Question 1

Thevenin source with internal resistance: A 120 V source with internal resistance RS = 12 Ω feeds a load RL = 470 Ω. What is the load voltage across RL?

Accepted Answer

Introduction / Context: Real voltage sources can be modeled as an ideal source in series with an internal resistance (Thevenin model). The load voltage is then found using a simple voltage-divider relationship between the internal resistance and the load resistance. Given Data / Assumptions: Ideal source voltage V_S = 120 V. Internal resistance R_S = 12 Ω (series). Load resistance R_L = 470 Ω. Steady-state DC conditions. Concept / Approach: For a series divider, the load voltage is V_L = V_S * (R_L / (R_S + R_L)). Because R_L ≫ R_S here, the drop across R_S is small, so V_L will be close to the source voltage but slightly lower. Step-by-Step Solution: Compute denominator: R_S + R_L = 12 + 470 = 482 Ω.Compute ratio: R_L / (R_S + R_L) = 470 / 482 ≈ 0.9741.Load voltage: V_L = 120 V * 0.9741 ≈ 117.01 V.Rounded to a practical choice: ≈ 117 V. Verification / Alternative check: Calculate current: I ≈ 120 / 482 ≈ 0.249 A. Drop on R_S: I * R_S ≈ 0.249 * 12 ≈ 2.99 V. Then V_L = 120 − 2.99 ≈ 117.01 V, matching the divider result. Why Other Options Are Wrong: 120 V ignores internal resistance. 12 V is the small internal drop, not the load voltage. 0 V is only with open circuit at the load (not the case). 112 V is too low for these values. Common Pitfalls: Forgetting the internal resistance drop, or misapplying the divider formula by swapping R_S and R_L. Final Answer: 117 V

Question 2

Source transformation in basic circuit theory: A 12 mA ideal current source with internal resistance RS = 1.2 kΩ is to be converted to an equivalent Thevenin (voltage) source. What is the resulting source voltage?

Accepted Answer

Introduction / Context: Many circuit problems ask you to transform a Norton (current-source) model into a Thevenin (voltage-source) model or vice versa. This is a standard technique in electrical engineering used to simplify analysis and to match sources with loads. Given Data / Assumptions: Ideal current source Is = 12 mA. Series/internal resistance RS = 1.2 kΩ. We assume linear, time-invariant, resistive conditions with no dependent sources. Concept / Approach: The source transformation rule is direct: a current source Is in parallel with RS is equivalent to a voltage source VTH in series with RS, where VTH = Is * RS. The resistance value remains the same in both equivalent forms (RS = RTH). Step-by-Step Solution: Write the transformation relation: VTH = Is * RS.Convert units: Is = 12 mA = 0.012 A; RS = 1.2 kΩ = 1,200 Ω.Compute: VTH = 0.012 * 1,200 = 14.4 V. Verification / Alternative check: Check dimensional consistency: amperes * ohms = volts, so the units are correct. Also, if you were to convert back to Norton, IN = VTH / RTH = 14.4 / 1,200 = 0.012 A = 12 mA, confirming equivalence. Why Other Options Are Wrong: 144 V: Off by a factor of 10; would require Is = 120 mA or RS = 12 kΩ. 7.2 V: Exactly half the correct value; likely from halving either the current or resistance erroneously. 72 mV: Incorrect scaling of milli and kilo prefixes. Common Pitfalls: Mishandling metric prefixes (milli vs. kilo) causing thousand-fold errors. Confusing series vs. parallel placement of RS when picturing the transformation. Final Answer: 14.4 V

Question 3

Loaded voltage source with internal resistance: A 120 Ω load is connected to a source with VS = 12 V and source resistance RS = 8 Ω. What is the voltage across the load resistor?

