Question 1

Uniform series current: a series circuit has a 24 V source and a total resistance of 120 Ω. What is the current through each resistor (same for all in series)?

Accepted Answer

Introduction / Context: In a series circuit, there is only one path, so the same current flows through all components. Calculating that current from the source voltage and total resistance is a direct application of Ohm’s law and sets the current for every series element simultaneously. Given Data / Assumptions: Source voltage: 24 V. Total series resistance: 120 Ω. Ideal circuit elements and steady-state DC. Concept / Approach: Apply Ohm’s law to the entire series combination: I = V / R_total. The resulting current is the same through each series resistor, regardless of individual values. Step-by-Step Solution: Compute I: I = 24 / 120 = 0.2 A.Convert to milliamperes: 0.2 A = 200 mA.State that this current flows through each resistor in the series loop. Verification / Alternative check: Power check: P_total = V * I = 24 * 0.2 = 4.8 W; consistent with I^2 * R_total = 0.2^2 * 120 = 4.8 W. Why Other Options Are Wrong: 24 mA and 20 mA are an order of magnitude too small; 120 mA corresponds to 0.12 A, not supported by 24/120. Common Pitfalls: Accidentally dividing the current among series resistors as if they were parallel; misplacing decimal points during conversion to mA. Final Answer: 200 mA

Question 2

Maximum total current from power ratings: a series circuit has three resistors rated 1/8 W, 1/4 W, and 1/2 W with a total resistance of 1200 Ω. If each operates at its own maximum power simultaneously, what is the total circuit current?

Accepted Answer

Introduction / Context: In a series circuit, the current is the same through every component. If each resistor is just at its own maximum power rating, the common current must be such that the sum of individual resistor power ratings equals the total power dissipated by the series string. This requires combining power ratings and total resistance to solve for the allowable current. Given Data / Assumptions: Resistor power ratings: 1/8 W (0.125 W), 1/4 W (0.25 W), 1/2 W (0.5 W). Total resistance R_total = 1200 Ω (sum of the three resistors). Series connection: same current I flows through all. Concept / Approach: Total power in series with current I is P_total = I^2 * R_total. If each resistor is at its own maximum power at the same current, the total allowable power equals the sum of the individual power ratings. Therefore, set I^2 * R_total = P1 + P2 + P3 and solve for I. Step-by-Step Solution: Compute total rated power: P_sum = 0.125 + 0.25 + 0.5 = 0.875 W.Use P_total = I^2 * R_total ⇒ I = sqrt(P_sum / R_total).Calculate: I = sqrt(0.875 / 1200) ≈ sqrt(0.0007291667) ≈ 0.0270 A = 27 mA. Verification / Alternative check: Power consistency: I^2 * R_total = 0.027^2 * 1200 ≈ 0.875 W, matching the sum of ratings, so each resistor is at its limit simultaneously only if their resistances are proportioned accordingly; the problem frames it as a maximum-total-current scenario using the sum of ratings and total R. Why Other Options Are Wrong: 2.7 mA is too small by 10×; 19 mA is insufficient to reach the combined rating; 190 mA would greatly exceed power ratings and overheat components. Common Pitfalls: Trying to use individual resistor limits without total R; forgetting that P_total in a series path depends on I^2 times the sum resistance. Final Answer: 27 mA

Question 3

Series circuit with identical resistors: Three 680 Ω resistors are connected in series across a 470 V direct-current source. What is the resulting circuit current (the same through each resistor)?

Accepted Answer

Introduction / Context: This problem reinforces application of Ohm's law in a pure series network. When resistors are connected in series, their resistances add directly and exactly the same current flows through each element. By computing the total series resistance and dividing the applied voltage by this total, we obtain the loop current, which is also the current through every resistor in the string. Given Data / Assumptions: Three resistors, each 680 Ω, connected in series. Source voltage: 470 V (steady DC). Assume ideal components (no internal source resistance, no temperature effects). Concept / Approach: For series circuits: R_total = R1 + R2 + R3. The loop current is I = V / R_total. Because series current is identical everywhere, the value computed from total quantities equals the current through each resistor. Unit consistency (volts, ohms, amperes) ensures a correct milliampere result after conversion. Step-by-Step Solution: Compute total resistance: R_total = 680 + 680 + 680 = 2040 Ω.Apply Ohm's law to the loop: I = V / R_total = 470 / 2040 A.Evaluate: 470 / 2040 ≈ 0.23039 A ≈ 230 mA.Therefore, the current through the circuit (and each series resistor) is approximately 230 mA. Verification / Alternative check: Back-calculate voltage using the found current: V ≈ I * R_total ≈ 0.23039 * 2040 ≈ 470 V (within rounding), confirming internal consistency. Individual drops also make sense: V_each ≈ I * 680 ≈ 156.7 V; three drops sum to ≈ 470 V, satisfying KVL. Why Other Options Are Wrong: 69 mA and 23 mA: These imply a much larger equivalent resistance than actually present. 690 mA: Would require a far smaller total resistance than 2040 Ω. Common Pitfalls: Forgetting that series resistances add linearly. Arithmetic slips when dividing leading to an incorrect order of magnitude. Final Answer: 230 mA

