that the positive terminal of one connects to the negative terminal of the next and their labeled polarities are oriented to produce additive rises around the loop, the total series voltage equals the algebraic sum of individual voltages. This orientation is called “series aiding.” If the polarities oppose, the net voltage equals the difference (series opposing). Step-by-Step Solution: Define source orientations with polarity signs.Traverse the loop and algebraically add rises/drops.If both sources present rises in the same direction, V_total = V1 + V2 (series aiding).Therefore, the terminology “series aiding” accurately describes same-polarity addition. Verification / Alternative check: Example: two 9 V batteries placed plus-to-minus produce 18 V overall to the load when their polarities aid. Reversing one battery yields approximately 0 V net (neglecting internal resistance), the series-opposing case. Why Other Options Are Wrong: Requirement of equal voltages is unnecessary; 5 V and 3 V still add to 8 V when aiding. Involving a current source is irrelevant; the term describes voltage sources. Applicability is not limited to AC or DC; it is a general polarity concept. Common Pitfalls: Miswiring polarities so the intended aiding becomes opposing. Always verify with polarity marks and a loop traversal using Kirchhoff’s Voltage Law. Final Answer: True

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