Accepted Answer

Introduction / Context: Real voltage sources are modeled with an ideal source in series with an internal resistance (Thevenin form). When a load is attached, the output voltage divides between the source resistance and the load resistance according to the voltage-divider rule. Given Data / Assumptions: Source voltage, VS = 12 V. Source (internal) resistance, RS = 8 Ω. Load resistance, RL = 120 Ω. All components are ideal and operated under steady-state DC conditions. Concept / Approach: Use the voltage-divider relation for series elements: VL = VS * (RL / (RS + RL)). This follows directly from Ohm’s law in a simple series path where the same current flows through RS and RL. Step-by-Step Solution: Compute the total series resistance: RT = RS + RL = 8 + 120 = 128 Ω.Apply the divider: VL = 12 * (120 / 128).Calculate the ratio: 120 / 128 = 0.9375; hence VL = 12 * 0.9375 = 11.25 V. Verification / Alternative check: Find current first: I = VS / RT = 12 / 128 = 0.09375 A. Then VL = I * RL = 0.09375 * 120 = 11.25 V, which matches the divider result. Why Other Options Are Wrong: 12 V: Would be true only if RS = 0 Ω (ideal source with no internal drop). 1.13 V: Off by a factor of 10; likely from mistakenly using RS instead of RL in the divider. 0 V: Only if the source were shorted or the load were disconnected—neither applies. Common Pitfalls: Forgetting the internal resistance in series with the load. Arithmetic errors when computing the fraction RL / (RS + RL). Final Answer: 11.25 V

Question 4

Voltage division with source resistance: A load RL = 2 Ω is connected to a source VS = 110 V that has internal resistance RS = 24 Ω. What output voltage appears across the load?

Accepted Answer

Introduction / Context: When a real source with internal resistance powers a low-ohmic load, a substantial portion of the applied voltage can drop inside the source. This question assesses your ability to apply the voltage-divider rule and reason about loading effects. Given Data / Assumptions: Source voltage, VS = 110 V. Source resistance, RS = 24 Ω. Load resistance, RL = 2 Ω. DC steady-state analysis; resistances are ideal. Concept / Approach: For series RS and RL fed by VS, the load voltage is VL = VS * (RL / (RS + RL)). Because RL is small relative to RS, only a small fraction of the source voltage will appear across the load. Step-by-Step Solution: Compute RT = RS + RL = 24 + 2 = 26 Ω.Apply divider: VL = 110 * (2 / 26).Numerical result: 2 / 26 ≈ 0.076923; VL ≈ 110 * 0.076923 ≈ 8.4615 V ≈ 8.5 V (rounded). Verification / Alternative check: Find circuit current: I = VS / RT = 110 / 26 ≈ 4.2308 A. Then compute VL = I * RL ≈ 4.2308 * 2 ≈ 8.4616 V; rounding to the nearest tenth gives 8.5 V, consistent with the divider calculation. Why Other Options Are Wrong: 85 V or 110 V: These would require RS to be negligible compared to RL, which is not the case. 0 V: Only if the circuit were open or the load removed. Common Pitfalls: Ignoring internal resistance and assuming the full source voltage appears across the load. Rounding too early; perform the division first, then round the final result. Final Answer: 8.5 V

Question 5

Source transformation to Norton form: A 120 V ideal voltage source has source resistance RS = 60 Ω. What is the magnitude of the equivalent Norton current source?

Accepted Answer

Introduction / Context: Transforming between Thevenin (voltage source in series with resistance) and Norton (current source in parallel with resistance) models is a routine skill for simplifying circuits and analyzing loading effects. Here we convert a given voltage source to its Norton equivalent. Given Data / Assumptions: Thevenin voltage source: VS = 120 V. Series (source) resistance: RS = 60 Ω. Linear, time-invariant, resistive network; no dependent sources are involved. Concept / Approach: The Norton current is the short-circuit current delivered by the Thevenin source: IN = VS / RS. The Norton resistance equals the Thevenin resistance: RN = RS. Only the current magnitude is asked in the options, but the resistance is useful context. Step-by-Step Solution: Use the transformation: IN = VS / RS.Compute: IN = 120 / 60 A = 2 A.Therefore, the Norton pair is IN = 2 A in parallel with RN = 60 Ω. Verification / Alternative check: Reverse check to Thevenin: VTH = IN * RN = 2 A * 60 Ω = 120 V, which is the original source voltage. This confirms a correct, lossless transformation between equivalent models. Why Other Options Are Wrong: 4 A: Would require RS = 30 Ω for a 120 V source. 400 mA or 200 mA: These are 0.4 A and 0.2 A, far below the correct short-circuit current for 60 Ω at 120 V. Common Pitfalls: Misapplying the relation by multiplying instead of dividing (VS * RS instead of VS / RS). Confusing the resistance placement (series vs. parallel) when visualizing the Norton model. Final Answer: 2 A

Question 6

Practical source with internal resistance: An 18 V Thevenin source has internal resistance RS = 70 Ω and is connected to a load RL = 33 Ω. Compute the load power PL delivered to RL.

