Question 1

Voltage division: Does any simple series circuit act as a voltage divider across its series elements?  Interpret the phrase “voltage divider” for a resistive series network driven by a DC source.

Accepted Answer

Introduction / Context: Voltage dividers are ubiquitous in sensing, biasing, and signal-level adjustment. Recognizing that any resistive series chain divides the applied voltage in proportion to element resistances is essential. Given Data / Assumptions: Two or more resistors in series across a DC source. Load, if present, is assumed sufficiently high not to disturb the ideal divider (or we consider the unloaded case). Steady-state DC. Concept / Approach: In a series chain carrying current I, each resistor Rk develops a voltage drop Vk = I * Rk. Because I is the same through all series elements, the drops are proportional to their resistances. The total source voltage equals the sum of these drops. This proportionality is exactly what is meant by a “voltage divider.” Step-by-Step Solution: Compute series current: I = V_source / ΣR.Element drop: Vk = I * Rk = V_source * (Rk / ΣR).Voltage division rule: Vk / V_source = Rk / ΣR.Therefore, any resistive series network divides voltage according to resistor ratios. Verification / Alternative check: Example: R1 = 1 kΩ, R2 = 3 kΩ across 8 V. Drops are V1 = 8 * (1/4) = 2 V and V2 = 8 * (3/4) = 6 V. Ratio matches resistances 1:3, confirming divider behavior. Why Other Options Are Wrong: Equal values are not required; the divider works for any positive resistances. Knowing current is convenient but not a prerequisite; the divider formula directly uses ratios. AC/DC distinction is irrelevant for resistors; the principle holds for steady-state AC magnitudes too (ignoring reactive loading). Common Pitfalls: Ignoring loading: connecting a low-impedance load to the tap changes the effective lower resistance and the division ratio. Use Thevenin equivalents to model divider output under load. Final Answer: True

Question 2

Kirchhoff’s Voltage Law (KVL): In any single closed loop, is the algebraic sum of all voltages equal to zero?  Interpret “sum around the loop” to include both rises and drops with sign.

Accepted Answer

Introduction / Context: Kirchhoff’s Voltage Law (KVL) is a fundamental law derived from energy conservation and electrostatic fields in lumped circuits. It states that the algebraic sum of voltages around any closed path is zero. Given Data / Assumptions: Lumped-circuit model applies; electromagnetic radiation and time-varying magnetic coupling are negligible for the loop in question. Voltages are summed algebraically, with rises taken as positive and drops as negative (or vice versa consistently). Applies to DC and AC steady-state analysis. Concept / Approach: Voltage is potential difference. Traversing a closed loop and summing all potential rises and drops should return to the starting potential, yielding a net sum of zero. If sources are present, the sum of drops equals the sum of rises; representing rises with opposite sign leads to a zero total. Step-by-Step Solution: Choose a loop direction and sign convention.Record each element’s voltage as +V (rise) or −V (drop) consistent with polarity.Sum all terms: ΣV_loop = 0.Interpretation: energy gained from sources equals energy lost in elements over one loop traversal. Verification / Alternative check: Example: A loop with a 10 V source and two drops of 6 V and 4 V. Algebraic sum is +10 − 6 − 4 = 0. Alternatively, “sum of drops equals source,” which is the same statement rearranged. Why Other Options Are Wrong: “False” ignores energy conservation in lumped circuits. Limiting KVL to DC is incorrect; it applies in AC circuit theory as well. Component equality or absence of sources is irrelevant; KVL still holds when properly signed. Common Pitfalls: Misreading “sum of drops” (all positive) as zero. The correct version is the algebraic sum (rises and drops with signs) equals zero. Maintain consistent polarity marking to avoid sign errors. Final Answer: True

Question 3

Series circuits — definition check without a diagram: A correct identification rule is: “Two components are in series if the same current flows through both, sharing a single uninterrupted path with only one common node between them.” Evaluate this …

