Govt. Exams
Entrance Exams
Coupling coefficient k = M/√(L₁L₂), where 0 ≤ k ≤ 1. k=1 indicates perfect coupling, k=0 means no coupling.
Norton equivalent: IN = Isc (short-circuit current) and RN = Rth (equivalent resistance). Norton and Thevenin equivalents are related: Vth = IN × RN
Mesh analysis works with dependent sources by expressing the controlling variable in terms of mesh currents, then solving the resulting equations.
Star-delta transformation converts between two three-terminal network configurations, simplifying circuit analysis by eliminating nodes that cannot be solved directly.
Reciprocity theorem: If a voltage source at port 1 produces current at port 2, then the same source at port 2 produces equal current at port 1. Applicable for bilateral linear networks.
For a connected planar circuit: Number of independent loops = b - n + 1 (also known as cyclomatic complexity or mesh rank)
Maximum power transfer theorem: Load resistance RL should equal Thevenin resistance Rth for maximum power delivery. Maximum power = Vth²/(4Rth)
Number of independent mesh equations = b - n + 1, where b=branches, n=nodes. Here: 8 - 5 + 1 = 4
P = S × PF = 1000 × 0.8 = 800W. Q = √(S² - P²) = √(1000000 - 640000) = √360000 = 600 VAR
XL = 2πfL = 2π×50×0.5 = 157.08Ω. Z = √(R² + XL²) = √(2500 + 24674) = √27174 ≈ 164.8Ω... Recalculating: Z = √(50² + 157.08²) = √(2500 + 24674) = √27174 ≈ 164.8Ω. Given options suggest 173.2Ω.