Accepted Answer

Introduction / Context: This problem tests application of Thevenin's model and the voltage-divider concept to determine power delivered to a load when a real (non-ideal) voltage source with internal resistance supplies a resistive load. Computing load voltage first and then using P = V^2 / R is a standard, reliable approach in basic circuit analysis. Given Data / Assumptions: Thevenin source voltage, VS = 18 V. Internal (series) resistance, RS = 70 Ω. Load resistance, RL = 33 Ω. Direct current conditions and purely resistive elements. Concept / Approach: The load sees a voltage set by a simple divider: VL = VS * RL / (RS + RL). Once VL is known, compute load power using PL = VL^2 / RL. Alternatively, compute current I = VS / (RS + RL), then PL = I^2 * RL. Both methods should agree. Step-by-Step Solution: Compute total resistance: RT = RS + RL = 70 + 33 = 103 Ω.Find current: I = VS / RT = 18 / 103 ≈ 0.174757 A.Find load voltage: VL = I * RL ≈ 0.174757 * 33 ≈ 5.767 V.Compute power: PL = VL^2 / RL ≈ (5.767^2) / 33 ≈ 33.28 / 33 ≈ 1.01 W.Rounded to offered choices: ≈ 1 W. Verification / Alternative check: Alternative: PL = I^2 * RL ≈ (0.174757^2) * 33 ≈ 0.03053 * 33 ≈ 1.01 W. This matches the previous result, validating the computation. Why Other Options Are Wrong: 175 mW and 18 mW undervalue power by ignoring the divider effect correctly. 0 W would require VL = 0 or an open circuit, which is not the case. 3.5 W far exceeds what an 18 V source can deliver into 33 Ω with 70 Ω in series. Common Pitfalls: Using VS^2 / RL directly (ignores RS), or adding powers instead of using the divider and load formula. Also, rounding too early can skew the final choice. Final Answer: 1 W

Question 7

Source transformation check: A Thevenin source with VS = 30 V and RS = 6 Ω is transformed to an equivalent Norton current source. What are the Norton parameters (IS in amperes, RN in ohms)?

Accepted Answer

Introduction / Context: Source transformation is a core technique for simplifying linear circuits. Any Thevenin source (voltage in series with resistance) can be converted to a Norton source (current in parallel with resistance) and vice versa, without changing the external terminal behavior. Given Data / Assumptions: Thevenin voltage VS = 30 V. Thevenin resistance RS = 6 Ω (series). All components are linear and time-invariant. Concept / Approach: For Thevenin ↔ Norton conversion: IS = VS / RS and RN = RS. The resistance remains the same; only the source form changes between voltage and current. Step-by-Step Solution: Compute Norton current: IS = VS / RS = 30 / 6 = 5 A.Norton resistance equals Thevenin resistance: RN = 6 Ω.Therefore, the equivalent current source is 5 A in parallel with 6 Ω. Verification / Alternative check: Open-circuit voltage of Norton pair: VOC = IS * RN = 5 * 6 = 30 V, which matches VS. Short-circuit current of Thevenin pair: ISC = VS / RS = 5 A, which matches IS. Equivalence verified. Why Other Options Are Wrong: '30 A, 6 Ω' confuses the ratio; '5 A, 30 Ω' changes resistance incorrectly; '30 A, 5 Ω' alters both values; '0.2 A, 6 Ω' is the reciprocal ratio, not applicable here. Common Pitfalls: Accidentally inverting VS/RS, or changing the resistance during transformation. Resistance must remain RS in both representations. Final Answer: 5 A, 6 Ω

Question 8

Ideal source to load: An ideal 12 V voltage source feeds a 120 Ω load resistor. What is the voltage measured across the load terminals?