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Introduction / Context: Many textbook questions rely on a figure to decide whether components are in series or parallel. Applying the Recovery-First Policy, we remove the dependency on a missing diagram and test the core definition instead. Knowing the precise topological rule lets you identify series connections in any circuit drawing. Given Data / Assumptions: Ideal wires and lumped components. No branching between the two devices under test. Current continuity is the criterion, not physical proximity. Concept / Approach: Components are in series if the same current must pass through them sequentially because there is only one path for current flow. This means the junction between them connects to nothing else (no additional branches). Parallel elements instead share the same two nodes and therefore the same voltage, not necessarily the same current. The series criterion is independent of component values and source type (DC or AC). Step-by-Step Solution: Check for branching between the two components—there should be none.Confirm that the current entering the first must exit through the second.Verify that they do not share the same two nodes (that would be parallel).Conclude the provided rule correctly defines a series connection. Verification / Alternative check: Apply Kirchhoff’s laws: the same branch current flows through series components; voltages add according to Ohm’s law, consistent with the definition. Why Other Options Are Wrong: Incorrect: Conflicts with the standard topological definition. Applies only to DC: AC behavior still follows the same series topology. Valid only if resistances equal: Series status does not depend on values. Depends on supply polarity: Polarity does not change network topology. Common Pitfalls: Judging by physical layout instead of connectivity; mistaking a node with hidden branches for a pure series junction; assuming equal current implies equal voltage (it does not). Final Answer: Correct

Question 4

Measurement reference — definition of ground: In practical electronic circuits, “ground” (or reference) is the node against which all other voltages are measured. Decide whether this statement accurately describes ground.

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Introduction / Context: Voltage is inherently a difference in electric potential between two points. To report a single number for “the voltage” at a node, engineers choose a reference node—commonly called ground (GND). Understanding that ground is a reference, not always literally the Earth, is essential for measurement, safety, and PCB design. Given Data / Assumptions: Ground refers to the designated reference node in the circuit schematic. Measuring instruments report V_node = V(node) - V(ground). Earth bonding may or may not be used depending on system class. Concept / Approach: Ground provides a common return path and a reference potential for signals and supplies. In many systems there are multiple grounds (analog, digital, chassis) that are tied at a single point. Whether connected to Earth or not, the chosen ground serves as the zero-volt reference for measurements and specifications throughout the circuit. Step-by-Step Solution: Identify the reference node on the schematic (usually the ground symbol).Understand that meter black lead connects to ground to measure node voltages.Recognize that absolute potential is not required; only differences matter.Conclude that defining ground as the measurement reference is accurate. Verification / Alternative check: Oscilloscope probes and DMMs default to ground-referenced measurements; datasheets specify output “with respect to GND,” confirming the definition in practice. Why Other Options Are Wrong: Incorrect: Ground is indeed the reference node by definition. True only for earth-grounded systems / AC power circuits / metal chassis: Ground as a reference applies irrespective of earthing method or enclosure material. Common Pitfalls: Assuming ground always equals Earth potential; mixing up safety ground, chassis ground, and signal return; creating ground loops by multiple bonding points. Final Answer: Correct

Question 5

Series resistors — quick sum check: If 7.3 kΩ, 1.8 kΩ, and 4.9 kΩ resistors are connected in series, is the total resistance equal to 14 kΩ? Verify the claim using series-resistance rules.

Accepted Answer

Introduction / Context: Being able to sanity-check series resistor totals quickly is invaluable for design and troubleshooting. Series combinations add directly because the same current flows through each resistor and each contributes its share of voltage drop. This problem asks you to confirm a specific numerical claim for three common E24 values. Given Data / Assumptions: Resistor values: 7.3 kΩ, 1.8 kΩ, 4.9 kΩ. Series connection: same current through all three resistors. Ideal components; tolerance effects ignored for the conceptual check. Concept / Approach: For series resistances, the equivalent resistance is the arithmetic sum: R_total = R1 + R2 + R3. Units should be consistent; since all are in kΩ, we can add directly in kΩ or convert to Ω first and convert back later. The calculation is straightforward but must be performed carefully to avoid simple arithmetic slips. Step-by-Step Solution: Write the series formula: R_total = R1 + R2 + R3.Substitute values in kΩ: R_total = 7.3 + 1.8 + 4.9 kΩ.Compute partial sum: 7.3 + 1.8 = 9.1 kΩ.Add the third value: 9.1 + 4.9 = 14.0 kΩ. Verification / Alternative check: Convert to ohms for confirmation: 7300 + 1800 + 4900 = 14,000 Ω, which equals 14 kΩ. Either way, the arithmetic agrees with the claim. Why Other Options Are Wrong: Incorrect: The sum is exactly 14 kΩ under ideal arithmetic. Valid only at 25 °C / analog meter only: Temperature and instrument type do not change the ideal series rule; tolerances might slightly vary measured values but not the nominal total. Cannot be determined without current: Equivalent resistance is independent of current magnitude. Common Pitfalls: Mistyping values (e.g., 7.3 as 7.03), mixing units (Ω vs kΩ), or mistakenly averaging instead of summing for series networks (averaging applies to some parallel intuition, not series). Final Answer: Correct

Question 6

Series circuits — assess the statement: “The total resistance of a series circuit equals the average (arithmetic mean) of all individual resistance values.” Is this claim valid for ideal series connections?