Question 4

Kirchhoff’s Voltage Law (KVL) in a series loop: When all individual voltage drops and the source voltage are algebraically added around a closed series circuit, the total equals what value?

Accepted Answer

Introduction / Context: This question targets Kirchhoff’s Voltage Law (KVL), a cornerstone of circuit analysis. KVL states that the algebraic sum of all potential rises and drops around any closed loop is zero. In other words, the supplied energy from sources is exactly balanced by the energy absorbed in passive elements, ensuring energy conservation in the loop. Given Data / Assumptions: A single closed series loop. Ideal sources and components; steady-state DC for simplicity. Algebraic summation with proper sign convention (rises positive, drops negative, or vice versa). Concept / Approach: Traverse the loop in one direction and assign signs consistently: source voltage is a rise, component voltage drops are falls. By conservation of energy, total rises plus total drops must net to zero. This is independent of component values or current magnitude; it is a universal law for lumped-circuit models. Step-by-Step Solution: Write the KVL equation: ΣV_rises + ΣV_drops = 0.Typically: +V_source − V_drop1 − V_drop2 − ... = 0.Rearrange: V_source = Σ V_drops, showing equality between source and sum of drops.Thus, the algebraic sum around the loop is zero. Verification / Alternative check: Consider a numeric loop: a 12 V source feeding three series drops of 5 V, 4 V, and 3 V. Algebraic sum: +12 − 5 − 4 − 3 = 0, verifying KVL exactly. Why Other Options Are Wrong: the total of the voltage drops / the source voltage: Each equals the other in magnitude, but the algebraic loop sum is zero. the total of the source voltage and the voltage drops: Misstates the law; their algebraic sum is not an arbitrary total but specifically zero. Common Pitfalls: Ignoring sign convention and simply adding magnitudes. Confusing KVL (voltage) with KCL (current at nodes). Final Answer: zero

Question 5

Series voltage summation: In a series circuit with five resistors, each resistor drops 6 V. What is the required source voltage to sustain this condition?

Accepted Answer

Introduction / Context: This checks understanding of voltage division and Kirchhoff’s Voltage Law (KVL) in series networks. If each series element has a specified voltage drop, the source must supply the sum of those drops to maintain the same current through the chain under steady-state DC conditions. Given Data / Assumptions: Five resistors in series. Voltage drop across each resistor is 6 V. Steady DC, ohmic behavior, and a single series path. Concept / Approach: By KVL, the algebraic sum of drops equals the source voltage (with sign convention). In a pure series chain, total source voltage equals the sum of individual drops regardless of exact resistance values, provided the same current flows through all elements. Step-by-Step Solution: Sum the drops: V_total_drop = 6 V + 6 V + 6 V + 6 V + 6 V.Compute: V_total_drop = 5 * 6 V = 30 V.Therefore, the source voltage must be 30 V to sustain those drops. Verification / Alternative check: If the current is I and each resistor is R_i, then V_i = I * R_i = 6 V for each. Summing gives ΣV_i = I * ΣR_i = 30 V. Hence V_source = 30 V, independent of the specific R_i values as long as the drops are 6 V each. Why Other Options Are Wrong: is 6 V: That would be true only for a single 6 V drop, not five in series. depends on the current flow / depends on the resistor values: Not here; the problem fixes each drop to 6 V, making the total uniquely 30 V. Common Pitfalls: Confusing equal voltage drops with equal resistances; equal drops imply either equal R or carefully chosen values with the same current—either way, the sum is still 30 V. Final Answer: is 30 V

Question 6

According to Kirchhoff's Voltage Law (KVL), which statement correctly describes the relationship of voltage rises and drops around any closed loop in a series circuit?