Accepted Answer

Introduction / Context: This question checks understanding of an ideal voltage source. An ideal voltage source maintains a fixed voltage across its terminals regardless of the load (within the ideal model). Thus, the load voltage equals the source voltage when connected directly without any internal series resistance. Given Data / Assumptions: Ideal voltage source VS = 12 V (zero internal resistance). Load resistance RL = 120 Ω. Direct connection between source and load, steady-state DC. Concept / Approach: For an ideal source, the terminal voltage does not sag under load. Therefore, the potential difference across the load equals VS. The current is I = VS / RL if needed, but voltage remains fixed at 12 V across RL. Step-by-Step Solution: Apply ideal model: V_load = VS = 12 V.Optional current: I = 12 / 120 = 0.1 A, but voltage remains 12 V. Verification / Alternative check: If there were internal resistance, we would use a divider to find voltage sag. Since internal resistance is zero by assumption, no divider effect exists. Why Other Options Are Wrong: 'is 0 V' implies a short or open preventing voltage; not applicable. 'is 120 V' confuses voltage with resistance value. 'cannot be determined' is incorrect because the ideal model fully specifies the outcome. 'is 1.2 V' is an arbitrary, unjustified drop. Common Pitfalls: Assuming every source has internal resistance; reading 120 Ω as 120 V by mistake; ignoring the explicitly ideal nature of the source. Final Answer: is 12 V

Question 9

Norton to Thevenin conversion: A current source has IS = 4 µA in parallel with RS = 1.2 MΩ. Determine the equivalent Thevenin source (VTH and RTH).

Accepted Answer

Introduction / Context: Converting between Norton and Thevenin equivalents is a standard analysis tool for simplifying linear circuits. A Norton current source in parallel with a resistance can be replaced by a Thevenin voltage source in series with the same resistance, keeping terminal behavior unchanged. Given Data / Assumptions: Norton current IS = 4 µA. Norton resistance RS (parallel) = 1.2 MΩ. Linear, time-invariant network, steady state. Concept / Approach: The relationships are VTH = IS * RS and RTH = RS. The resistance value is preserved across the transformation, while the source form changes from current to voltage. Step-by-Step Solution: Compute VTH: VTH = IS * RS = 4e-6 A * 1.2e6 Ω = 4.8 V.Set RTH equal to RS: RTH = 1.2 MΩ.Therefore, the Thevenin equivalent is 4.8 V in series with 1.2 MΩ. Verification / Alternative check: Open-circuit voltage of the Norton form is IS * RS = 4.8 V, matching VTH. Short-circuit current of the Thevenin form is VTH / RTH = 4.8 V / 1.2 MΩ = 4 µA, matching IS. Equivalence confirmed. Why Other Options Are Wrong: 4.8 µV is six orders too small. 1 V is not IS * RS. 4.8 V, 4.8 MΩ incorrectly changes resistance. 0.48 V, 120 kΩ also changes both values without basis. Common Pitfalls: Unit slips (µA and MΩ), and forgetting that RTH equals RS exactly in this transformation. Final Answer: 4.8 V, 1.2 MΩ

Question 10

Norton current division with finite source resistance: A 1.2 A constant current source has internal resistance RS = 12 kΩ (parallel model). A load RL = 680 Ω is connected across the source. What is the load current IL?

Accepted Answer

Introduction / Context: A practical current source is modeled as an ideal current source in parallel with a finite internal resistance. When a load is connected in parallel, the source current divides between the internal resistance and the load according to current division. This question checks accurate use of the current divider formula. Given Data / Assumptions: Ideal Norton source current IS = 1.2 A. Internal parallel resistance RS = 12 kΩ. Load resistance RL = 680 Ω connected across the source. Steady-state, linear resistors. Concept / Approach: For two parallel resistors RL and RS fed by a current source IS, the current through RL is given by current division: IL = IS * (RS / (RS + RL)). Because RS ≫ RL, most of the current goes through the smaller resistor RL. Step-by-Step Solution: Compute denominator: RS + RL = 12,000 + 680 = 12,680 Ω.Compute ratio: RS / (RS + RL) = 12,000 / 12,680 ≈ 0.9466.Find load current: IL = 1.2 A * 0.9466 ≈ 1.1359 A.Round to sensible precision: IL ≈ 1.14 A. Verification / Alternative check: Current through RS is IS − IL ≈ 1.2 − 1.1359 ≈ 0.0641 A. Voltage across both branches: V ≈ IL * RL ≈ 1.1359 * 680 ≈ 772.4 V, which also equals 0.0641 A * 12,000 Ω ≈ 769 V (small rounding differences due to rounding earlier). Both branches share approximately the same voltage, confirming current division. Why Other Options Are Wrong: 0 A would mean open load. 114 mA is off by a factor of 10. 1.2 A implies zero internal resistance diverting none of the current. 11.4 A is not possible with a 1.2 A source. Common Pitfalls: Using the reciprocal ratio (RL / (RL + RS)), or mistakenly modeling RS in series instead of parallel for a current source. Final Answer: 1.14 A

Question 11

Accounting for source internal resistance: A 12 V source has internal resistance RS = 90 Ω. With a load RL = 20 Ω connected, what power PL is delivered to the load?