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Introduction / Context: Understanding how resistances combine is foundational for circuit analysis. In a series circuit, there is a single path for current, and each resistor shares the same current. This question challenges a common misconception: that the total series resistance equals the average of the resistor values, rather than the sum. Clarifying this point prevents systematic errors in design and troubleshooting. Given Data / Assumptions: Ideal lumped components (no parasitic effects). Resistors R1, R2, …, Rn connected in series (one current path). Goal: compare “sum” versus “average” for total resistance. Concept / Approach: Kirchhoff’s Voltage Law (KVL) states that the sum of voltage drops around a loop equals the source voltage. With a common current I in a series chain, the total voltage drop is I*R1 + I*R2 + … + I*Rn. Equating with V = I*R_total directly yields R_total = R1 + R2 + … + Rn. An average would be (R1 + … + Rn) / n, which underestimates the real series total whenever n > 1 (unless all but one are zero, which is not a useful physical case). Step-by-Step Solution: Let series resistors be R1..Rn with current I.By Ohm’s law: V_drop,k = I * Rk for each k.By KVL: V_source = I*(R1 + R2 + … + Rn).Hence R_total = (V_source / I) = R1 + R2 + … + Rn (sum, not average). Verification / Alternative check: Take a numeric example: R1 = 10 Ω, R2 = 20 Ω. Sum = 30 Ω. Average = 15 Ω. Measuring current with a fixed source shows the 30 Ω result matches I = V / 30, not V / 15, confirming that average is incorrect. Why Other Options Are Wrong: Correct: Conflicts with R_total = sum of series resistances. Applies only when all resistors are equal: Even then, the total is n*R, not the average R. Applies only below 1 kΩ: Resistance combination rules are not value-range dependent. Common Pitfalls: Confusing series (resistances add) with parallel (conductances add); thinking “average” because of evenly shared current. Series totals always add arithmetically. Final Answer: Incorrect — total series resistance is the sum, not the average.

Question 7

Series-resistance rule — for ideal resistors connected in series, how is the total resistance calculated?

Accepted Answer

Introduction / Context: Series connections appear everywhere in electronics, from simple dividers to bias networks. Knowing how to combine resistances in series enables quick current estimates and power budgeting. This item asks for the correct method to find the equivalent resistance of several resistors in series. Given Data / Assumptions: Ideal resistors R1, R2, …, Rn in series. Single current flows through all series components. Standard Ohm’s law and Kirchhoff’s laws apply. Concept / Approach: With one common current I, each resistor drops V_k = I*R_k. The source must supply the sum of these drops, so V_total = I*(R1 + R2 + … + Rn). Therefore, the equivalent resistance is R_total = V_total / I = R1 + R2 + … + Rn. This is a direct consequence of KVL and Ohm’s law in a single-loop circuit. Step-by-Step Solution: Model the series chain with current I.Write drops: V1 = I*R1, V2 = I*R2, etc.Apply KVL: V_total = V1 + V2 + … + Vn.Factor I: V_total = I*(R1 + R2 + … + Rn) → R_total = sum of R_k. Verification / Alternative check: Measure with a bench supply: doubling one resistor doubles its portion of the drop, and the net acts like one larger resistor equal to the arithmetic sum, matching calculations and meter readings. Why Other Options Are Wrong: Product over sum: That is the two-resistor parallel shortcut, not series. Average: Underestimates the true series equivalent. Reciprocal of sum of reciprocals: That is the general parallel formula. Common Pitfalls: Memorizing the parallel formula and misapplying it to series, or assuming averages apply because the current is common. In series, resistances add directly. Final Answer: Correct — add individual resistances to obtain the total series resistance.

Question 8

KVL in series networks — the sum of the individual voltage drops across series resistors must equal the total applied source voltage. Is this fundamental statement accurate?