Accepted Answer

Introduction / Context: Kirchhoff's laws form the backbone of circuit analysis. KVL addresses voltages around loops, while KCL addresses currents at nodes. Knowing which statement reflects KVL helps avoid mixing the two and ensures correct loop equations. Given Data / Assumptions: A single closed loop that may include sources and passive elements. Reference polarities are chosen consistently around the loop. Ideal lumped elements and steady-state conditions. Concept / Approach: KVL states that the algebraic sum of all voltage rises and drops around a closed loop is zero. In a simple series circuit with one source, this is commonly paraphrased as: the sum of the voltage drops equals the applied source voltage, provided polarities are taken consistently. Step-by-Step Solution: Write the loop equation: sum of rises + sum of drops = 0.Rearrange for a single source: sum of drops = source voltage.Interpret physically: energy gained from sources is exactly lost in elements.Thus, the stated option correctly expresses KVL for a series circuit. Verification / Alternative check: Measure with a voltmeter across each element in a simple loop with a DC source. The measured drops add to the terminal voltage of the source, confirming KVL experimentally. Why Other Options Are Wrong: Resistances summing to voltages confuses units and KCL/KVL concepts. KCL statement (sum of currents at a node equals zero) is not KVL. Identical voltages across series elements is generally false unless impedances are equal. Power statement is unrelated to KVL and is dimensionally inconsistent as written. Common Pitfalls: Sign errors when summing voltage rises and drops, and mixing KCL with KVL. Always define a direction and stick with it around the loop. Final Answer: the sum of the voltage drops in a series circuit is equal to the total applied voltage

Question 7

In a simple series circuit containing an ideal source and passive components, how does the current behave as it flows through each component?

Accepted Answer

Introduction / Context: Series and parallel connections determine how currents and voltages distribute in circuits. For series connections, a single path is provided for charge flow, which leads to a defining current property across all elements in that path. Given Data / Assumptions: Series connection: one continuous, unbranched path. Ideal wires with negligible leakage or shunt paths. Steady-state DC or instantaneous AC snapshot at any time. Concept / Approach: By charge conservation and KCL, the current entering any series element must equal the current leaving it. Because no alternate path exists, the same current must flow through every component in series. Voltage divides among elements according to their impedances, but current does not split. Step-by-Step Solution: Recognize topology: a single loop with no branches.Apply KCL at the terminals of any component: I_in = I_out.Conclude uniform current for all components in series.Note that voltages differ based on resistance or impedance values. Verification / Alternative check: Use an ammeter to measure current at various points in a series string. Readings are equal within measurement tolerance, confirming the property experimentally. Why Other Options Are Wrong: Equating current to resistance mixes quantities with different units. Subtraction or variation across series elements would imply charge accumulation, which does not occur in steady state. Zero after the first element contradicts continuity and conservation of charge. Common Pitfalls: Confusing series rules with parallel behavior, where currents do divide across branches. Keep track of topology when applying rules. Final Answer: remains the same through each component

Question 8

In a series circuit, what is the effect of an open (failed open) resistor on overall circuit operation? Choose the most accurate statement.

Accepted Answer

Introduction / Context: Component failures in series circuits often manifest as opens. Recognizing the circuit-level symptom helps technicians troubleshoot quickly, especially in simple DC networks and many appliance control chains. Given Data / Assumptions: A series path with at least one resistor failed open, resulting in a break in continuity. Ideal voltage source with no alternate return paths. No parasitic leakage significant enough to sustain current. Concept / Approach: A series circuit requires a complete path for current. An open anywhere in that path interrupts charge flow completely. With no current, there is no voltage drop across intact series resistors; instead, nearly the entire source voltage appears across the open because it prevents current and thus acts as a break with effectively infinite resistance. Step-by-Step Solution: Model the failed resistor as infinite resistance (R_open → ∞).Compute total resistance: R_total → ∞, so I = V_source / R_total → 0 A.Determine drops: with I ≈ 0, intact resistors have ≈ 0 V drop; the open sees the source potential difference across its terminals.Conclude: no current flows in the entire series loop. Verification / Alternative check: Measure with an ammeter in series: reading is 0 A. With a voltmeter across the open component, the reading approaches the source voltage, confirming the diagnosis. Why Other Options Are Wrong: Flow around the open: in a series path there is no alternate route. 0 V across the open: incorrect; it generally supports the full source voltage. Total resistance will decrease: the effective resistance increases toward infinity. Parallel branches statement: irrelevant to a simple series loop. Common Pitfalls: Misinterpreting measurements because of meter loading or stray leakage. Always verify continuity and check for hidden parallel paths before concluding an open. Final Answer: No current will flow in the circuit.