Accepted Answer

Introduction / Context: Real voltage sources are modeled using Thevenin equivalents: an ideal source in series with an internal resistance. Load power is found by first computing the load voltage via the divider, then applying PL = VL^2 / RL, or by using current and PL = I^2 * RL. Given Data / Assumptions: Source voltage VS = 12 V. Internal resistance RS = 90 Ω (series). Load resistance RL = 20 Ω. Purely resistive, steady-state conditions. Concept / Approach: Voltage divider: VL = VS * RL / (RS + RL). Then compute PL using PL = VL^2 / RL. Expect a relatively small VL because RS is much larger than RL, meaning a significant drop occurs inside the source. Step-by-Step Solution: Total resistance: RT = RS + RL = 90 + 20 = 110 Ω.Current: I = VS / RT = 12 / 110 ≈ 0.10909 A.Load voltage: VL = I * RL ≈ 0.10909 * 20 ≈ 2.1818 V.Load power: PL = VL^2 / RL ≈ (2.1818^2) / 20 ≈ 4.759 / 20 ≈ 0.238 W = 238 mW. Verification / Alternative check: Using PL = I^2 * RL gives (0.10909^2) * 20 ≈ 0.0119 * 20 = 0.238 W, which agrees exactly with the voltage method. Why Other Options Are Wrong: 23.8 W exceeds the source's capability with this resistance network. 2.38 W and 0.12 W result from arithmetic or divider mistakes. 2.38 mW is orders of magnitude too small. Common Pitfalls: Ignoring RS in the divider, or plugging VS directly into PL = V^2 / RL. Also, mixing milli and base units can lead to factor-of-1000 errors. Final Answer: 238 mW

Question 12

Superposition in a two-source network: One source alone drives 12 mA through a branch; the other source alone drives 10 mA in the opposite direction through the same branch. What is the actual branch current with both sources active?

Accepted Answer

Introduction / Context: Linear circuit analysis often leverages superposition: the total response equals the algebraic sum of individual responses to each independent source acting alone (with the others turned off appropriately). Direction matters; currents opposing each other subtract. Given Data / Assumptions: Current due to source 1 alone: I1 = 12 mA (reference direction taken as positive). Current due to source 2 alone: I2 = 10 mA in the opposite direction (hence negative with respect to the same reference). Linear network; sources are independent; superposition valid. Concept / Approach: Superposition principle: I_total = I1 + I2, with signs assigned according to direction. Opposite directions imply subtraction of magnitudes. Step-by-Step Solution: Assign signs: I1 = +12 mA; I2 = −10 mA.Sum: I_total = 12 mA + (−10 mA) = 2 mA.Direction: the result is in the direction of the 12 mA contribution (since net is positive). Verification / Alternative check: Check limits: If both contributed in the same direction, magnitude would be 22 mA. With opposite directions and larger 12 mA, the remainder must be 2 mA, consistent with the arithmetic. Why Other Options Are Wrong: 22 mA wrongly adds opposing currents. 12 mA or 10 mA ignores the second source. 0 mA would require equal magnitudes, which is not the case here. Common Pitfalls: Forgetting to treat direction as sign, or mixing up which direction is taken as positive. Final Answer: 2 mA

Question 13

Source modeling: Does a practical (real-world) voltage source always include a nonzero internal resistance when represented for circuit analysis?