Accepted Answer

Introduction / Context: This statement encapsulates Kirchhoff’s Voltage Law (KVL) applied to a series resistive circuit. KVL is one of the two cornerstone conservation laws for lumped circuits, ensuring energy consistency around closed loops. The item tests whether you can connect KVL to observable behavior in series resistor chains. Given Data / Assumptions: Ideal source and ideal resistors in series. Closed loop such that KVL applies. Steady-state conditions (but the principle also holds instant-by-instant in AC). Concept / Approach: KVL states the algebraic sum of voltages around any closed loop is zero. Traversing a loop with a source and series drops yields V_source − V1 − V2 − … − Vn = 0, or equivalently V_source = V1 + V2 + … + Vn. Each drop V_k follows Ohm’s law V_k = I*R_k with common current I in series. Thus the sum of the drops equals the applied source voltage regardless of individual resistor values. Step-by-Step Solution: Assume series chain R1..Rn with loop current I.Compute each drop: V_k = I*R_k.Apply KVL: V_source = Σ V_k.Therefore, the statement holds for all series networks. Verification / Alternative check: Bench test with a DMM across each resistor and across the source shows that measured drops sum to the source voltage within meter tolerance, validating KVL experimentally for DC and snapshot values in AC. Why Other Options Are Wrong: Incorrect: Violates energy conservation around the loop. Only true for DC: KVL holds for AC as an instantaneous law in lumped circuits. Only when resistors are equal: Equality is irrelevant; drops scale with R. Common Pitfalls: Sign convention mistakes when summing rises and drops; forgetting that meter polarity affects the sign, not the magnitude relation that the algebraic sum around the loop is zero. Final Answer: Correct — by KVL, individual drops sum to the applied source voltage.

Question 9

Series-aiding sources — four 9 V batteries connected in series and aiding each other produce a total of 36 V. Is this description correct for ideal sources?

Accepted Answer

Introduction / Context: Stacking voltage sources is a common way to reach higher supply rails in portable systems. When sources are connected “series-aiding,” their voltages add algebraically with the same polarity orientation. This question checks your understanding by using four identical 9 V batteries as an example. Given Data / Assumptions: Four ideal 9 V sources. Series-aiding orientation (polarity aligned head-to-tail). Neglect internal resistance for the basic calculation. Concept / Approach: For ideal voltage sources connected in series, the net voltage equals the signed sum of individual voltages. “Aiding” means all polarities line up to produce a larger resultant. Therefore, 9 V + 9 V + 9 V + 9 V = 36 V. In practice, small internal resistances cause voltage sag under load, but the open-circuit sum remains 36 V and loaded values are close if currents are modest. Step-by-Step Solution: Identify orientation: series-aiding (same polarity).Add ideal source voltages: 9 + 9 + 9 + 9 = 36 V.Conclude total: V_total = 36 V (ideal).Note real-world caveat: internal resistance introduces droop under load. Verification / Alternative check: Measure open-circuit with a DMM: approximately 36 V. Under load, compute V_load = 36 V − I * (Σ r_internal) to estimate any droop; for light loads the reading remains near 36 V. Why Other Options Are Wrong: Incorrect: Opposes the fundamental series addition rule. Correct only if internal resistance is zero: Internal resistance affects load voltage, not the ideal series summation principle. Voltages never add: They do add algebraically when sources are in series. Common Pitfalls: Confusing series-aiding with series-opposing; reversing one cell flips the algebraic sum and reduces the total rather than increasing it. Final Answer: Correct — four 9 V sources in series-aiding give 36 V (ideal).

Question 10

Faults in series chains — a short circuit across one element in a series network will cause the total circuit current to decrease. Is this claim accurate for an ideal voltage source?

Accepted Answer

Introduction / Context: Troubleshooting often hinges on predicting how faults affect current. In a series circuit powered by an ideal voltage source, replacing a finite resistor with a short (near zero ohms) changes the equivalent resistance. This question tests whether you know in which direction the total current moves under such a fault. Given Data / Assumptions: Ideal voltage source of fixed value. Series network of resistors. Fault: one resistor becomes a short (its resistance → ~0 Ω). Concept / Approach: Total series resistance is the sum of individual resistances. If one resistance collapses to nearly zero, the sum decreases. Ohm’s law for the whole circuit is I_total = V_source / R_total. With a smaller denominator (R_total), the current increases, not decreases. Only non-idealities like source current limits, fuses, or saturation would reduce current, but those are separate protective effects, not ideal circuit behavior. Step-by-Step Solution: Original: R_total(original) = R1 + R2 + … + Rk + … + Rn.Fault: Rk → 0 → R_total(fault) = R_total(original) − Rk.Since Rk > 0 originally, R_total decreases.Therefore, I_total(fault) = V_source / R_total(fault) increases. Verification / Alternative check: Numerical example: V = 12 V, series 3 Ω + 3 Ω. Normal I = 12 / 6 = 2 A. Short one resistor to 0 Ω → R_total = 3 Ω → I = 12 / 3 = 4 A (increased). Why Other Options Are Wrong: Correct: Opposite to Ohm’s law with a fixed source voltage. Only correct with current sources: A current source fixes current; voltage then changes across the network, but that is not the scenario here. Only correct if other resistors are large: Magnitude changes, not the direction of the change, depend on values. Common Pitfalls: Associating the word “short” with “less current.” A short reduces resistance; with a voltage source, current rises and may blow protective devices. Final Answer: Incorrect — a short reduces total resistance and increases total current (ideal source).

