Electric Circuits

Electric Circuits – Verified PYQ Authority Guide

Electric Circuits is a sub-subject authority hub. It is designed to expose the important topic/concept clusters represented by verified SRO PYQs and guide students from broad revision into the exact solved questions that support each area. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.

PYQ evidence snapshot

15 verified PYQs are currently mapped to this Sub Subject hub. The represented years include 2026, 2024. Exam coverage currently includes Additional Assistant Engineer (Electrical), BMS. Subject context includes Electrical Engineering. These values come from live mappings and can expand automatically when new verified PYQs are added.

Most useful verified PYQs to solve first

Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.

1. Obtain the voltage v in the branch shown in Fig. Q6 for i2 = −2 A.
   BMS · 2024 · Dependent Voltage Source Polarity and KVL
   The controlling current is signed: i2 = −2 A. Hence vx = 15i2 = −30 V. The two source voltages add algebraically in the…
2. Calculate the power dissipated in the 8 Ω resistor in the circuit shown in Fig. Q4.
   BMS · 2024 · Nodal KCL and Resistor Power
   All four branches share the same two nodes, so one node-voltage equation solves the circuit. Let the top-node voltage be V. Then i₀ =…
3. The voltage and current through a circuit element are:v(t) = 628 sin(314t + 45°) Vi(t) = 10 sin(314t − 45°) AIdentify the circuit element and determine its value.
   BMS · 2024 · Inductive Reactance from Phase and Magnitude
   The phase difference identifies the element before any calculation: voltage is at +45° and current at −45°, so voltage leads current by 90°, which…
4. The dynamic behaviour of a series RLC circuit is described by:d2vc/dt2 + dvc/dt + vc = Vsu(t)where vc is the capacitor voltage and Vs is the DC supply voltage. Find the nature…
   BMS · 2024 · Damping Ratio of Second-Order Circuit
   Damping is determined from the homogeneous second-order equation, not from the forcing term. Comparing s² + s + 1 with s² + 2ζωₙs +…
5. The current through an element is shown in Fig. Q1. Determine the total charge that passed through the element from t = 0 s to t = 3 s.
   BMS · 2024 · Charge from Current / Area Under i-t Curve
   Current is the rate of flow of charge, so the required charge is the signed area under the current–time graph from 0 to 3…
6. A balanced delta-connected load of (4+j3) Ω per phase is connected to a balanced three-phase 440V supply. The phase current is 10A. Find the total active power.
   Additional Assistant Engineer (Electrical) · 2026 · Three-Phase Active Power
   A is the intended option if the stated phase current of 10 A and the 440 V line voltage are used: P = √3…
7. Voltage magnification factor of a series resonance circuit is:
   Additional Assistant Engineer (Electrical) · 2026 · Voltage Magnification / Q-Factor
   B — Q = ωL/R, with ω evaluated at resonance (ω = ω₀). The quality factor equals the voltage across either reactive component divided…
8. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R), choose the correct answer from the options given below. Assertion: In a pure…
   Additional Assistant Engineer (Electrical) · 2026 · Voltage-Current Phase Relation
   For an ideal inductor, v = L(di/dt). If current is sinusoidal, differentiating it advances the waveform by 90°, so voltage leads current by 90°.…

Formula & key-relationship bank from verified solutions

• vx = 15i2v = vx + 10v = 15(−2) + 10 = −20 V
• i0 = V/2id = i0/4 = V/8i8Ω = V/8KCL: 6 = V/2 + V/8 + V/8V = 8 VP8Ω = V²/R = 8²/8 = 8 W
• φ = φV − φI = 45° − (−45°) = 90°V leads I by 90° ⇒ ideal inductorXL = Vm/Im = 628/10 = 62.8 ΩXL = ωLL = 62.8/314 =…
• d²vc/dt² + dvc/dt + vc = Vsu(t)Homogeneous form: d²vc/dt² + dvc/dt + vc = 0Characteristic equation: s² + s + 1 = 0Standard form: s² + 2ζωns + ωn² =…
• i(t) = dq/dt ⇒ dq = i(t)dtq = ∫03 i(t)dtq = 10(1) + [(10 + 5)/2](1) + 5(1)q = 10 + 7.5 + 5 = 22.5 C1 A·s = 1…
• Δ: V_ph = V_L; I_L = √3I_ph; cosφ = R/|Z|; P = 3V_phI_phcosφ = √3V_LI_Lcosφ. Given-current route: 10.56 kW. Voltage–impedance route: 92.928 kW.

Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.

Core ideas repeatedly reinforced by the solved corpus

• The controlling current is signed: i2 = −2 A. Hence vx = 15i2 = −30 V. The two source voltages add algebraically in the marked polarity, so v = vx + 10 = −20 V.
• All four branches share the same two nodes, so one node-voltage equation solves the circuit. Let the top-node voltage be V. Then i₀ = V/2, the dependent source current is i₀/4 = V/8 and the 8 Ω current…
• The phase difference identifies the element before any calculation: voltage is at +45° and current at −45°, so voltage leads current by 90°, which is the ideal-inductor relation. Then Xₗ = 628/10 = 62.8 Ω and L =…
• Damping is determined from the homogeneous second-order equation, not from the forcing term. Comparing s² + s + 1 with s² + 2ζωₙs + ωₙ² gives ωₙ = 1 rad/s and ζ = 0.5. Since 0 < ζ…
• Current is the rate of flow of charge, so the required charge is the signed area under the current–time graph from 0 to 3 s. The interval contains a 10 A rectangle, a 10→5 A trapezoid and a…

Exam tips already validated in SRO solutions

• Write the dependent-source value beside the source before starting KVL; it prevents sign errors.
• For dependent-source circuits, express the controlling variable first. Never treat the dependent source as an independent fixed value.
• Use the phase relation first. Peak/peak and RMS/RMS ratios give the same impedance magnitude, but never mix one peak value with one RMS value.
• For a second-order system, always calculate ζ. Complex conjugate poles with a negative real part are the signature of stable underdamped behavior.
• For i–t graphs, think ‘charge = signed area’. Always respect the exact time interval before calculating.

Common mistakes to avoid

• Replacing i₂ = −2 A by |i₂| = 2 A. That reverses the dependent-source result and leads to a wrong branch voltage.
• Ignoring the arrow direction, forgetting i₀ = V/2, or using i₀/4 as a constant current independent of V.
• Reversing the mnemonic and choosing a capacitor, or converting only V or only I to RMS before taking the ratio.
• Calling the circuit critically damped because all coefficients are 1, or using the forcing term Vₛu(t) to decide the damping type.
• Using the visible graph beyond t = 3 s, or treating the 1–2 s sloping segment as a rectangle instead of a trapezoid.

Topic and concept coverage

Mapped topic labels include Three-Phase AC Circuits, AC Resonance, Network Analysis, Network Theorems, AC Circuits, AC Fundamentals, Current Division. The concept trail includes Balanced Delta to Star, Charge from Current / Area Under i-t Curve, Current Divider Using Conductances, Current-to-Voltage Source Conversion, Damping Ratio of Second-Order Circuit, Dependent Voltage Source Polarity and KVL, Effect of Reversing Phase Sequence, Inductive Reactance from Phase and Magnitude. Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.

Knowledge Graph navigation

Continue with Electrical Engineering, AC Circuits, AC Circuits, AC Circuits, AC Circuits, AC Circuits, Three-Phase AC Circuits, Dependent Sources, Series RLC Resonance, AC Resonance, Network Analysis. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.

How to revise this authority page efficiently

1. Solve before reading: answer a mapped PYQ first.
2. Read the exact explanation: verify the correct principle, formula, distractor logic and common mistake on that question page.
3. Move one level in the graph: use the closest concept/sub-topic/topic link rather than opening unrelated content.
4. Reattempt: solve another verified PYQ from this hub and check whether the same error repeats.

Quality scope: this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.