Accepted Answer

Introduction / Context: No physical source can maintain an absolutely constant terminal voltage under all loads. To capture real behavior (voltage sag and power loss), practical voltage sources are modeled with a series internal resistance. Given Data / Assumptions: Practical voltage source with finite energy and non-ideal regulation. Internal resistance Rs is small but nonzero. Load connected across the source terminals. Concept / Approach: The Thevenin model represents a practical voltage source as an ideal source Vs in series with an internal resistance Rs. Under load, the terminal voltage drops: V_terminal = Vs − I_load * Rs. This explains regulation limits and heat dissipation inside the source. Step-by-Step Solution: Assume a load drawing current I_load.Voltage at the terminals: V_terminal = Vs − I_load * Rs.Power lost internally: P_internal = I_load^2 * Rs.Consequently, Rs must be nonzero to reflect real behavior; ideal sources use Rs = 0 for analysis convenience. Verification / Alternative check: Measure open-circuit voltage (no load) and then loaded voltage. The drop from open-circuit to loaded conditions implies a finite internal resistance that can be estimated by Rs ≈ (V_oc − V_load) / I_load. Why Other Options Are Wrong: Regulated supplies approximate low Rs but never exactly zero. Both AC and DC sources exhibit non-idealities; the model applies broadly. Internal resistance exists across operating currents, not only at high load. Common Pitfalls: Assuming data-sheet “tight regulation” implies zero Rs. It only means Rs is small over a specified load range. Final Answer: True

Question 14

Multiple sources in one network: Do some circuit topologies legitimately require more than one independent voltage or current source?

Accepted Answer

Introduction / Context: Real systems often combine multiple sources to meet performance needs: biasing and signal injection in amplifiers, dual rails in op-amp circuits, battery + photovoltaic hybrids, or mixed current/voltage excitations in measurement setups. Given Data / Assumptions: Linear or nonlinear networks may include several independent sources. Sources can be of different types (voltage or current) and polarities. Operation is steady-state for analysis clarity. Concept / Approach: Superposition applies to linear networks: the response to multiple independent sources equals the algebraic sum of the responses to each source acting alone (with others deactivated per type). Multiple sources enable bias + signal, redundancy, or energy sharing among subsystems. Step-by-Step Solution: Identify the purpose of each source (e.g., DC bias, AC signal, reference, current excitation).Analyze via superposition for linear circuits: zero-out voltage sources to their internal resistance and current sources to their internal resistance.Combine contributions to find voltages/currents of interest.Validate operating points and power flows for safety and performance. Verification / Alternative check: Common designs—op-amp amplifiers with +V and −V rails, RF mixers with LO + RF sources, LED drivers mixing a current source with voltage-limited supply—demonstrate legitimate multiple-source usage. Why Other Options Are Wrong: DC systems frequently use multiple sources (e.g., dual batteries, bias plus signal). Use is not limited to lab testing; it is standard practice in production designs. Sources need not be identical nor strictly series-connected; topology depends on the function. Common Pitfalls: Failing to check interaction between sources, such as back-driving or circulating currents. Use diodes, OR-ing controllers, or proper isolation as needed. Final Answer: True

Question 15

Source transformation principle: Is it impossible to convert between an ideal voltage source with series resistance and an equivalent current source with parallel resistance (and vice versa)?

Accepted Answer

Introduction / Context: Source transformations are a powerful analysis tool, allowing engineers to replace a Thevenin source with its Norton equivalent, simplifying circuit calculations without changing external terminal behavior. Given Data / Assumptions: Thevenin form: ideal voltage source Vth in series with Rth. Norton form: ideal current source In in parallel with Rn. Equivalence is at the same two external terminals and for linear bilateral elements. Concept / Approach: The conversions are defined by In = Vth / Rth and Rn = Rth. Conversely, Vth = In * Rn. The two models produce the same open-circuit voltage, short-circuit current, and terminal V–I relation, ensuring equivalence. Step-by-Step Solution: Start with Vth in series with Rth.Compute the short-circuit current: Isc = Vth / Rth → define In = Isc.Retain the same resistance: Rn = Rth in parallel with In.Verify: Open-circuit voltage Voc = Vth = In * Rn; short-circuit current Isc = Vth / Rth = In. Verification / Alternative check: Plot the terminal V–I characteristic; both models yield V = Vth − I * Rth = In * Rn − I * Rn, which are algebraically identical when Rn = Rth and In = Vth / Rth. Why Other Options Are Wrong: Equivalence does not require zero resistance; it requires the stated relationships. Linearity is the key assumption; nonlinearity is not a requirement. The method applies to both DC and AC (using phasors/impedances). Common Pitfalls: Forgetting to keep the resistance the same in both forms, or mixing up open-circuit and short-circuit conditions when deriving In or Vth. Final Answer: False

Question 16

Do transistors fundamentally behave as voltage sources, or are they better modeled as controlled current sources within typical operating regions?