Question 11

Open-circuit in series — consider an ideal series circuit that develops an open in one component. Which statement best reflects the condition across the open break and the source?

Accepted Answer

Introduction / Context: Open-circuit faults are common in connectors, fuses, and fractured solder joints. Recognizing the electrical signature of an open in a series path is critical for diagnostics. This item asks you to identify what happens to current and voltages when a series path is interrupted by an open break. Given Data / Assumptions: Ideal voltage source. Series chain of components with one section “open” (infinite resistance). No alternative paths bypass the open (single path only). Concept / Approach: With a series open, the circuit is incomplete; therefore, current is zero everywhere in the loop: I_total = 0 A. Without current, the normal I*R drops on intact resistors disappear (each finite resistor drop is 0 V). The source still maintains its terminal voltage, and by KVL the entire source voltage appears across the open gap (the element or connection where the break occurred). This is why an open fuse often has the full supply voltage across it during operation. Step-by-Step Solution: Series path interrupted → I_total = 0 A.Finite resistors: V_k = I*R_k = 0 V.KVL: V_source = V_open + Σ V_resistors = V_open + 0.Therefore, V_open = V_source appears across the open. Verification / Alternative check: Measure with a voltmeter: across any intact resistor you will read ~0 V; across the open terminals you will read near the source voltage. This is the classic signature of an open series component. Why Other Options Are Wrong: Current increases: Impossible without a closed loop. Open sees smallest drop: Incorrect; it sees the full source voltage. Source collapses to 0 V: Ideal sources maintain their set voltage; collapse suggests current limiting or failure, not the ideal model. Common Pitfalls: Confusing a short with an open; assuming all components still drop voltage despite zero current. In series, no current means no I*R drops on finite resistors. Final Answer: Correct — current is zero and the full source voltage appears across the open break.

Question 12

Series-opposing sources — when two voltage sources are series-opposing, should their voltages be added arithmetically to get the total? Evaluate this statement.

Accepted Answer

Introduction / Context: Multiple sources in series combine according to their polarities. “Series-aiding” means voltages add; “series-opposing” means they subtract. This question checks whether you recognize that opposing sources reduce the net voltage instead of increasing it by addition. Given Data / Assumptions: Two ideal voltage sources in series. Opposing polarity orientation (one source fights the other). Linear, lumped circuit model. Concept / Approach: The correct way to combine series sources is to take their algebraic sum with sign, not a blind arithmetic sum. If V1 and V2 are oriented so that one is a rise while the other is a drop in the same loop traversal, the net is V_net = V1 − V2 (magnitude per polarity). Only when the sources aid each other do they add: V_net = V1 + V2. Therefore, the statement “series-opposing sources are added” is wrong. Step-by-Step Solution: Assign loop direction and source polarities.Write KVL including algebraic signs for rises/drops.For opposing orientation: V_net = |V1 − V2| (with sign by chosen direction).Conclude: They do not add; they subtract. Verification / Alternative check: Example: 12 V source opposing a 9 V source → net 3 V. A DMM across the pair confirms ~3 V with polarity set by the larger source orientation, matching algebraic summation, not addition. Why Other Options Are Wrong: Correct: Contradicts basic source combination rules. Only if identical / Only for AC: Irrelevant; algebraic sum applies regardless of equality or AC/DC as long as phasor polarities are considered for AC. Common Pitfalls: Ignoring polarity arrows and simply summing magnitudes. Always mark polarities and signs before applying KVL. Final Answer: Incorrect — series-opposing sources subtract; use the algebraic sum with signs.

Question 13

Dependence of total series resistance — does the equivalent resistance of a series circuit “always depend only on the highest-value resistor” present in that circuit?