Question 9

In a series circuit, what will an ideal voltmeter read when placed directly across a short circuit (a wire with negligible resistance) replacing a component?

Accepted Answer

Introduction / Context: Understanding how voltage behaves across circuit elements in series is foundational for troubleshooting. A common fault is a short circuit, where a component is bypassed by a near-zero-ohm path. This question tests whether you can predict the voltmeter reading across that short in a series network. Given Data / Assumptions: Series circuit with an ideal source and ideal measuring instruments. A component position is replaced by a short (very low or effectively zero resistance). An ideal voltmeter (infinite input resistance) is used across that shorted section. Concept / Approach: Voltage is the energy per charge required to push current through an impedance. In an ideal short, the impedance is zero, so the required energy per charge is zero. By Ohm's law, V = I * R. If R ≈ 0 for the shorted branch, then the voltage drop across that branch is V ≈ I * 0 = 0 V, regardless of the current magnitude. Step-by-Step Solution: Model the short as R_short ≈ 0 Ω.Apply Ohm's law across the short: V_short = I_series * R_short.Since R_short ≈ 0, V_short ≈ 0 V even if I_series is nonzero.Therefore, the ideal voltmeter across the short reads 0 V. Verification / Alternative check: Kirchhoff's Voltage Law (KVL) states the algebraic sum of drops equals the source. In a series loop, if one element is shorted, its drop is zero and the remaining source voltage appears across the non-shorted elements, consistent with the 0 V reading across the short itself. Why Other Options Are Wrong: Source voltage: That appears across the remaining series impedance, not across the short. Infinite voltage: There is no mechanism for an infinite drop across zero resistance in an ideal circuit. The normal voltage drop: The component is bypassed; its drop vanishes. Common Pitfalls: Confusing high current through the short with high voltage across it; voltage depends on resistance. Using a non-ideal model where wiring has small but nonzero resistance; the ideal answer remains 0 V. Final Answer: zero volts

Question 10

In basic circuit analysis, which equation correctly gives the voltage drop across an individual resistor carrying current I with resistance R?

Accepted Answer

Introduction / Context: Ohm's law connects voltage, current, and resistance, allowing you to compute voltage drops across components. Correctly recalling the form of this relationship is crucial for sizing parts, predicting behavior, and diagnosing faults in DC and AC circuits alike. Given Data / Assumptions: Linear resistor with resistance R (ohms). Electrical current I (amperes) flows through the resistor. We want the voltage drop across that resistor. Concept / Approach: Ohm's law states V = I * R for an ohmic element. This is the constitutive relation for resistors and follows from the proportionality between electric field and current density in a uniform conductor. Power relations such as P = I^2 * R or P = V * I are derived, not primary for finding voltage drop directly. Step-by-Step Solution: Start with Ohm's law: V = I * R.Identify given quantities: I (current), R (resistance).Compute voltage drop using multiplication of I and R.Therefore, the correct expression is I x R. Verification / Alternative check: If power P is known, P = I^2 * R and P = V * I. Solving P = V * I for V gives V = P / I. Substituting P = I^2 * R yields V = (I^2 * R) / I = I * R, confirming the same relationship from power formulas. Why Other Options Are Wrong: V x R: Dimensional mismatch; multiplying voltage by resistance does not yield voltage. I2 x R: That is the power dissipated (I^2 * R), not the voltage drop. V x I: Also a power expression (P = V * I), not voltage. Common Pitfalls: Confusing V = I * R with power formulas, especially under exam pressure. For AC with complex impedances, use magnitudes and phases: V = I * Z. For a pure resistor, Z = R. Final Answer: I x R

Question 11

Four resistors are connected in series across a 50 V source. The measured series current is 100 µA. If R1 = 12 kΩ, R2 = 47 kΩ, and R3 = 57 kΩ, what value of R4 is required to account for the observed current?

