Question 1

Direct measurement across a single resistor — in the network, resistor R3 alone is connected between nodes A and B (no other elements in parallel with it). If the measured voltage between A and B is 9 V, what is the voltage across R3 (VR3)?

Accepted Answer

Introduction / Context: When a single element is the only component connected between two nodes, the element voltage equals the node-to-node voltage by definition. This is a straightforward but very common situation when taking measurements on boards and in simulations. Given Data / Assumptions: R3 is the only component connected directly between nodes A and B. The measured node voltage difference is V_AB = 9 V. No additional parallel paths exist across A–B. Concept / Approach: Element voltage is the potential difference between its terminals. If those terminals are exactly nodes A and B, then the element voltage equals V_AB. No knowledge of resistance value or currents is needed to equate VR3 with the measured A–B voltage in this configuration. Step-by-Step Solution: Identify the terminals of R3 as node A (one end) and node B (the other end).Recognize VR3 is defined as V_A − V_B (with a chosen polarity).Given V_AB = 9 V, conclude VR3 = 9 V in magnitude with the same polarity convention.No further circuit details are required because R3 spans the measured nodes. Verification / Alternative check: Use an ideal voltmeter directly across R3; it reads the same 9 V as the A–B measurement because it is the same two points. Why Other Options Are Wrong: 8.1 V or 0.9 V: would imply a divider or series sharing not present.“More information is needed”: not in this topology; node-to-node equals element voltage.0 V: would correspond to a short or equal potentials, which contradicts V_AB = 9 V. Common Pitfalls: Misidentifying what nodes an element actually connects to; reversing polarity sign conventions (magnitude remains 9 V either way). Final Answer: 9 V

Question 2

Thevenin equivalent form — which option correctly describes the standard Thevenin representation of any linear two-terminal network as seen from a pair of output terminals?

Accepted Answer

Introduction / Context: Thevenin’s theorem is a powerful simplification tool. It allows you to replace any linear, bilateral two-terminal network with an equivalent source and resistance that behave identically from the perspective of the external load. Recognizing the correct canonical form is essential before you compute V_TH and R_TH. Given Data / Assumptions: The original network is linear and bilateral (resistors, independent/dependent sources that are linear). We are looking from a specific pair of output terminals. Frequency effects are ignored unless reactive elements are converted to equivalent impedances (then R_TH becomes Z_TH). Concept / Approach: The Thevenin equivalent is defined as a single ideal voltage source V_TH in series with a single resistance R_TH (or impedance Z_TH). V_TH equals the open-circuit voltage at the terminals. R_TH equals the equivalent resistance seen looking back into the network with independent sources deactivated (voltage sources shorted, current sources opened), or equivalently the ratio of V_TH to I_SC for purely resistive linear circuits. Step-by-Step Solution: Compute V_TH by finding the open-circuit terminal voltage.Compute R_TH by deactivating independent sources and finding the resistance seen at the terminals (or use R_TH = V_TH / I_SC).Construct the equivalent: an ideal V_TH source in series with R_TH.Attach any load RL and analyze easily via a simple series division. Verification / Alternative check: Confirm equivalence by checking that, for any RL, the original network and the Thevenin model produce identical terminal voltage and current. Why Other Options Are Wrong: Current source in series with resistance: that is Norton converted incorrectly; Norton uses a current source in parallel with resistance.Series–parallel ladder or many sources: not a canonical reduced form.Transformer-only model: unrelated to the general linear two-terminal reduction unless the original network is specifically a transformer circuit. Common Pitfalls: Mixing up Norton and Thevenin forms; forgetting to deactivate sources properly when finding R_TH; applying the theorem to nonlinear networks. Final Answer: A voltage source in series with a resistance

Question 3

Open-circuit fault effect between A and B — suppose nodes A and B are connected only through a single resistor R3 (no alternate paths). If R3 fails open, what is the resulting total resistance RT measured between A and B?

Accepted Answer

Introduction / Context: An open-circuit failure removes a current path. When there is only a single conduction path between two nodes, opening that element isolates the nodes and makes the equivalent resistance between them unbounded (infinite). Recognizing this outcome is vital for fault analysis and troubleshooting. Given Data / Assumptions: Nodes A and B are connected solely through resistor R3. No other series or parallel paths exist between A and B. R3 fails open (break in continuity). Concept / Approach: Resistance between two nodes is defined as the ratio V/I under a small test stimulus. If there is no conductive path, any finite applied voltage produces zero current, so R = V / I → ∞. Therefore, the equivalent resistance becomes infinite when the only branch is open. This is independent of the original resistance value of R3 prior to failure. Step-by-Step Solution: Model the intact circuit as a single branch: RT_intact = R3.Introduce an open in R3: current path between A and B is removed.Apply the definition R = V / I: with I = 0 A for any finite V, R → ∞.Conclude RT_open is infinite (open circuit between A and B). Verification / Alternative check: In measurement, an ohmmeter shows “OL” or very large resistance when probes are placed across A and B after the open occurs. Circuit simulators report no DC path between the nodes. Why Other Options Are Wrong: Finite values like 100 Ω, 110 Ω, 900 Ω, or 10 Ω imply a remaining conductive path, which contradicts the single-path assumption. Common Pitfalls: Assuming other leakage paths exist (they do not in this idealized scenario); confusing “large” with “infinite” — in analysis, we model an ideal open as infinite resistance. Final Answer: Infinite resistance

Series-Parallel Circuits Questions