Accepted Answer

Introduction / Context: Designers sometimes use rules of thumb when one element dominates. However, rigorous analysis of series circuits requires summation of all resistances. This item probes whether you know that every series element contributes to the total, not just the largest one, even if approximation may be acceptable in special contexts. Given Data / Assumptions: Series chain of N resistors. Ideal lumped model. No element is bypassed or shorted. Concept / Approach: The series formula is exact: R_total = R1 + R2 + … + Rn. While a large resistor may dominate numerically, the exact total still includes the smaller ones. Approximations (e.g., neglecting 1 Ω alongside 10 kΩ) are engineering conveniences, not the governing law. Therefore, the claim that total resistance “always depends only” on the largest value is false. Step-by-Step Solution: Write exact relation: R_total = Σ R_k for k = 1..n.Evaluate contribution: Each R_k adds positively to R_total.Consider dominance: If R_max ≫ others, R_total ≈ R_max + small terms, but not solely R_max.Conclude the statement is incorrect literally. Verification / Alternative check: Example: 9,900 Ω + 100 Ω = 10,000 Ω. The 100 Ω contributes 1% and cannot be ignored for precise work. Bench measurements reflect the full sum within tolerances. Why Other Options Are Wrong: Correct: Misstates the series rule. Correct only if >10×: Even then, the smaller parts still add; the claim “only” remains wrong. Temperature stability: Unrelated to the additive rule; it affects value drift, not whether each resistor counts. Common Pitfalls: Mistaking a convenient approximation for an exact law; overlooking that billing, power, and tolerance stacks rely on the exact sum, not a dominant-single-value simplification. Final Answer: Incorrect — the total series resistance is the sum of all resistors, not merely the largest one.

Question 14

Applied example — three resistors of 5 Ω, 10 Ω, and 20 Ω are connected in series. Is the total (equivalent) resistance equal to 35 Ω under ideal conditions?

Accepted Answer

Introduction / Context: Concrete numerical examples reinforce the series-resistance rule. Here, you are asked to validate a straightforward calculation for three resistors connected in series. Such checks are essential when sizing supplies and estimating current and power distribution in a chain. Given Data / Assumptions: Resistors: 5 Ω, 10 Ω, 20 Ω. Series connection (single current path). Ideal components; ignore tolerance and temperature coefficients. Concept / Approach: The series combination rule says: R_total = R1 + R2 + R3. Since the current is common to all three, the voltage drops add to the source voltage, and the resistances add arithmetically to give the equivalent seen by the source. No reciprocals are used for series addition; those apply to parallel networks. Step-by-Step Solution: List values: R1 = 5 Ω, R2 = 10 Ω, R3 = 20 Ω.Compute sum: R_total = 5 + 10 + 20 = 35 Ω.Therefore, the statement that the total is 35 Ω is correct.If a source V is applied, current would be I = V / 35 (for completeness). Verification / Alternative check: Measure with an ohmmeter across the three in series. Within tolerance, the reading will approach 35 Ω. Any deviation comes from component tolerances and lead/contact resistances, not from the combination rule. Why Other Options Are Wrong: Incorrect: Conflicts with the series sum rule. Correct only at 25 °C: Temperature affects value slightly but not the arithmetic rule. Series uses reciprocals: Reciprocals are for parallel, not series. Common Pitfalls: Accidentally applying the parallel formula to a series problem or overlooking unit symbols (Ω vs kΩ) when summing values. Final Answer: Correct — 5 Ω + 10 Ω + 20 Ω = 35 Ω in series.

Question 15

Power accounting — in a purely resistive series circuit, does the total power dissipated equal the sum of the powers dissipated by each resistor, or does it exceed that sum?

Accepted Answer

Introduction / Context: Energy conservation in circuits dictates that the power delivered by sources is absorbed by elements as heat or stored energy. In steady-state resistive networks, all source power ends up as heat in the resistors. This question checks whether you understand that total power is an additive quantity across elements, not something that mysteriously exceeds the parts’ contributions. Given Data / Assumptions: Purely resistive series network driven by a source. Steady state (no reactive storage). Ideal interconnects without parasitic losses. Concept / Approach: Use P = V*I at the source, and P_k = I^2 * R_k (or V_k^2 / R_k) at each resistor. Since the same current I flows in series, the total resistor power is Σ (I^2 * R_k) = I^2 * Σ R_k. The equivalent resistance is R_total = Σ R_k, so the power seen from the source is P_total = I^2 * R_total = I^2 * Σ R_k, exactly the same as the sum of the individual powers. There is no extra “hidden” power term in an ideal resistive loop. Step-by-Step Solution: Write element powers: P_k = I^2 * R_k.Sum them: Σ P_k = I^2 * Σ R_k.Compute source power: P_source = I^2 * R_total with R_total = Σ R_k.Therefore, P_source = Σ P_k (equality, not excess). Verification / Alternative check: Measure current I and each drop V_k, compute P_k = V_k * I. Summing P_k matches the source measurement V_source * I within meter tolerance, confirming conservation of energy. Why Other Options Are Wrong: Exceeds the sum: Violates conservation of energy in an ideal resistive loop. Less than the sum: Also violates conservation; nothing else absorbs the “missing” power. Only for equal resistors: Equality of values is irrelevant to the additivity of power. Common Pitfalls: Confusing instantaneous versus average power, or mixing AC reactive elements (which store and return energy) with purely resistive networks. In a DC or resistive AC case, powers simply add. Final Answer: Correct — total power equals the sum of the individual resistor powers in a series resistive circuit.