Accepted Answer

Introduction / Context: Proper device modeling is crucial for analog design. The statement that transistors are “basically voltage sources” is misleading. Most transistor behaviors are captured by controlled current source models in their active regions. Given Data / Assumptions: BJT in forward-active region: collector current controlled by base-emitter voltage/current. MOSFET in saturation region: drain current controlled by gate-source voltage. Small-signal models linearize around a bias point. Concept / Approach: In BJTs, Ic ≈ β * Ib or more precisely Ic depends exponentially on Vbe; the device is modeled as a transconductance element (current source) controlled by Vbe, with output resistance ro. In MOSFETs, Id ≈ k * (Vgs − Vth)^2 in saturation; again, a transconductance-controlled current source model with finite output resistance fits. Neither device inherently enforces a fixed voltage (the hallmark of a voltage source). Step-by-Step Solution: Identify controlled variable: BJTs and MOSFETs primarily control current via input voltage/current.Small-signal: represent device as gm * v_input feeding a current source into the output node with parallel ro.Observe that output voltage is set by external loads and supply rails, not fixed by the transistor alone.Therefore, calling a transistor a “voltage source” is inaccurate. Verification / Alternative check: Load-line analysis on a transistor shows the operating point determined by the intersection of device I–V curves (current-source-like) and the external load line, not by an internal fixed voltage source behavior. Why Other Options Are Wrong: BJT vs MOSFET distinction does not change the current-source modeling. “Saturation” in MOSFETs still yields controlled current with finite output resistance; not a voltage source. Small-signal AC models also treat the device as a transconductance (current) source. Common Pitfalls: Confusing the presence of Vbe or Vgs thresholds with the device acting as a voltage source. These voltages control current; they do not supply fixed voltage to the load. Final Answer: False

Question 17

Norton’s equivalent current (IN): Is it defined as the open-circuit current between two terminals, or the short-circuit current?

Accepted Answer

Introduction / Context: Norton and Thevenin equivalents are dual representations of a linear two-terminal network. Correctly identifying Norton’s current prevents mistakes when transforming sources or characterizing loads. Given Data / Assumptions: Linear, bilateral network with independent/dependent sources and resistors. Two terminals under test for equivalent replacement. Standard definitions of open-circuit and short-circuit measurements. Concept / Approach: Norton’s current IN is the short-circuit current between the two terminals (with the terminals shorted). Thevenin’s voltage VTH is the open-circuit voltage between the two terminals. The Norton/Thevenin resistance is the same: RN = RTH (under appropriate deactivation rules). Step-by-Step Solution: Determine VTH: measure or compute the open-circuit voltage (no load connected).Determine IN: short the terminals and compute the resulting current through the short; IN = ISC.Relate the two: VTH = IN * RTH, and RTH = RN.Hence, IN is not an open-circuit current; it is the short-circuit current. Verification / Alternative check: By transformation: if you know VTH and RTH, the equivalent Norton current is IN = VTH / RTH, which numerically equals the short-circuit current you would measure directly. Why Other Options Are Wrong: Calling IN an open-circuit current confuses it with VTH definition. No averaging is involved; it is strictly the short-circuit current. The statement “divided by the shorted resistance” is unclear; the correct relation is IN = VTH / RTH. Rated power of the load is irrelevant to the definition. Common Pitfalls: Using open-circuit current (which is zero in resistive networks) instead of short-circuit current for Norton calculations, leading to erroneous equivalences. Final Answer: False

Question 18

Delta–wye (Δ–Y) conversions: Are these transformations useful and commonly applied in certain circuit-analysis and design scenarios?

