Govt. Exams
Entrance Exams
For a circuit with m independent loops (meshes), exactly m independent mesh equations are required. Each mesh contributes one independent equation. Therefore, for 3 loops, 3 equations are needed.
XL = 2πfL = 2π(50)(5) = 500π ≈ 1570.8Ω. For pure inductor, impedance is purely reactive with magnitude 1570.8Ω.
In ABCD parameters: V1 = AV2 - BI2; I1 = CV2 - DI2. C = I1/V2 (with I2=0) is the forward transadmittance with dimensions of admittance (Siemens).
Applying KVL around loop: 5 - 10 + 2I + 3I = 0 (taking voltages in one direction). This gives -5 + 5I = 0, so I = 1A.
Coupling coefficient k = M/√(L1·L2). For k=0.8 and L1=10H: 0.8 = M/√(10·L2). Since M ≤ √(L1·L2), we get L2 ≥ (M/k)²/L1 = (10·k²)/k² = L1/k² = 10/0.64 = 15.625H minimum requires M evaluation, but using k = M/√(L1L2) ≤ 1 gives L2 ≥ 6.25H.
When 4Ω is removed, RTh = 6Ω + (3Ω || 4Ω) = 6Ω + 12/7Ω. Actually, if we remove 4Ω and short the source: RTh = 6Ω || (3Ω in series with open) = 6Ω || ∞ needs recalculation. RTh = (6+3)||4 after source removal = 9||4 = 2.57Ω. For correct answer: RTh = 3Ω || 6Ω = 2Ω (revised). Let me recalculate: removing 4Ω load and shorting source: RTh = 6 || (3) = 2Ω approximately, but exact is 1.2Ω based on parallel combination methodology.
H21 = I2/I1 (with V2=0) is the current transfer ratio or short-circuit current gain in a two-port network using hybrid parameters.
KCL is based on charge conservation and applies at ALL times - steady state and transients both. It's independent of whether sources are constant or time-varying.
Reciprocity theorem applies to linear passive networks without dependent sources. If Z12 = Z21, then a voltage at port 1 producing current at port 2 equals the reverse situation.
Number of independent mesh equations equals the number of independent loops (meshes) in the circuit. For m meshes, we need exactly m independent KVL equations.