Question 16

Series circuits — as additional resistors are added in series (one after another in a single path), the total equivalent resistance of the circuit increases. Evaluate this statement for ideal resistors.

Accepted Answer

Introduction / Context: Understanding how total resistance changes when components are added is foundational for circuit design and troubleshooting. In a series connection, components share exactly one continuous path for current. Knowing how equivalent resistance behaves helps predict changes in current, voltage division, and power dissipation when adding or removing parts. Given Data / Assumptions: Ideal, linear resistors are connected strictly in series. Temperature effects and tolerance are ignored. Single DC source and steady-state conditions are assumed for intuition, though the rule is topology-based and source-agnostic. Concept / Approach: For resistors in series, the equivalent resistance is the arithmetic sum: R_total = R1 + R2 + … + Rn. Each added resistor contributes a positive amount of ohmic opposition to current. Therefore, adding any additional positive resistance increases R_total, which for a fixed source voltage reduces circuit current via Ohm’s law I = V/R_total. Step-by-Step Solution: Model the original circuit with R_total1 = ΣRi.Add one more series resistor Rx > 0.Compute the new equivalent: R_total2 = R_total1 + Rx.Since Rx > 0, R_total2 > R_total1, confirming the statement. Verification / Alternative check: Try numbers: Two 1 kΩ resistors in series → 2 kΩ. Add 470 Ω → 2.47 kΩ. With a 10 V source, current drops from 10/2000 = 5 mA to 10/2470 ≈ 4.05 mA, consistent with increased total resistance. Why Other Options Are Wrong: Incorrect: contradicts R_total = ΣRi for series networks.“Only AC” or “only equal values”: series summation holds regardless of frequency or equality of values (for ideal resistors).“Only with a capacitor”: passive capacitors are irrelevant to the algebraic sum of series resistances. Common Pitfalls: Confusing series with parallel (where adding a branch can reduce R_total); assuming physical proximity implies series—node analysis must confirm a single current path. Final Answer: Correct

Question 17

Series-path definition — a “series circuit” between two nodes provides only one continuous path for current flow between those points. Assess this definition.

Accepted Answer

Introduction / Context: Series and parallel are topological relationships that dictate how voltage and current distribute in circuits. Correctly identifying a series path is crucial before applying Ohm’s law, voltage division, and Kirchhoff’s laws. Misclassification leads to wrong calculations of currents, voltages, and power ratings. Given Data / Assumptions: The statement defines a series circuit as a single current path between two nodes. Components are ideal and connections are perfect conductors. Steady-state analysis is considered for simplicity. Concept / Approach: In a strictly series connection, every electron that leaves the source must pass through each element sequentially and return—there is no branching node that creates alternative paths. Consequently, the same current flows through all series elements, while voltages across them generally differ according to their individual impedances (V_i = I * R_i for resistors). Step-by-Step Solution: Mark the two nodes under consideration (start and return).Trace the conductive path and check for any node where current could split.If no branching exists, all elements on that path are in series and share identical current.Apply voltage division if needed: V_i = (R_i / ΣR) * V_source for resistive series networks. Verification / Alternative check: Use Kirchhoff’s Current Law at each intermediate node; with one path only, the current in equals the current out and equals the same I everywhere. Measurements with an ammeter in multiple series locations will read the same current (within instrument tolerance). Why Other Options Are Wrong: “Incorrect”: conflicts with the standard definition found in textbooks and datasheets.AC-only / identical resistors / low-current caveats: series topology is independent of frequency, value equality, and magnitude of current. Common Pitfalls: Assuming components are in series just because they are drawn in a line—node labeling must confirm a single path; ignoring hidden branches like measurement shunts or protection paths. Final Answer: Correct

Question 18

Series current continuity — in an ideal series circuit at steady state, the current leaving a resistor is equal to the current entering that resistor. Evaluate this statement.