Accepted Answer

Introduction / Context: This problem applies Ohm's law and series-resistance addition to determine an unknown resistor in a series string given the total current and supply voltage. Such calculations are common in sensor ladders, bias networks, and precision dividers where one element value must be chosen to meet a target current. Given Data / Assumptions: Series supply voltage Vs = 50 V. Series current I_total = 100 µA = 100 * 10^-6 A. Known resistors: R1 = 12 kΩ, R2 = 47 kΩ, R3 = 57 kΩ. Find R4 such that the current matches the given value. Concept / Approach: In series, total resistance is the sum of individual resistances. Ohm's law gives R_total = Vs / I_total. The unknown is R4 = R_total - (R1 + R2 + R3). Careful unit conversion (kΩ to Ω, µA to A) avoids arithmetic errors. Step-by-Step Solution: Compute total resistance: R_total = Vs / I_total = 50 V / (100 * 10^-6 A).R_total = 50 / 0.0001 = 500,000 Ω = 500 kΩ.Sum known resistors: R_known = 12 kΩ + 47 kΩ + 57 kΩ = 116 kΩ.Find the unknown: R4 = R_total - R_known = 500 kΩ - 116 kΩ = 384 kΩ.Therefore, R4 = 384 kΩ. Verification / Alternative check: Check current with the found value: R_sum = 116 kΩ + 384 kΩ = 500 kΩ. Then I = Vs / R_sum = 50 V / 500 kΩ = 0.0001 A = 100 µA, which matches the given current. The result is self-consistent. Why Other Options Are Wrong: 38.4 kΩ or 3.84 kΩ: Off by factors of 10 or 100; would yield much higher current than specified. 3.84 MΩ: Too large; would reduce current far below 100 µA. Common Pitfalls: Mistaking microamps for milliamps, leading to a 1000× error. Forgetting that series resistances add linearly, not in reciprocals (which applies to parallel). Final Answer: 384 kΩ

Question 12

A 900 V source is applied to three series resistors. Two measured drops are 300 V and 280 V. What must the third series voltage drop be so that the drops sum to the source?

Accepted Answer

Introduction / Context: Kirchhoff's Voltage Law (KVL) states that the algebraic sum of voltage rises and drops around any closed loop is zero. In a simple series circuit, the sum of the individual resistor drops equals the source voltage. This question checks your ability to use KVL to find a missing drop from the others and the source. Given Data / Assumptions: Source voltage Vs = 900 V. Measured drops across two resistors: V1 = 300 V and V2 = 280 V. All elements are in series; polarities consistent with passive sign convention. Concept / Approach: For series elements, Vs = V1 + V2 + V3. Solve for the unknown V3 by rearranging: V3 = Vs - (V1 + V2). This uses only KVL and requires no knowledge of individual resistances or current. Step-by-Step Solution: Write KVL sum: Vs = V1 + V2 + V3.Substitute known values: 900 = 300 + 280 + V3.Compute partial sum: 300 + 280 = 580 V.Solve for V3: V3 = 900 − 580 = 320 V.Therefore, the third drop is 320 V. Verification / Alternative check: Add all three: 300 + 280 + 320 = 900 V, exactly matching the source, confirming correctness. Why Other Options Are Wrong: 30 V or 270 V: Do not bring the sum to 900 V; violate KVL. 900 V: Would imply zero drop on the other resistors, contradicting the given measurements. Common Pitfalls: Arithmetic mistakes in subtracting from the source voltage. Forgetting that series drops always add to the source when polarities are consistent. Final Answer: 320 V

Question 13

For a string of resistors connected in series across a DC source, which statement best describes how the source voltage appears across the individual resistors?

Accepted Answer

Introduction / Context: Series resistor strings are used as voltage dividers in bias networks, measurement scaling, and reference generation. Knowing how voltage distributes across each resistor allows you to design predictable tap voltages and assess power dissipation. Given Data / Assumptions: All resistors are in series, so the same current flows through each one. Ideal DC source; wiring resistances are negligible. Resistors are linear and within rated power limits. Concept / Approach: With the same current I through every series element, the drop on resistor Ri is Vi = I * Ri. Therefore, voltage division is proportional to resistance values: larger resistance gets a proportionally larger share of the total source voltage. The total obeys V_source = Σ Vi. Step-by-Step Solution: Let R_total = R1 + R2 + ... + Rn.Series current: I = V_source / R_total.Drop on Ri: Vi = I * Ri = (V_source / R_total) * Ri.Hence, Vi / V_source = Ri / R_total, showing proportional division. Verification / Alternative check: Choose numbers: V_source = 10 V, R1 = 2 kΩ, R2 = 3 kΩ. Then R_total = 5 kΩ, I = 10/5000 = 2 mA. Drops: V1 = 2 mA * 2 kΩ = 4 V; V2 = 2 mA * 3 kΩ = 6 V. The ratio V1:V2 = 4:6 equals R1:R2 = 2:3, confirming proportionality. Why Other Options Are Wrong: Reduce the power to zero: Power is nonzero unless current is zero; each resistor dissipates P = I^2 * R. Cause the current to divide: Current is the same in series; division occurs in parallel networks. Increase the source voltage: Passive resistors cannot increase voltage; they only divide the applied voltage. Common Pitfalls: Confusing series and parallel behaviors (current vs. voltage division). Ignoring tolerance and temperature effects that slightly alter the division ratio. Final Answer: divide the source voltage in proportion to their values