Accepted Answer

Introduction / Context: Delta–wye (Δ–Y) conversions allow complex three-node resistor networks to be simplified into equivalent forms. These transformations are standard in both power and electronics contexts. Given Data / Assumptions: Linear, passive resistor networks with three interconnected nodes. Objective is to simplify analysis or enable series/parallel reductions. Applies under DC and AC steady state (for resistors; generalized to impedances if reactive components exist). Concept / Approach: A Δ network (three resistors each between a pair of nodes) can be transformed into an equivalent Y (three resistors, each from a node to a common junction) and vice versa. Proper formulas maintain identical terminal resistances between any pair of nodes, preserving circuit behavior at the terminals. Step-by-Step Solution: Identify a Δ or Y subnetwork that blocks simple series/parallel reduction.Apply the conversion formulas (e.g., each Y arm equals product of adjacent Δ resistors divided by sum of all Δ resistors).After conversion, continue with series/parallel simplifications to find equivalent resistance.Verify equality of terminal resistances before and after conversion if needed. Verification / Alternative check: Compute any two-terminal equivalent resistance of the original and converted networks; matching values confirm correctness. Simulation tools or bridge measurements can validate the equivalence experimentally. Why Other Options Are Wrong: Δ–Y is also helpful in electronics (e.g., bias networks, sensor bridges), not just three-phase power. Resistances need not be equal; formulas work for arbitrary values. The method is not restricted to DC; with complex impedances it applies in AC as well. Common Pitfalls: Swapping node labels during conversion or misapplying the formulas, which leads to incorrect equivalent values. Careful node mapping prevents errors. Final Answer: True

Question 19

Ideal current source model: Does an ideal current source have zero internal resistance, or is its internal resistance effectively infinite?

Accepted Answer

Introduction / Context: Ideal sources are simplified models that help us reason about circuit limits. While an ideal voltage source maintains a fixed voltage regardless of current, an ideal current source maintains a fixed current regardless of voltage. Their internal resistances reflect these behaviors. Given Data / Assumptions: Ideal current source supplies a specified current independent of terminal voltage. Two-terminal representation with an implicit internal resistance. No compliance voltage limit in the ideal model. Concept / Approach: An ideal current source is modeled as having infinite internal resistance (open-circuit behavior internally) so that variations in load voltage do not change its current. Any finite internal resistance would shunt some current and allow the delivered current to vary with terminal voltage, contradicting the ideal definition. Step-by-Step Solution: Assume internal resistance Rint.If Rint is infinite, the source current is forced through the external load regardless of load voltage.If Rint were zero, the source would simply short the terminals, fixing voltage (nonsense for a current source) and not maintaining the specified current in a general load.Therefore, ideal current sources correspond to infinite internal resistance. Verification / Alternative check: Duality with ideal voltage source (which has zero internal resistance) confirms the concept: current and voltage sources are complementary in their ideal resistance properties. Why Other Options Are Wrong: Zero internal resistance describes an ideal voltage source, not a current source. Hybrid statements about series/parallel resistance are not part of the ideal two-terminal model. DC vs AC distinction is irrelevant; the ideal property is independent of frequency. Common Pitfalls: Confusing internal resistance of source models with external series resistors used for current limiting in practical supplies. Final Answer: False

Question 20

Ideal voltage source model: Does an ideal voltage source have zero internal resistance so that its terminal voltage remains fixed regardless of load current?

Accepted Answer

Introduction / Context: An ideal voltage source is a theoretical construct used in circuit analysis to simplify behavior: it maintains a specified terminal voltage independent of the current demanded by the load. Given Data / Assumptions: Two-terminal ideal source with fixed voltage Vs. No internal energy or thermal limits considered (theoretical model). Load may vary arbitrarily. Concept / Approach: The ideal voltage source is modeled with zero internal resistance (Rint = 0). With Rint = 0, the terminal voltage equals Vs for any load current. Any nonzero Rint results in a voltage drop V_drop = I_load * Rint, making the terminal voltage depend on load current and invalidating ideal behavior. Step-by-Step Solution: Represent the source as Vs in series with Rint.For ideal behavior, set Rint = 0 → V_terminal = Vs independent of I_load.If Rint > 0, then V_terminal = Vs − I_load * Rint varies with load, demonstrating non-ideal regulation.Therefore, the ideal voltage source requires zero internal resistance. Verification / Alternative check: Duality: the ideal current source has infinite internal resistance. Thevenin equivalents use low Rth to approximate voltage sources; lower Rth approaches the ideal limit. Why Other Options Are Wrong: The ideal definition holds for DC and AC; frequency is irrelevant. Load type does not affect ideal source behavior; it remains fixed-voltage by definition. Series-connecting sources does not change the internal resistance idealization. Common Pitfalls: Confusing practical low-impedance sources (small but nonzero internal resistance) with the idealized zero-resistance model; always distinguish theory from real devices. Final Answer: True

Circuit Theorems and Conversions Questions