KSEB Sub Engineer (Electrical) 2023 — Kerala PSC PYQ Practice with Answers

Correct answer (Option D):\nThe resistance of a material is governed by the laws of electrical resistance.\nFormula: R = ρ × (L / A)\nWhere R is resistance, ρ is resistivity (nature of material), L is length, and A is cross-sectional area.\nFrom the formula, resistance varies directly with length and inversely with cross-sectional area.\nIt also depends on the nature of the material and its temperature (due to the temperature coefficient of resistance).\nTherefore, only statement (iv) is correct.\nOption D is correct.\n\nWhy others are wrong:\nOption A includes statement (i), which incorrectly states resistance varies directly with area.\nOption B includes statement (ii), which incorrectly states resistance varies inversely with length.\nOption C includes both incorrect statements (i) and (ii).\n\nStudy tip:\nRemember the factors affecting resistance using the formula R = ρL/A. Temperature affects the resistivity ρ, which increases for conductors and decreases for semiconductors as temperature rises.

Correct answer (Option A):\nElectrical conductivity (σ) is defined as the reciprocal of electrical resistivity (ρ).\nFormula: σ = 1 / ρ\nThe SI unit of resistivity is Ohm-meter (Ω·m).\nTherefore, the unit of conductivity is 1 / (Ω·m).\nThis is also written as mho/m or Siemens per meter (S/m).\nSiemens (S) is the SI derived unit of electrical conductance.\nOption A is correct.\n\nWhy others are wrong:\nOption B (Siemens per square meter) is dimensionally incorrect for conductivity.\nOption C (Ohm per meter) is not a standard unit for these basic electrical properties.\nOption D (Ohm-meter) is the standard unit of electrical resistivity, not conductivity.\n\nStudy tip:\nDo not confuse conductance with conductivity. Conductance is the reciprocal of resistance (measured in Siemens), while conductivity is the reciprocal of resistivity (measured in Siemens/meter).

Correct answer (Option A):\nThe resistance of a wire is directly proportional to its length when the material and cross-sectional area are identical.\nFormula: R = ρ × (L / A)\nGiven: R_A = 600Ω, R_B = 200Ω. Both wires share the same ρ (material) and A (area).\nStep 1: Set up the proportional ratio for length and resistance.\nL_A / L_B = R_A / R_B\nStep 2: Substitute the known resistance values.\nL_A / L_B = 600 / 200\nStep 3: Simplify the ratio.\nL_A / L_B = 3.\nTherefore, wire A is exactly 3 times longer than wire B.\nOption A is correct.\n\nWhy others are wrong:\nOption B (2) implies a 400Ω vs 200Ω relationship, which is mathematically incorrect.\nOption C (0.33) is the inverted ratio (L_B / L_A = 200/600), mistakenly calculating how much shorter B is relative to A.\nOption D (6) implies an incorrect arithmetic scaling.\n\nStudy tip:\nWhenever resistivity (material) and area are constant, simply divide the two resistance values to find the direct length ratio. R ∝ L.

Correct answer (Option C):\nWhen Norton equivalent circuits are connected in parallel, their current sources add algebraically, and their internal Norton resistances combine in parallel.\nGiven:\nCircuit 1: I₁ = 4A, R₁ = 2Ω\nCircuit 2: I₂ = 4A, R₂ = 2Ω\nStep 1: Total Norton current (In) = I₁ + I₂\nIn = 4A + 4A = 8A\nStep 2: Total Norton resistance (Rn) = (R₁ × R₂) / (R₁ + R₂)\nRn = (2 × 2) / (2 + 2) = 4 / 4 = 1Ω\nAnswer: 8A, 1Ω.\nOption C is correct.\n\nWhy others are wrong:\nOption A incorrectly adds the resistances in series instead of parallel.\nOption B incorrectly subtracts the currents, which would only happen if polarities were opposite.\nOption D represents an incorrect combination logic for both the current source and the resistance.\n\nStudy tip:\nNorton equivalent circuits in parallel behave identically to ideal current sources in parallel. Always add the parallel currents and compute the equivalent parallel resistance.

Correct answer (Option B):\nThe Superposition theorem states that in any linear, bilateral network containing multiple independent sources, the response (voltage or current) in any branch is the algebraic sum of the responses caused by each independent source acting alone.\nBecause the theorem relies on proportional scaling and additivity, it is fundamentally derived from the principle of linearity.\nWithout a linear relationship between voltage and current (like Ohm's Law), superposition cannot be applied.\nOption B is correct.\n\nWhy others are wrong:\nOption A (Duality) refers to pairs of electrical concepts that mirror each other (like Thevenin and Norton), not superposition.\nOption C (Reciprocity) deals with interchanging voltage sources and ammeters in a network, which is a different theorem.\nOption D (Non-linearity) invalidates the use of the Superposition theorem entirely.\n\nStudy tip:\nRemember that the Superposition theorem cannot be used to directly calculate power, because power relies on the square of current or voltage, which is a non-linear relationship.