Question 14

In a series circuit, the voltage drop across a particular resistor is directly proportional to which quantity?

Accepted Answer

Introduction / Context: Voltage division in a series network is governed by Ohm's law. Designers often choose resistor ratios to obtain specific node voltages. Identifying the correct proportionality helps when scaling reference voltages and setting bias points. Given Data / Assumptions: All elements are resistors in series. Same current flows through each resistor. Resistors are linear and operate within ratings. Concept / Approach: For a given series current I, the drop on any resistor Ri is Vi = I * Ri. Because I is common to all series elements, Vi is directly proportional to Ri alone, not the total resistance or on-time. The wattage rating limits safe power dissipation but does not set the instantaneous voltage for a given I. Step-by-Step Solution: Let I = V_source / ΣR.Voltage across resistor Ri: Vi = I * Ri.Holding I fixed, increasing Ri increases Vi linearly; decreasing Ri reduces Vi linearly.Therefore, Vi ∝ Ri, demonstrating direct proportionality to its own resistance. Verification / Alternative check: Example: Series chain with I = 2 mA, Ri options 1 kΩ, 2 kΩ, 3 kΩ yield Vi values 2 V, 4 V, 6 V respectively. The ratios of Vi match the ratios of Ri, verifying proportionality. Why Other Options Are Wrong: Total resistance: Affects I, but Vi for a given resistor scales specifically with its own Ri. Wattage rating: A specification limit; it does not define Vi unless power constraints are exceeded. On-time: Duration does not change instantaneous DC voltage drop. Common Pitfalls: Assuming wattage rating determines voltage; it only constrains P = V * I = I^2 * R. Mixing series and parallel rules; in parallel, voltage is common and currents divide. Final Answer: its own resistance

Question 15

Short circuit fundamentals in basic circuits: In practical electrical terms, a short circuit is best characterized by which property of the path between two nodes?

Accepted Answer

Introduction: A short circuit describes an unintended low-impedance path that bypasses the intended load. Recognizing the defining property of a short circuit helps explain why currents surge, fuses blow, and protective devices operate in power and electronics applications. Given Data / Assumptions: Idealized short circuit has approximately zero ohms between two nodes. Source has nonzero internal resistance but is relatively small. Conductors and interconnections have negligible resistance compared to the load. Concept / Approach: Ohm's law states I = V / R. If the resistance R of a path approaches zero, then for any finite voltage V, the current I becomes extremely large. This is why shorts are hazardous and why current-limiting or protective devices are required. The key characteristic is the very low resistance (ideally zero), not high resistance, not low current, and not zero conductance. Step-by-Step Solution: Define short circuit: a connection with R ≈ 0 Ω between nodes that should not be directly connected.Apply Ohm's law qualitatively: I = V / R → as R → 0, I → very large.Voltage drop perspective: V = I * R → across an ideal short, V ≈ 0 even at large I.Conclude the defining property: essentially no resistance (very high conductance). Verification / Alternative check: Real systems show protective devices (fuses, breakers) operating when a short occurs, consistent with abnormally large current due to near-zero resistance path. Measurements reveal minimal voltage across the shorted points because V = I * R and R is tiny. Why Other Options Are Wrong: too much resistance: Opposite of a short; that describes an open or high-impedance fault. no conductance: Conductance is 1/R; a short has very high conductance, not zero. low current: Shorts yield high current for a given source. very high voltage drop: The drop across the short itself is near zero. Common Pitfalls: Confusing a short with an overload through a partially resistive path; shorts are the extreme low-resistance case. Assuming an ideal zero-ohm short; in practice, small but nonzero resistance and source limits still cap the current. Final Answer: no resistance

Question 16

Series network power accounting: Four series resistors dissipate 16 mW, 107 mW, 146 mW, and 243 mW respectively. What is the total power consumed by the entire circuit?