Accepted Answer

Introduction / Context: Current continuity is a direct consequence of charge conservation. In a series circuit, every element experiences the same current because there is only one path for charges to move. Recognizing this allows you to simplify analysis and avoid mistakes such as summing currents in series networks (which is unnecessary and incorrect). Given Data / Assumptions: Ideal conductors and resistors. Steady-state DC (though the principle applies to AC instantaneously as well). No parallel leakage paths or measurement shunts. Concept / Approach: Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents at a node is zero. In series, a node exists between elements but does not branch; thus, current entering that node must equal current leaving it. Consequently, current in any series element is identical to current in every other series element. Step-by-Step Solution: Select any resistor in a series chain.Label the entering current as I_in and the leaving current as I_out.Apply KCL to the node on either side of the resistor: ΣI = 0 implies I_in = I_out.Conclude that the statement is correct for ideal series circuits. Verification / Alternative check: Measure with an ammeter placed in different series positions; readings are the same. Simulations (SPICE) confirm identical branch currents when no parallel branches exist. Why Other Options Are Wrong: “Incorrect” and the conditional options contradict KCL and the nature of a single, unbranched path. Common Pitfalls: Confusing series with parallel (in parallel, currents differ by branch conductance); overlooking small unintended branches like meter shunts that slightly alter currents. Final Answer: Correct

Question 19

Single-resistor series example — consider a simple circuit with one ideal resistor R1 connected directly across an ideal 10 V DC source. What is the voltage across R1?

Accepted Answer

Introduction / Context: This problem reinforces the idea that in a one-element series circuit, the entire source voltage appears across that element. It is a direct application of Kirchhoff’s Voltage Law (KVL) and Ohm’s law and sets the stage for understanding voltage division when more than one element is present. Given Data / Assumptions: Ideal 10 V DC source. Only one component in the loop: resistor R1. Ideal wires, no internal source resistance. Concept / Approach: KVL states that the algebraic sum of voltages around any closed loop is zero. With a single resistor in the loop, the resistor must drop the full source voltage to satisfy KVL. Ohm’s law relates current and resistance, but the drop is set by the source magnitude because there are no other elements to share it. Step-by-Step Solution: Write KVL: +V_source − V_R1 = 0.Substitute the given source: +10 − V_R1 = 0.Solve for V_R1: V_R1 = 10 V.Note: Current I = 10 / R1, but the exact R1 value does not change the fact that V_R1 = 10 V. Verification / Alternative check: Measure with an ideal voltmeter connected across R1; it reads the node-to-node source voltage because the resistor is directly across the source terminals. Why Other Options Are Wrong: 5 V: would require a second equal drop in series; not present.“Depends only on resistance” or “more information required”: the lone element must take the entire 10 V.0 V: implies a short circuit or zero source, which contradicts the setup. Common Pitfalls: Assuming “voltage division” always applies; it only applies when multiple series elements share the source voltage. Final Answer: 10 V

Question 20

Kirchhoff’s Voltage Law (KVL) in series loops — the sum of all individual voltage drops around a series circuit equals the source voltage. Assess this statement for ideal components.

Accepted Answer

Introduction / Context: Kirchhoff’s Voltage Law is a cornerstone of circuit analysis. It expresses energy conservation around a closed path: the total rise from sources equals the total drop across elements. In series circuits, this means the source voltage is apportioned among the series elements according to their impedances. Given Data / Assumptions: Ideal wiring and components (no parasitic EMF sources). Closed single-loop series circuit. Steady-state analysis for simplicity; KVL is general and also applies instantaneously in AC. Concept / Approach: KVL states ΣV_rises − ΣV_drops = 0. For a single source V_S and series elements with drops V1, V2, …, Vn, we have V_S = V1 + V2 + … + Vn. This enables voltage-divider design and power budgeting in series networks. Step-by-Step Solution: Define loop direction and label polarities using the passive sign convention.Write KVL: +V_S − V1 − V2 − … − Vn = 0.Rearrange: V_S = V1 + V2 + … + Vn.Use Ohm’s law as needed: Vi = I * Ri, where I is the common series current. Verification / Alternative check: Measure all individual drops and sum them; the total equals the measured source voltage within meter tolerance. SPICE simulations enforce KVL numerically, providing another check. Why Other Options Are Wrong: “Incorrect” and conditional options contradict a fundamental conservation law; equality of resistances, frequency, or waveform type does not invalidate KVL for lumped circuits. Common Pitfalls: Mixing source internal resistance into “external” drops without accounting for it; mislabeling polarities and signs; assuming wiring is ideal while significant wiring drops exist in high-current layouts. Final Answer: Correct

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