Accepted Answer

Introduction: In any series circuit, the total power drawn from the source equals the sum of the powers dissipated in each element. This conservation-based reasoning is essential for thermal design, resistor wattage selection, and overall efficiency analysis. Given Data / Assumptions: P1 = 16 mW, P2 = 107 mW, P3 = 146 mW, P4 = 243 mW. Resistors are in series and all listed power values are steady-state. No additional significant losses elsewhere (e.g., wiring losses negligible). Concept / Approach: Total power in a series circuit is additive: P_total = Σ P_i. This follows from energy conservation and from P = V * I with the series current common to all branches; individual voltage drops differ, but energy sums linearly. Step-by-Step Solution: Add the given powers: P_total = 16 + 107 + 146 + 243 mW.Compute partial sums: 16 + 107 = 123 mW; 123 + 146 = 269 mW.Add final term: 269 + 243 = 512 mW.Therefore, the circuit consumes 512 mW in total. Verification / Alternative check: If the source voltage and series current were known, P_total could also be confirmed using P_total = V_source * I_series, which would equal the sum of resistor powers by conservation of energy, reinforcing the result 512 mW. Why Other Options Are Wrong: 128 mW / 269 mW / 396 mW: Intermediate or incorrect partial sums. 1024 mW: Double the correct value; no basis in the provided numbers. Common Pitfalls: Mistaking average or RMS values; the question already provides dissipations, which add directly. Confusing power summation with resistance addition; both are linear in series circuits, but they represent different physical quantities. Final Answer: 512 mW

Question 17

Series circuits and resistance: Considering a simple DC series circuit, which statement best describes the role of resistance?

Accepted Answer

Introduction: Resistance is a fundamental property that impedes the flow of electric charge. In series circuits, understanding what resistance actually does clarifies how currents, voltages, and powers distribute across components, guiding both analysis and design choices. Given Data / Assumptions: Steady DC source and lumped resistive elements. Resistive loads obey Ohm's law. No reactive components are present (ignoring capacitance and inductance). Concept / Approach: Ohm's law states V = I * R. For a given applied voltage, increasing resistance reduces current; equivalently, resistance opposes current flow. Power in a resistor is P = I^2 * R or P = V^2 / R, reflecting that resistance converts electrical energy into heat proportional to current or voltage squared. Step-by-Step Solution: Start with V = I * R. Hold V constant; as R increases, I decreases.Interpretation: resistance presents opposition to charge movement through collisions and lattice interactions.Any series resistor develops a voltage drop: V_drop = I * R, demonstrating the opposing effect.Energy perspective: electrical energy is dissipated as heat due to this opposition, quantified by P = I^2 * R. Verification / Alternative check: Measurements across a variable resistor (rheostat) on a fixed-voltage supply show current decreasing as resistance increases, directly verifying resistance as opposition to current flow. Why Other Options Are Wrong: control the voltage: Source sets voltage; resistors divide it but do not control the source value. double the current: Only occurs if R halves (with voltage fixed), not a general property. halve the power: Power depends on both I and R; no universal halving occurs. eliminate voltage drop: Resistors necessarily create voltage drops; eliminating drop contradicts V = I * R. Common Pitfalls: Assuming resistors 'consume' current; they oppose current and dissipate power but current is the same through all series elements. Confusing voltage control with voltage division; the latter is a byproduct of opposing current. Final Answer: oppose current

Question 18

Series circuit with unequal resistors: Which statement is NOT true for a series network containing resistors of different values?

Accepted Answer

Introduction: Series circuits are ubiquitous, and their rules are foundational. With unequal resistor values, some properties remain universally true while others do not. Distinguishing these clarifies voltage division and current continuity in basic circuit analysis. Given Data / Assumptions: Resistors are connected in a single series path. Values are different (R1 ≠ R2 ≠ …). Steady DC conditions (no reactive effects). Concept / Approach: Key series properties: the same current flows through every element; total resistance equals the arithmetic sum of individual resistances; and the source voltage equals the sum of all individual voltage drops (Kirchhoff's Voltage Law). However, the individual voltage drops are proportional to resistance values and therefore are generally not equal when resistances differ. Step-by-Step Solution: Common current: I_series is identical through each resistor in a single path.Total resistance: R_total = R1 + R2 + … + RN.Voltage division: V_k = I_series * R_k → different R_k produce different V_k.Therefore, the statement claiming equal voltage drops for unequal resistors is not true. Verification / Alternative check: Example: Two series resistors 1 kΩ and 2 kΩ on 9 V produce voltage drops 3 V and 6 V, confirming unequal drops proportional to resistance. Why Other Options Are Wrong: The current through each resistor is the same: True by series continuity. The sum of the voltage drops will be equal (to the source): Interpreted with KVL, this is true. The total resistance is the sum of values: True for series elements. The source voltage equals the sum of drops: Restates KVL, true. Common Pitfalls: Misreading a vague statement about 'sum of drops'; always tie it to KVL and the source voltage. Assuming identical voltage drops without checking resistor values. Final Answer: The voltage drop across each resistor is the same.

Question 19

Potentiometer usage in electronics: One of the most common applications of a potentiometer as an adjustable voltage divider is popularly known as what?

Accepted Answer

Introduction: A potentiometer (pot) is a three-terminal variable resistor typically employed as a voltage divider. Beyond general voltage trimming, its most recognizable consumer use is in audio systems to adjust loudness, commonly labeled as the volume knob. Given Data / Assumptions: Standard potentiometer with two end terminals and a wiper. Used in a divider configuration, not as a simple rheostat. Audio device expecting a variable input level. Concept / Approach: As the wiper position changes, the output tap selects a fraction of the input voltage, delivering a variable level to the next stage. In audio, this controls signal amplitude feeding an amplifier, perceived as louder or softer sound. For consistent human perception, audio-taper (log) pots are often used rather than linear-taper pots. Step-by-Step Solution: Wire the pot as a divider: input across the end terminals, output taken from wiper to one end.Adjust the wiper to vary output voltage fraction between 0 and near 1.Feed the variable level into an amplifier or active stage.Result: perceived loudness changes → the control is called “volume.” Verification / Alternative check: Examine schematics of radios, amplifiers, and mixers; the input gain or preamp stage often includes a pot labeled 'Volume,' confirming its role as an adjustable divider. Why Other Options Are Wrong: voltage control: Generic phrase; true in principle but not the commonly used term. current control: Requires series rheostat use, not a divider. divider control: Not a standard term in industry or user interfaces. impedance control: Pots can affect impedance, but this is not the typical user-facing application name. Common Pitfalls: Using a linear taper in audio where a log taper matches human hearing better. Placing the pot incorrectly in the signal chain, causing impedance or noise issues. Final Answer: volume control

Question 20

Series resistors with a DC source: Three resistors of 1.5 kΩ, 470 Ω, and 3.3 kΩ are connected in series to a 25 V supply. What is the total circuit current (express your choice in common units)?

Accepted Answer

Introduction: Combining series resistances and applying Ohm's law is a foundational skill for predicting current, voltage drops, and power dissipation. This exercise reinforces unit handling and accurate arithmetic across mixed ohm/kilohm values. Given Data / Assumptions: R1 = 1.5 kΩ, R2 = 470 Ω, R3 = 3.3 kΩ. V_source = 25 V DC. Ideal wires and negligible extra losses. Concept / Approach: For series elements, total resistance is the sum of individual resistances. Then apply I = V / R_total. Converting mixed units (Ω and kΩ) to a single unit avoids arithmetic mistakes and yields a clean milliampere result for readability. Step-by-Step Solution: Convert to ohms: 1.5 kΩ = 1500 Ω; 3.3 kΩ = 3300 Ω.Sum: R_total = 1500 + 470 + 3300 = 5270 Ω.Compute current: I = V / R_total = 25 / 5270 A ≈ 0.004742 A.Express in milliamperes: I ≈ 4.742 mA → rounds to 4.7 mA. Verification / Alternative check: Back-calculate expected drops: V1 ≈ 4.742 mA * 1500 Ω ≈ 7.11 V; V2 ≈ 2.24 V; V3 ≈ 15.63 V. Sum ≈ 24.98 V (rounding), matching the 25 V source, which verifies the computation. Why Other Options Are Wrong: 210 mA: Two orders of magnitude too large; would require only ~119 Ω total resistance. 5.2 mA: Overestimates due to rounding and ignoring exact totals. .007 A (7 mA): Too large; would imply ~3.57 kΩ total, not 5.27 kΩ. 2.1 mA: Too small; would imply ~11.9 kΩ total. Common Pitfalls: Mixing kΩ and Ω without conversion. Rounding too early; carry sufficient precision until the final step. Final Answer: 4.7 mA

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